the cohomology of the mod 2 steenrod algebra: a computer ...the cohomology of the mod 2 steenrod...

Contemporary Mathematics

The Cohomology of the Mod 2 Steenrod Algebra: A

Computer Calculation

Robert R. Bruner

Abstract. The cohomology of the mod 2 Steenrod algebra for homologicaldegree s < 40 and internal degree t < 141 has been calculated by the techniqueof minimal resolutions. The most extensive previous calculation is that ofTangora, and is contained in pp. 18-56. In addition, we have calculated chainmaps induced by all the indecomposable elements in this range, and haveused this to determine the complete product structure. Even in the range inwhich the vector space structure was known due to Tangora’s work, some ofthe products, and more significantly, the knowledge that we now have all theproducts, is new. As we shall show in applications to the homotopy groups ofspheres, this product structure has many consequences.

1. Introduction

While the algebraic topologist who who simply wishes to determine the valueof a homotopy group may not care about the details of the programming, the datacan be trusted only if the algorithms and the programs implementing them arecorrect. Accordingly we will describe the main features of the programs which haveproduced these calculations. First, however, we describe how to read the tables.

2. Key to the Tables

The attached tables describe the cohomology of the Steenrod algebra in therange s < 40, t < 141, with all products. This has been computed using the pro-grams described in [1, 2]. The product structure has been calculated by computingchain maps for all the indecomposable elements found. The periodicity operatorP (x) =< h4, h

30, x > was computed from the chain map induced by the indecom-

posable x, when x is indecomposable, and from a null-homotopy of h30h4 in other

cases. The programs described in [1, 2] compute resolutions, that is Tor ratherthan Ext. Dualization, to produce Ext, and computation and sorting of productswas done using MAGMA, which greatly speeded the processing of an overwhelm-ing amount of data and eliminated the errors which would otherwise certainly havecrept in.

In the main chart, the product structure is complete, in that any product notlisted is zero. A filter to remove redundant products would shorten the entries atthe price of requiring multiple cross-references to check relations. Instead, we have

c©0000 (copyright holder)

1

2 ROBERT R. BRUNER

simply listed all nonzero monomials, sorted by their value in terms of the basisfound by the machine. Thus, the entry in the 37 stem

7 (10) h1t = h22n = c1f0

(01) h20x

(11) h3r

means that h3r = h1t + h20x. Within each entry, the monomials are listed in

lexicographic order, where the generators are ordered firstly by increasing filtration(cohomological degree), then by internal degree, then arbitrarily. This is the orderin which the generators are listed in the table of geneators. There, we give the namesof the 464 generators which appear in this range, their filtration and total degree(‘stem’), and their value in terms of the basis found by the machine. For example,in filtration 4, stem 18, we have the element f0, with value (10). This means thatExt4,22 is two dimensional and that f0 is the first basis vector in the machine’sinternal representation. By contrast, f1 has value (11). We made the latter choicebecause we are able to compute Sq0 in this case, and want f1 = Sq0(f0). In general,we have tried to choose generators in Sq0-families. Unfortunately, it is a difficultproblem to compute Sq0 mechanically at present. However, by using the connectionwith the root invariant we are able to identify a number of Sq0’s [3]. In particular,we are certain that ai+1 = Sq0(ai) for a ∈ {h, c, d, e, f, g, p, n, x, r, t, m, }, except form1 and t1, for which indeterminacy in the root invariant leaves us with two possiblechoices for each. Otherwise unambiguous identification of the first member of thefamily results in unambiguous identification of the whole family. Further, manyfamilies start in bidegrees which are one dimensional, so their definition is clear.The irritating exception is f0. The traditional definitions of f0 in terms of Masseyproducts all have nonzero indeterminacy, but there is an unambiguous definition interms of the Steenrod operations: f0 = Sq1(c0). Although computation of Steenrodoperations by mechanical means is out of reach in general, it is possible that wecould accomplish this one since it is in such a low dimension. We also suspect thatSq0(D3) = D31, Sq0(D1) = D11 and Sq0(H1) = H11, but cannot prove these bycurrently available means, so have resisted naming the elements as if this were so.There is the further difficulty that past naming conventions are rather incoherentin stems above 50, so that we would have clashes. For example D1, D2, and D3 arein filtrations 5,6, and 4, respectively. Clearly it is time to resort to more systematicnaming conventions. Finally, in the absence of any way to identify generatorswith elements already known in the cohomology of the Steenrod algebra, we haveresorted to precise but ugly names like x12,50, which means the 50th generator themachine found in filtration 12.

3. What Has Been Calculated

We have calculated a minimal resolution in the category of modules over theSteerod algebra for the cohomology of the sphere S0, the stunted projective spacesP−n for −55 < −n < 0, and Pn for n = 1, 2, 3, ???, and for the cofibers C2, Cη, Cν, ???.

In addition we have computed the chain maps induced by the inclusion ofthe bottom cell S−n −→ P−n and the −1-cell S−1 −→ P−n, as well as all 465indecomposable elements of ExtA(F2, F2). That is, for a set of multiplicative gen-

erators x ∈ Exts,tA (F2, F2) we have comupted the chain map induced by the cocycleCs −→ ΣtF2.

THE COHOMOLOGY OF THE MOD 2 STEENROD ALGEBRA 3

What is found in the tables and charts.

4. Algorithms and Data Structures

The resolutions and chain maps are organized in directories reflecting the cate-gorical relationships between them. That is, each module has a directory, containingits definition (dimF2

, degrees of the generators, the action of A on the generators).The programs conmstruct the minimal resolution of the module in this directory.Any chain maps to this resolution will produce temporary files in this directorycontaining cycles whose lifts are needed.

Each chain map has a subdirectory of its domain’s directory which containsthe definition of the chain map (its homological and internal degrees, it’s domainand codomain, and the cocycle). The program constructs the chain map in thisdirectory.

Similarly, a null homotopy of fg lives in a subdirectory of the map g, and pointsto f .

The processing is divided into two main stages. One stage is the calculationof the resolutions and chain maps. This is done by a small package of C programsdesigned to handle the rather large data structures which arise as efficiently aspossible. The other stage is the processing of this data to compute the groupsExtA(M, F2) and the homomorphisms ExtA(M, F2) −→ ExtA(N, F2). This is doneby shell scripts which do simple text manipulation and by MAGMA programswhich process the output of the shell scripts. The ability to write these programsin terms of data structures such as vector spaces and homomorphisms makes thesepprograms shorter and clearer, but generally less efficient. It is clear that the cal-cuations will gradually be rewritten in these higher level languages as the growthof computers compensates for the overhead associated with languages with sophis-ticated data types.

Data files defined by the user.Data files generated by the programs.(permanent and workfiles)Format of elements and files.

Algorithmsaddgengenimkergenimgenkerliftmapstartmapaugconsistencycheckconvert

MAGMA programs

4 ROBERT R. BRUNER

5. Generators

Name s n value precursor stemh0 1 0 (1)h1 1 1 (1) 0h2 1 3 (1) 1h3 1 7 (1) 3h4 1 15 (1) 7h5 1 31 (1) 15h6 1 63 (1) 31h7 1 127 (1) 63c0 3 8 (1)c1 3 19 (1) 8c2 3 41 (1) 19c3 3 85 (1) 41d0 4 14 (1) 5e0 4 17 (1)f0 4 18 (10) 7g 4 20 (1) 8d1 4 32 (1) 14p 4 33 (1)e1 4 38 (11) 17f1 4 40 (11) 18g2 4 44 (1) 20D3 4 61 (1)d2 4 68 (1) 32p′ 4 69 (1)p1 4 70 (11) 33e2 4 80 (11) 38f2 4 84 (10) 40g3 4 92 (1) 44D31 4 126 (10) 61


Name s n value precursor stemPh1 5 9 (1) 2Ph2 5 11 (1) 3n 5 31 (10) 13x 5 37 (1) 16D1 5 52 (1)H1 5 62 (100)n1 5 67 (10) 31Q3 5 67 (01) 31x1 5 79 (1) 37D11 5 109 (1) 52x5,77 5 125 (1) 60x5,80 5 128 (1)H11 5 129 (100) 62r 6 30 (1) 12q 6 32 (1) 13t 6 36 (1) 15y 6 38 (10) 16C 6 50 (1) 22G 6 54 (1) 24D2 6 58 (1) 26A′ 6 61 (11)A 6 61 (01)A′′ 6 64 (1) 29r1 6 66 (1) 30x6,47 6 71 (10)x6,53 6 76 (1) 35t1 6 78 (110) 36x6,68 6 85 (10)C1 6 106 (1) 50x6,89 6 108 (10) 51G1 6 114 (1) 54x6,94 6 124 (1) 59x6,97 6 126 (10) 60x6,99 6 127 (10)x6,101 6 128 (1000) 61x6,102 6 128 (0100) 61x6,107 6 132 (010) 63x6,110 6 134 (1) 64

6 ROBERT R. BRUNER

Name s n value precursor stemPc0 7 16 (1)i 7 23 (1) 8j 7 26 (1)k 7 29 (1) 11l 7 32 (1)m 7 35 (1) 14B1 7 46 (1)B2 7 48 (10)Q2 7 57 (1) 25B3 7 60 (1)x7,33 7 63 (100) 28x7,34 7 63 (010) 28x7,40 7 66 (10)x7,53 7 75 (1) 34m1 7 77 (1010) 35x7,57 7 77 (0100) 35x7,74 7 87 (1) 40x7,79 7 95 (10) 44x7,81 7 97 (10) 45x7,83 7 99 (100) 46x7,84 7 99 (010) 46x7,88 7 101 (010) 47x7,90 7 103 (10) 48x7,92 7 105 (1) 49x7,93 7 107 (10) 50x7,97 7 112 (1)x7,101 7 121 (10) 57x7,103 7 124 (100)x7,109 7 127 (10000) 60x7,110 7 127 (01000) 60x7,118 7 130 (1)x7,124 7 133 (100) 63


Name s n value precursor stemPd0 8 22 (1) 7Pe0 8 25 (1)N 8 46 (1) 19x8,32 8 62 (100) 27x8,33 8 62 (010) 27G21 8 68 (10) 30PD3 8 69 (01)x8,51 8 74 (10) 33x8,57 8 77 (100)x8,75 8 91 (1)x8,78 8 93 (10)x8,80 8 94 (1) 43x8,83 8 96 (10) 44x8,93 8 101 (10)x8,105 8 112 (100) 52x8,113 8 123 (1)x8,114 8 124 (1) 58x8,115 8 125 (10)x8,116 8 125 (01)x8,117 8 126 (100000) 59x8,118 8 126 (010000) 59x8,119 8 126 (001000) 59x8,120 8 126 (000100) 59x8,124 8 127 (0100000)x8,132 8 129 (01)x8,133 8 130 (10) 61x8,136 8 131 (0100)x8,139 8 132 (10000) 62x8,140 8 132 (01000) 62

8 ROBERT R. BRUNER

Name s n value precursor stemP 2h1 9 17 (1) 4P 2h2 9 19 (1) 5u 9 39 (1) 15v 9 42 (1)w 9 45 (1) 18B4 9 60 (10)X1 9 61 (1) 26x9,39 9 67 (10) 29x9,40 9 67 (01) 29x9,51 9 76 (10)x9,55 9 78 (10)x9,86 9 99 (10) 45x9,97 9 104 (10)x9,99 9 105 (1) 48x9,102 9 107 (1) 49x9,107 9 111 (1000) 51x9,109 9 111 (0010) 51x9,111 9 113 (1) 52x9,112 9 114 (10)x9,115 9 118 (10)x9,116 9 118 (01)x9,117 9 119 (1) 55x9,118 9 120 (1)x9,119 9 121 (10) 56x9,121 9 123 (10) 57x9,123 9 124 (100)x9,124 9 124 (010)x9,126 9 125 (10000) 58x9,129 9 125 (00010) 58x9,131 9 126 (100000)x9,145 9 129 (1000) 60x9,146 9 129 (0100) 60x9,154 9 131 (00100) 61


Name s n value precursor stemz 10 41 (1)x′ 10 53 (1)R1 10 54 (10) 22Q1 10 56 (01) 23B21 10 59 (1)x10,27 10 62 (100) 26x10,28 10 62 (010) 26x10,32 10 64 (10) 27B23 10 65 (1)B5 10 66 (10) 28PD2 10 66 (01) 28PA 10 69 (1)P 2h2

5 10 78 (11) 34Px6,53 10 84 (1) 37x10,60 10 87 (1)x10,63 10 90 (1) 40x10,65 10 92 (10) 41x10,67 10 93 (100)x10,70 10 94 (100) 42x10,73 10 95 (10)x10,76 10 97 (10)x10,82 10 100 (100) 45x10,100 10 109 (10)x10,102 10 110 (100) 50x10,107 10 112 (10) 51x10,109 10 113 (1)x10,113 10 117 (10)x10,114 10 117 (01)x10,116 10 118 (010) 54x10,118 10 119 (10)x10,120 10 120 (100) 55x10,124 10 123 (100)x10,127 10 124 (10000) 57x10,128 10 124 (01000) 57x10,132 10 125 (10000)x10,133 10 125 (01000)x10,137 10 126 (10000) 58x10,143 10 127 (010000)x10,148 10 128 (1000) 59x10,149 10 128 (0100) 59x10,152 10 129 (100)x10,155 10 130 (10000) 60

10 ROBERT R. BRUNER

Name s n value precursor stemP 2c0 11 24 (1)Pj 11 34 (1)x11,35 11 67 (10) 28x11,59 11 89 (1) 39x11,61 11 91 (10) 40x11,80 11 101 (010) 45x11,91 11 108 (10)x11,101 11 115 (1) 52x11,103 11 117 (100) 53x11,106 11 118 (100)x11,109 11 119 (1000) 54x11,113 11 120 (100)x11,116 11 121 (1) 55x11,118 11 122 (01)x11,119 11 123 (10000) 56x11,120 11 123 (01000) 56x11,124 11 124 (10000)x11,125 11 124 (01000)x11,126 11 124 (00100)x11,134 11 126 (100000)x11,147 11 129 (100000) 59x11,148 11 129 (010000) 59


Name s n value precursor stemP 2d0 12 30 (1) 9P 2e0 12 33 (1)x12,37 12 71 (10)P 2D3 12 77 (10)x12,44 12 80 (1) 34x12,45 12 81 (1)x12,48 12 86 (10) 37x12,51 12 88 (100) 38x12,55 12 90 (1) 39x12,58 12 92 (10) 40x12,60 12 93 (10)x12,64 12 96 (10) 42x12,78 12 103 (10)x12,80 12 104 (100) 46x12,85 12 107 (1)x12,86 12 109 (10)x12,93 12 114 (01) 51x12,96 12 117 (1000)x12,100 12 118 (100) 53x12,106 12 120 (10000) 54x12,107 12 120 (01000) 54x12,116 12 123 (100)x12,124 12 125 (10000)x12,125 12 125 (01000)x12,137 12 128 (10000) 58x12,140 12 128 (00010) 58

12 ROBERT R. BRUNER

Name s n value precursor stemP 3h1 13 25 (1) 6P 3h2 13 27 (1) 7Q 13 47 (10) 17Pu 13 47 (01) 17Pv 13 50 (1)R2 13 65 (01) 26P 2D1 13 68 (10)W1 13 69 (1) 28x13,34 13 71 (010) 29x13,35 13 71 (001) 29x13,42 13 79 (1) 33x13,46 13 85 (1) 36x13,73 13 100 (100)x13,85 13 107 (1) 47x13,87 13 109 (1) 48x13,88 13 110 (10)x13,91 13 112 (10)x13,93 13 113 (10) 50Px9,99 13 113 (01) 50x13,95 13 115 (10) 51x13,97 13 116 (100)x13,113 13 122 (100)x13,116 13 123 (100) 55x13,117 13 123 (010) 55x13,132 13 127 (01000) 57


Name s n value precursor stemPQ1 14 64 (10) 25x14,42 14 80 (10) 33x14,46 14 84 (1) 35P 3h2

5 14 86 (10) 36x14,67 14 98 (100) 42x14,74 14 102 (10) 44x14,79 14 106 (10) 46x14,82 14 108 (1) 47y14,83 14 109 (11)x14,84 14 109 (01)x14,91 14 112 (01) 49x14,104 14 118 (1000) 52Px10,102 14 118 (1111) 52x14,108 14 119 (10)x14,110 14 120 (10) 53Px10,109 14 121 (1)x14,117 14 124 (10000) 55x14,118 14 124 (01000) 55Px10,113 14 125 (111)x14,126 14 126 (0100) 56

14 ROBERT R. BRUNER

Name s n value precursor stemP 3c0 15 32 (1)P 2i 15 39 (1) 12P 2j 15 42 (1)x15,41 15 83 (1) 34x15,42 15 84 (10)x15,43 15 84 (01)x15,47 15 87 (10) 36x15,56 15 94 (1)x15,58 15 96 (10)x15,65 15 102 (1)x15,68 15 105 (10) 45x15,74 15 108 (01)x15,78 15 110 (10)x15,81 15 111 (0100) 48x15,82 15 111 (0010) 48x15,90 15 114 (10)x15,96 15 116 (0010)x15,97 15 116 (0001)x15,98 15 117 (100) 51x15,103 15 119 (100) 52x15,108 15 122 (10)x15,109 15 122 (01)x15,110 15 123 (100) 54x15,113 15 124 (1000)x15,114 15 124 (0100)x15,117 15 125 (10000) 55x15,119 15 125 (00100) 55


Name s n value precursor stemP 3d0 16 38 (1) 11P 3e0 16 41 (1)x16,32 16 76 (1) 30x16,33 16 77 (10)x16,35 16 79 (1)x16,37 16 80 (01) 32x16,38 16 82 (1) 33x16,42 16 85 (100)x16,48 16 88 (1) 36x16,54 16 94 (1) 39Px12,60 16 101 (1)x16,77 16 110 (1000) 47x16,78 16 110 (0100) 47Px12,80 16 112 (0100) 48Px12,85 16 115 (10)x16,95 16 116 (1000) 50Px12,86 16 117 (00100)x16,109 16 121 (010)x16,112 16 122 (010) 53x16,117 16 124 (10000) 54P 4h1 17 33 (1) 8P 4h2 17 35 (1) 9P 2u 17 55 (1) 19P 2v 17 58 (1)R1 17 70 (10)PR2 17 73 (10) 28x17,50 17 87 (1) 35x17,52 17 90 (10)x17,57 17 93 (1) 38x17,76 17 108 (100)x17,79 17 109 (10) 46x17,80 17 109 (01) 46x17,93 17 115 (10) 49x17,94 17 115 (01) 49Px13,87 17 117 (1000) 50P 2x9,97 17 120 (100)P 2x9,99 17 121 (0101) 52

16 ROBERT R. BRUNER

Name s n value precursor stemx18,20 18 69 (10)P 2Q1 18 72 (10) 27x18,50 18 89 (1)x18,55 18 92 (1) 37x18,57 18 95 (1)x18,60 18 98 (1) 40x18,63 18 101 (10)x18,68 18 104 (010) 43x18,72 18 107 (10)x18,77 18 110 (1000) 46x18,78 18 110 (0100) 46x18,83 18 112 (010) 47x18,85 18 113 (10)P 2x10,76 18 113 (01)x18,87 18 114 (100) 48Px14,79 18 114 (011) 48Px14,82 18 116 (1000) 49Px14,84 18 117 (01)P 4c0 19 40 (1)P 3j 19 50 (1)x19,49 19 94 (1)x19,58 19 102 (10)P 2x11,61 19 107 (101) 44Px15,65 19 110 (0100)x19,86 19 115 (10) 48Px15,78 19 118 (1)P 4d0 20 46 (1) 13P 4e0 20 49 (1)Px16,35 20 87 (1)x20,91 20 119 (1000)P 2x12,80 20 120 (100) 50


Name s n value precursor stemP 5h1 21 41 (1) 10P 5h2 21 43 (1) 11P 3u 21 63 (10) 21P 3v 21 66 (1)P 2R2 21 81 (10) 30x21,43 21 95 (10) 37Px17,50 21 95 (01) 37Px17,52 21 98 (1)x21,84 21 117 (01) 48x21,87 21 119 (010) 49P 3Q1 22 80 (10) 29x22,39 22 94 (1) 36Px18,50 22 97 (1)Px18,55 22 100 (1) 39Px18,68 22 112 (10) 45x22,71 22 113 (100)x22,78 22 116 (010) 47P 5c0 23 48 (1)P 4i 23 55 (1) 16P 4j 23 58 (1)P 5d0 24 54 (1) 15P 5e0 24 57 (1)P 2x16,32 24 92 (1) 34P 2x16,35 24 95 (11)P 6h1 25 49 (1) 12P 6h2 25 51 (1) 13P 4u 25 71 (1) 23P 4v 25 74 (1)x25,24 25 86 (10)P 3R2 25 89 (11) 32P 2x17,50 25 103 (1) 39P 2x17,52 25 106 (10)P 4x′ 26 85 (10)P 4Q1 26 88 (11) 31P 2x18,50 26 105 (1)

18 ROBERT R. BRUNER

Name s n value precursor stemP 6c0 27 56 (1)P 5j 27 66 (1)P 6d0 28 62 (1) 17P 6e0 28 65 (1)P 3x16,35 28 103 (1)P 7h1 29 57 (1) 14P 7h2 29 59 (1) 15P 4Q 29 79 (11) 25P 5u 29 79 (01) 25P 5v 29 82 (1)P 4R2 29 97 (10) 34P 3x17,50 29 111 (1) 41P 5Q1 30 96 (11) 33P 7c0 31 64 (1)P 6i 31 71 (1) 20P 6j 31 74 (1)P 7d0 32 70 (1) 19P 7e0 32 73 (1)P 4x16,32 32 108 (1) 38P 8h1 33 65 (1) 16P 8h2 33 67 (1) 17P 6u 33 87 (1) 27P 6v 33 90 (1)P 4R1 33 102 (11)P 5R2 33 105 (10) 36P 4x18,20 34 101 (11)P 6Q1 34 104 (11) 35P 8c0 35 72 (1)P 7j 35 82 (1)P 8d0 36 78 (1) 21P 8e0 36 81 (1)P 9h1 37 73 (1) 18P 9h2 37 75 (1) 19P 7u 37 95 (10) 29P 7v 37 98 (1)P 9c0 39 80 (1)P 8i 39 87 (1) 24P 8j 39 90 (1)

6. The tables

Stem 11 (1) h1

Stem 22 (1) h2

1


Stem 31 (1) h2

2 (1) h0h2

3 (1) h20h2 = h3

1

Stem 4

Stem 5

Stem 62 (1) h2

2

Stem 71 (1) h3

2 (1) h0h3

3 (1) h20h3

4 (1) h30h3

Stem 82 (1) h1h3

3 (1) c0

Stem 93 (1) h2

1h3 = h32

4 (1) h1c0

5 (1) Ph1

Stem 106 (1) h1Ph1

Stem 115 (1) Ph2

6 (1) h0Ph2

7 (1) h20Ph2 = h2

1Ph1

Stem 12

Stem 13

Stem 142 (1) h2

3

3 (1) h0h23

4 (1) d0

5 (1) h0d0

6 (1) h20d0 = h2Ph2

20 ROBERT R. BRUNER

Stem 151 (1) h4

2 (1) h0h4

3 (1) h20h4

4 (1) h30h4

5 (10) h1d0

(01) h40h4

6 (1) h50h4

7 (1) h60h4

8 (1) h70h4

Stem 162 (1) h1h4

6 (1) h21d0 = h3Ph1 = c2

0

7 (1) Pc0

Stem 173 (1) h2

1h4

4 (1) e0

5 (1) h0e0 = h2d0

6 (1) h20e0 = h0h2d0

7 (1) h30e0 = h2

0h2d0 = h31d0 = h1h3Ph1 = h1c

20 = h2

2Ph2

8 (1) h1Pc0 = c0Ph1

9 (1) P 2h1

Stem 182 (1) h2h4

3 (1) h0h2h4

4 (10) f0

(01) h20h2h4 = h3

1h4

5 (1) h0f0 = h1e0

10 (1) h1P2h1 = Ph2

1

Stem 193 (1) c1

9 (1) P 2h2

10 (1) h0P2h2

11 (1) h20P

2h2 = h21P

2h1 = h1Ph21

Stem 204 (1) g

5 (1) h0g = h2e0

6 (1) h20g = h0h2e0 = h2

2d0

Stem 213 (1) h2

2h4 = h33

5 (1) h1g = h2f0


Stem 224 (1) h2c1

8 (1) Pd0

9 (1) h0Pd0

10 (1) h20Pd0 = h2P

2h2 = Ph22

Stem 234 (1) h4c0

5 (1) h2g

6 (1) h0h2g = h22e0

7 (1) i

8 (1) h0i

9 (01) h20i

(11) h1Pd0 = d0Ph1

10 (1) h30i

11 (1) h40i

12 (1) h50i

Stem 245 (1) h1h4c0 = h3e0

10 (1) h21Pd0 = h1d0Ph1 = h3P

2h1 = c0Pc0

11 (1) P 2c0

Stem 258 (1) Pe0

9 (1) h0Pe0 = h2Pd0 = d0Ph2

10 (1) h20Pe0 = h0h2Pd0 = h0d0Ph2

11 (1) h30Pe0 = h2

0h2Pd0 = h20d0Ph2 = h3

1Pd0 = h21d0Ph1 =

h1h3P2h1 = h1c0Pc0 = h2

2P2h2 = h2Ph2

2 = h3Ph21 = c2

0Ph1

12 (1) h1P2c0 = c0P

2h1 = Ph1Pc0

13 (1) P 3h1

Stem 266 (1) h2

2g = h4Ph2

7 (1) j

8 (1) h0j = h2i

9 (1) h20j = h0h2i = h1Pe0 = e0Ph1

14 (1) h1P3h1 = Ph1P

2h1

Stem 2713 (1) P 3h2

14 (1) h0P3h2

15 (1) h20P

3h2 = h21P

3h1 = h1Ph1P2h1 = Ph3

1

Stem 288 (1) d2

0

9 (1) h0d20 = h2Pe0 = e0Ph2

10 (1) h20d

20 = h0h2Pe0 = h0e0Ph2 = h2

2Pd0 = h2d0Ph2

22 ROBERT R. BRUNER

Stem 297 (1) k

8 (1) h0k = h2j

9 (1) h20k = h0h2j = h1d

20 = h2

2i = f0Ph2 = gPh1

Stem 302 (1) h2

4

3 (1) h0h24

4 (1) h20h

24

5 (1) h30h

24

6 (1) r

7 (1) h0r

8 (1) h20r = h3i

9 (1) h30r = h0h3i

10 (1) h40r = h2

0h3i

11 (1) h50r = h3

0h3i = c0Pd0 = d0Pc0

12 (1) P 2d0

13 (1) h0P2d0

14 (1) h20P

2d0 = h2P3h2 = Ph2P

2h2

Stem 311 (1) h5

2 (1) h0h5

3 (10) h1h24

(01) h20h5

4 (1) h30h5

5 (10) n

(01) h40h5

6 (1) h50h5

7 (1) h60h5

8 (10) d0e0

(01) h70h5

9 (10) h0d0e0 = h2d20 = gPh2

(01) h80h5

10 (10) h20d0e0 = h0h2d

20 = h0gPh2 = h2

2Pe0 = h2e0Ph2 = c0i

(01) h90h5

11 (1) h100 h5

12 (1) h110 h5

13 (10) h1P2d0 = d0P

2h1 = Ph1Pd0

(01) h120 h5

14 (1) h130 h5

15 (1) h140 h5

16 (1) h150 h5


Stem 322 (1) h1h5

4 (1) d1

6 (1) q

7 (1) l

8 (1) h0l = h2k = d0f0

9 (1) h20l = h0h2k = h0d0f0 = h1d0e0 = h2

2j

14 (1) h21P

2d0 = h1d0P2h1 = h1Ph1Pd0 = h3P

3h1 = c0P2c0 = d0Ph2

1 =Pc2

0

15 (1) P 3c0

Stem 333 (1) h2

1h5

4 (1) p

5 (1) h0p = h1d1

7 (1) h1q = h2r

12 (1) P 2e0

13 (1) h0P2e0 = h2P

2d0 = d0P2h2 = Ph2Pd0

14 (1) h20P

2e0 = h0h2P2d0 = h0d0P

2h2 = h0Ph2Pd0

15 (1) h30P

2e0 = h20h2P

2d0 = h20d0P

2h2 = h20Ph2Pd0 = h3

1P2d0 =

h21d0P

2h1 = h21Ph1Pd0 = h1h3P

3h1 = h1c0P2c0 = h1d0Ph2

1 =h1Pc2

0 = h22P

3h2 = h2Ph2P2h2 = h3Ph1P

2h1 = c20P

2h1 =c0Ph1Pc0 = Ph3

2

16 (1) h1P3c0 = c0P

3h1 = Ph1P2c0 = Pc0P

2h1

17 (1) P 4h1

Stem 342 (1) h2h5

3 (1) h0h2h5

4 (1) h20h2h5 = h3

1h5

6 (1) h2n

8 (1) d0g = e20

9 (1) h0d0g = h0e20 = h2d0e0

10 (1) h20d0g = h2

0e20 = h0h2d0e0 = h2

2d20 = h2gPh2 = h4P

2h2 = c0j

11 (1) Pj

12 (1) h0Pj = Ph2i

13 (1) h20Pj = h0Ph2i = h1P

2e0 = e0P2h1 = Ph1Pe0

18 (1) h1P4h1 = Ph1P

3h1 = P 2h21

Stem 355 (1) h2d1 = h4g

7 (1) m

8 (1) h0m = h2l = e0f0

9 (1) h20m = h0h2l = h0e0f0 = h1d0g = h1e

20 = h2

2k = h2d0f0

17 (1) P 4h2

18 (1) h0P4h2

19 (1) h20P

4h2 = h21P

4h1 = h1Ph1P3h1 = h1P

2h21 = Ph2

1P2h1

24 ROBERT R. BRUNER

Stem 366 (1) t

12 (1) d0Pd0

13 (1) h0d0Pd0 = h2P2e0 = e0P

2h2 = Ph2Pe0

14 (1) h20d0Pd0 = h0h2P

2e0 = h0e0P2h2 = h0Ph2Pe0 = h2

2P2d0 =

h2d0P2h2 = h2Ph2Pd0 = d0Ph2

2

Stem 373 (1) h2

2h5

5 (1) x

6 (1) h0x

7 (10) h1t = h22n = c1f0

(01) h20x

(11) h3r

8 (10) e0g

(01) h30x = h0h3r

9 (1) h40x = h2

0h3r = h0e0g = h2d0g = h2e20 = h2

3i = h4Pd0

10 (1) h50x = h3

0h3r = h20e0g = h0h2d0g = h0h2e

20 = h0h

23i = h0h4Pd0 =

h22d0e0 = c0k

11 (1) d0i

12 (1) h0d0i = h2Pj = Ph2j

13 (1) h20d0i = h0h2Pj = h0Ph2j = h1d0Pd0 = h2Ph2i = d2

0Ph1 =f0P

2h2 = gP 2h1

Stem 382 (1) h3h5

3 (1) h0h3h5

4 (01) h20h3h5

(11) e1

5 (1) h30h3h5

6 (10) y

(01) h1x = h22d1 = h2h4g = h3n = c2

1

7 (1) h0y

8 (1) h20y = h2m = f0g

9 (1) h30y = h0h2m = h0f0g = h1e0g = h2

2l = h2e0f0 = c0r

16 (1) P 3d0

17 (1) h0P3d0

18 (1) h20P

3d0 = h2P4h2 = Ph2P

3h2 = P 2h22


Stem 393 (1) h1h3h5

4 (1) h5c0

5 (1) h1e1 = h3d1

7 (1) h1y = h2t = h3q = c1g

9 (1) u

12 (1) d0Pe0 = e0Pd0

13 (1) h0d0Pe0 = h0e0Pd0 = h2d0Pd0 = d20Ph2 = gP 2h2

14 (1) h20d0Pe0 = h2

0e0Pd0 = h0h2d0Pd0 = h0d20Ph2 = h0gP 2h2 =

h22P

2e0 = h2e0P2h2 = h2Ph2Pe0 = e0Ph2

2 = Pc0i

15 (1) P 2i

16 (1) h0P2i

17 (01) h20P

2i

(11) h1P3d0 = d0P

3h1 = Ph1P2d0 = Pd0P

2h1

18 (1) h30P

2i

19 (1) h40P

2i

20 (1) h50P

2i

Stem 404 (01) h2

1h3h5 = h32h5

(11) f1

5 (01) h0f1 = h3p

(11) h1h5c0

6 (10) h5Ph1

(01) h20f1 = h0h3p = h2

1e1 = h1h3d1

8 (1) g2

10 (1) h1u

11 (1) d0j = e0i

12 (1) h0d0j = h0e0i = h2d0i = f0Pd0 = Ph2k

13 (1) h20d0j = h2

0e0i = h0h2d0i = h0f0Pd0 = h0Ph2k = h1d0Pe0 =h1e0Pd0 = h2

2Pj = h2Ph2j = d0e0Ph1

18 (1) h21P

3d0 = h1d0P3h1 = h1Ph1P

2d0 = h1Pd0P2h1 = h3P

4h1 =c0P

3c0 = d0Ph1P2h1 = Ph2

1Pd0 = Pc0P2c0

19 (1) P 4c0

26 ROBERT R. BRUNER

Stem 413 (1) c2

4 (1) h0c2

5 (1) h20c2 = h1f1 = h2e1

7 (1) h1h5Ph1

10 (1) z

11 (1) h0z = h21u = f0i = Ph1q = Ph2r

16 (1) P 3e0

17 (1) h0P3e0 = h2P

3d0 = d0P3h2 = Ph2P

2d0 = Pd0P2h2

18 (1) h20P

3e0 = h0h2P3d0 = h0d0P

3h2 = h0Ph2P2d0 = h0Pd0P

2h2

19 (1) h30P

3e0 = h20h2P

3d0 = h20d0P

3h2 = h20Ph2P

2d0 = h20Pd0P

2h2 =h3

1P3d0 = h2

1d0P3h1 = h2

1Ph1P2d0 = h2

1Pd0P2h1 = h1h3P

4h1 =h1c0P

3c0 = h1d0Ph1P2h1 = h1Ph2

1Pd0 = h1Pc0P2c0 =

h22P

4h2 = h2Ph2P3h2 = h2P

2h22 = h3Ph1P

3h1 = h3P2h2

1 =c20P

3h1 = c0Ph1P2c0 = c0Pc0P

2h1 = d0Ph31 = Ph1Pc2

0 =Ph2

2P2h2

20 (1) h1P4c0 = c0P


3h1 = P 2h1P2c0

21 (1) P 5h1

Stem 426 (1) h5Ph2

7 (1) h0h5Ph2

8 (1) h20h5Ph2 = h2

1h5Ph1

9 (1) v

12 (1) d30 = e0Pe0 = gPd0

13 (1) h0d30 = h0e0Pe0 = h0gPd0 = h2d0Pe0 = h2e0Pd0 = d0e0Ph2

14 (1) h20d

30 = h2

0e0Pe0 = h20gPd0 = h0h2d0Pe0 = h0h2e0Pd0 =

h0d0e0Ph2 = h22d0Pd0 = h2d

20Ph2 = h2gP 2h2 = h4P

3h2 =c0Pj = gPh2

2 = Pc0j

15 (1) P 2j

16 (1) h0P2j = h2P

2i = iP 2h2

17 (1) h20P

2j = h0h2P2i = h0iP

2h2 = h1P3e0 = e0P

3h1 = Ph1P2e0 =

Pe0P2h1

22 (1) h1P5h1 = Ph1P

4h1 = P 2h1P3h1

Stem 4311 (1) d0k = e0j = gi

12 (1) h0d0k = h0e0j = h0gi = h2d0j = h2e0i = f0Pe0 = Ph2l

13 (1) h20d0k = h2

0e0j = h20gi = h0h2d0j = h0h2e0i = h0f0Pe0 =

h0Ph2l = h1d30 = h1e0Pe0 = h1gPd0 = h2

2d0i = h2f0Pd0 =h2Ph2k = d0f0Ph2 = d0gPh1 = e2

0Ph1

21 (1) P 5h2

22 (1) h0P5h2

23 (1) h20P

5h2 = h21P

5h1 = h1Ph1P4h1 = h1P

2h1P3h1 = Ph2

1P3h1 =

Ph1P2h2

1


Stem 444 (1) g2

5 (1) h0g2

6 (1) h20g2 = h3x

10 (1) d0r

16 (1) d0P2d0 = Pd2

0

17 (1) h0d0P2d0 = h0Pd2

0 = h2P3e0 = e0P

3h2 = Ph2P2e0 = Pe0P

2h2

18 (1) h20d0P

2d0 = h20Pd2

0 = h0h2P3e0 = h0e0P

3h2 = h0Ph2P2e0 =

h0Pe0P2h2 = h2

2P3d0 = h2d0P


2h2 =d0Ph2P

2h2 = Ph22Pd0

Stem 453 (1) h2

3h5 = h34

4 (1) h0h23h5 = h0h

34

5 (10) h5d0

(01) h1g2 = h3e1

6 (1) h0h5d0

7 (1) h20h5d0 = h2h5Ph2 = h3y

9 (1) w

12 (1) d20e0 = gPe0

15 (1) iPd0

16 (1) h0iPd0 = h2P2j = Ph2Pj = jP 2h2

17 (1) h20iPd0 = h0h2P

2j = h0Ph2Pj = h0jP2h2 = h1d0P

2d0 =h1Pd2

0 = h22P

2i = h2iP2h2 = d2

0P2h1 = d0Ph1Pd0 = f0P

3h2 =gP 3h1 = Ph2

2i

Stem 466 (1) h1h5d0

7 (1) B1

8 (1) N

11 (1) d0l = e0k = gj

14 (1) i2

15 (1) h0i2

16 (1) h20i

2 = h3P2i

17 (1) h30i

2 = h0h3P2i

18 (1) h40i

2 = h20h3P

2i

19 (1) h50i

2 = h30h3P

2i = c0P3d0 = d0P

3c0 = Pc0P2d0 = Pd0P

2c0

20 (1) P 4d0

21 (1) h0P4d0

22 (1) h20P

4d0 = h2P5h2 = Ph2P

4h2 = P 2h2P3h2

28 ROBERT R. BRUNER

Stem 475 (1) h2g2 = h3f1

6 (1) h0h2g2 = h0h3f1 = h23p

7 (1) h21h5d0 = h3h5Ph1 = h4q = h5c

20

8 (10) h5Pc0

(01) h1B1

10 (1) e0r

13 (10) Q

(01) Pu

14 (1) h0Q

15 (1) h20Q

16 (10) d0P2e0 = e0P

2d0 = Pd0Pe0

(01) h30Q

17 (01) h40Q

(11) h0d0P2e0 = h0e0P

2d0 = h0Pd0Pe0 = h2d0P2d0 = h2Pd2

0 =d20P

2h2 = d0Ph2Pd0 = gP 3h2

18 (01) h50Q

(11) h20d0P

2e0 = h20e0P

2d0 = h20Pd0Pe0 = h0h2d0P

2d0 = h0h2Pd20 =

h0d20P

2h2 = h0d0Ph2Pd0 = h0gP 3h2 = h22P

3e0 = h2e0P3h2 =

h2Ph2P2e0 = h2Pe0P

2h2 = c0P2i = e0Ph2P

2h2 = Ph22Pe0 =

iP 2c0

19 (1) h60Q

20 (1) h70Q

21 (10) h1P4d0 = d0P


3h1 = P 2h1P2d0

(01) h80Q

22 (1) h90Q

23 (1) h100 Q

24 (1) h110 Q


Stem 484 (1) h3c2

5 (1) h5e0

6 (1) h0h5e0 = h2h5d0

7 (10) B2

(01) h20h5e0 = h0h2h5d0

8 (1) h0B2

9 (10) h1h5Pc0 = h5c0Ph1

(01) h20B2 = h2

1B1

12 (1) d20g = d0e

20

14 (1) h1Q = h1Pu = Ph1u

15 (1) d0Pj = iPe0 = jPd0

16 (1) h0d0Pj = h0iPe0 = h0jPd0 = h2iPd0 = d0Ph2i = f0P2d0 =

kP 2h2

17 (1) h20d0Pj = h2

0iPe0 = h20jPd0 = h0h2iPd0 = h0d0Ph2i =

h0f0P2d0 = h0kP 2h2 = h1d0P

2e0 = h1e0P2d0 = h1Pd0Pe0 =

h22P

2j = h2Ph2Pj = h2jP2h2 = d0e0P

2h1 = d0Ph1Pe0 =e0Ph1Pd0 = Ph2

2j

22 (1) h21P

4d0 = h1d0P4h1 = h1Ph1P

3d0 = h1Pd0P3h1 =

h1P2h1P

2d0 = h3P5h1 = c0P

4c0 = d0Ph1P3h1 = d0P

2h21 =

Ph21P

2d0 = Ph1Pd0P2h1 = Pc0P

3c0 = P 2c20

23 (1) P 5c0

Stem 495 (1) h5f0

6 (1) h0h5f0 = h1h5e0

11 (1) d0m = e0l = gk

14 (1) ij

15 (1) h0ij = h21Q = h2

1Pu = h1Ph1u = h2i2 = rP 2h2 = qP 2h1

20 (1) P 4e0

21 (1) h0P4e0 = h2P

4d0 = d0P4h2 = Ph2P

3d0 = Pd0P3h2 = P 2h2P

2d0

22 (1) h20P

4e0 = h0h2P4d0 = h0d0P


3h2 =h0P

2h2P2d0

23 (1) h30P

4e0 = h20h2P

4d0 = h20d0P

4h2 = h20Ph2P

3d0 = h20Pd0P

3h2 =h2

0P2h2P

2d0 = h31P

4d0 = h21d0P

4h1 = h21Ph1P

3d0 =h2

1Pd0P3h1 = h2

1P2h1P

2d0 = h1h3P5h1 = h1c0P

4c0 =h1d0Ph1P

3h1 = h1d0P2h2

1 = h1Ph21P

2d0 = h1Ph1Pd0P2h1 =

h1Pc0P3c0 = h1P

2c20 = h2

2P5h2 = h2Ph2P

4h2 = h2P2h2P

3h2 =h3Ph1P

4h1 = h3P2h1P

3h1 = c20P

4h1 = c0Ph1P3c0 =

c0Pc0P3h1 = c0P

2h1P2c0 = d0Ph2

1P2h1 = Ph3

1Pd0 =Ph1Pc0P

2c0 = Ph22P

3h2 = Ph2P2h2

2 = Pc20P

2h1

24 (1) h1P5c0 = c0P


4h1 = P 2h1P3c0 =

P 2c0P3h1

25 (1) P 6h1

30 ROBERT R. BRUNER

Stem 504 (1) h5c1

6 (1) C

10 (1) gr

13 (1) Pv

16 (1) d20Pd0 = e0P

2e0 = gP 2d0 = Pe20

17 (1) h0d20Pd0 = h0e0P

2e0 = h0gP 2d0 = h0Pe20 = h2d0P

2e0 =h2e0P

2d0 = h2Pd0Pe0 = d0e0P2h2 = d0Ph2Pe0 = e0Ph2Pd0

18 (1) h20d

20Pd0 = h2

0e0P2e0 = h2

0gP 2d0 = h20Pe2

0 = h0h2d0P2e0 =

h0h2e0P2d0 = h0h2Pd0Pe0 = h0d0e0P

2h2 = h0d0Ph2Pe0 =h0e0Ph2Pd0 = h2

2d0P2d0 = h2

2Pd20 = h2d

20P

2h2 = h2d0Ph2Pd0 =h2gP 3h2 = h4P

4h2 = c0P2j = d2

0Ph22 = gPh2P

2h2 = Pc0Pj =jP 2c0

19 (1) P 3j

20 (1) h0P3j = Ph2P

2i = iP 3h2

21 (1) h20P

3j = h0Ph2P2i = h0iP

3h2 = h1P4e0 = e0P

4h1 = Ph1P3e0 =

Pe0P3h1 = P 2h1P

2e0

26 (1) h1P6h1 = Ph1P

5h1 = P 2h1P4h1 = P 3h2

1

Stem 515 (1) h3g2 = h5g

6 (1) h0h3g2 = h0h5g = h2h5e0

7 (1) h20h3g2 = h2

0h5g = h0h2h5e0 = h22h5d0 = h2

3x

8 (1) h2B2

9 (1) gn

12 (1) d0e0g = e30

15 (1) d20i = e0Pj = jPe0 = kPd0

16 (1) h0d20i = h0e0Pj = h0jPe0 = h0kPd0 = h2d0Pj = h2iPe0 =

h2jPd0 = d0Ph2j = e0Ph2i = f0P2e0 = lP 2h2

17 (1) h20d

20i = h2

0e0Pj = h20jPe0 = h2

0kPd0 = h0h2d0Pj = h0h2iPe0 =h0h2jPd0 = h0d0Ph2j = h0e0Ph2i = h0f0P

2e0 = h0lP2h2 =

h1d20Pd0 = h1e0P

2e0 = h1gP 2d0 = h1Pe20 = h2

2iPd0 =h2d0Ph2i = h2f0P

2d0 = h2kP 2h2 = d30Ph1 = d0f0P

2h2 =d0gP 2h1 = e2

0P2h1 = e0Ph1Pe0 = f0Ph2Pd0 = gPh1Pd0 = Ph2

2k

25 (1) P 6h2

26 (1) h0P6h2

27 (1) h20P

6h2 = h21P

6h1 = h1Ph1P5h1 = h1P

2h1P4h1 = h1P

3h21 =

Ph21P

4h1 = Ph1P2h1P

3h1 = P 2h31


Stem 525 (1) D1

6 (1) h1h3g2 = h1h5g = h2h5f0 = h23e1

8 (1) gd1

11 (1) e0m = gl

14 (1) rPd0 = ik = j2

20 (1) d0P3d0 = Pd0P

2d0

21 (1) h0d0P3d0 = h0Pd0P

2d0 = h2P4e0 = e0P

4h2 = Ph2P3e0 =

Pe0P3h2 = P 2h2P

2e0

22 (1) h20d0P

3d0 = h20Pd0P

2d0 = h0h2P4e0 = h0e0P

4h2 =h0Ph2P

3e0 = h0Pe0P3h2 = h0P

2h2P2e0 = h2

2P4d0 =

h2d0P4h2 = h2Ph2P

3d0 = h2Pd0P3h2 = h2P

2h2P2d0 =

d0Ph2P3h2 = d0P

2h22 = Ph2

2P2d0 = Ph2Pd0P

2h2

Stem 535 (1) h2h5c1 = h4e1

7 (1) h2C

9 (1) h5Pd0

10 (1) x′

11 (1) h0x′

12 (1) h20x

′

13 (10) d0u

(01) h30x

′

(11) ri

14 (1) h40x

′ = h0ri

15 (1) h50x

′ = h20ri = h3i

2

16 (01) h60x

′ = h30ri = h0h3i

2

(11) d20Pe0 = d0e0Pd0 = gP 2e0

17 (1) h70x

′ = h40ri = h2

0h3i2 = h0d

20Pe0 = h0d0e0Pd0 = h0gP 2e0 =

h2d20Pd0 = h2e0P

2e0 = h2gP 2d0 = h2Pe20 = h2

3P2i = h4P

3d0 =d30Ph2 = d0gP 2h2 = e2

0P2h2 = e0Ph2Pe0 = gPh2Pd0

18 (1) h80x

′ = h50ri = h3

0h3i2 = h2

0d20Pe0 = h2

0d0e0Pd0 = h20gP 2e0 =

h0h2d20Pd0 = h0h2e0P

2e0 = h0h2gP 2d0 = h0h2Pe20 =

h0h23P

2i = h0h4P3d0 = h0d

30Ph2 = h0d0gP 2h2 = h0e

20P

2h2 =h0e0Ph2Pe0 = h0gPh2Pd0 = h2

2d0P2e0 = h2

2e0P2d0 =

h22Pd0Pe0 = h2d0e0P

2h2 = h2d0Ph2Pe0 = h2e0Ph2Pd0 =c0iPd0 = d0e0Ph2

2 = d0Pc0i = kP 2c0

19 (1) d0P2i = iP 2d0

20 (1) h0d0P2i = h0iP

2d0 = h2P3j = Ph2P

2j = jP 3h2 = P 2h2Pj

21 (1) h20d0P

2i = h20iP

2d0 = h0h2P3j = h0Ph2P

2j = h0jP3h2 =

h0P2h2Pj = h1d0P

3d0 = h1Pd0P2d0 = h2Ph2P

2i = h2iP3h2 =

d20P

3h1 = d0Ph1P2d0 = d0Pd0P

2h1 = f0P4h2 = gP 4h1 =

Ph1Pd20 = Ph2iP

2h2

32 ROBERT R. BRUNER

Stem 546 (1) G

8 (1) h5i

9 (1) h0h5i

10 (10) R1

(01) h20h5i = h1h5Pd0 = h4u = h5d0Ph1 = c0B1

11 (10) h1x′

(01) h0R1

12 (10) d0g2 = e2

0g

(01) h20R1

13 (1) h30R1

14 (1) h40R1 = h3Q

15 (01) h50R1 = h0h3Q

(11) d20j = d0e0i = gPj = kPe0 = lPd0

16 (1) h60R1 = h2

0h3Q = h0d20j = h0d0e0i = h0gPj = h0kPe0 =

h0lPd0 = h2d20i = h2e0Pj = h2jPe0 = h2kPd0 = d0f0Pd0 =

d0Ph2k = e0Ph2j = gPh2i = mP 2h2

17 (1) h70R1 = h3

0h3Q = h20d

20j = h2

0d0e0i = h20gPj = h2

0kPe0 =h2

0lPd0 = h0h2d20i = h0h2e0Pj = h0h2jPe0 = h0h2kPd0 =

h0d0f0Pd0 = h0d0Ph2k = h0e0Ph2j = h0gPh2i = h0mP 2h2 =h1d

20Pe0 = h1d0e0Pd0 = h1gP 2e0 = h2

2d0Pj = h22iPe0 =

h22jPd0 = h2d0Ph2j = h2e0Ph2i = h2f0P

2e0 = h2lP2h2 = c0i

2 =d20e0Ph1 = e0f0P

2h2 = e0gP 2h1 = f0Ph2Pe0 = gPh1Pe0 =Ph2

2l = rP 2c0

24 (1) P 5d0

25 (1) h0P5d0

26 (1) h20P

5d0 = h2P6h2 = Ph2P

5h2 = P 2h2P4h2 = P 3h2

2


Stem 557 (1) h1G

11 (1) gm

12 (1) h21x

′ = Ph1B1

14 (1) d0z = rPe0 = il = jk

17 (1) P 2u

20 (1) d0P3e0 = e0P

3d0 = Pd0P2e0 = Pe0P

2d0

21 (1) h0d0P3e0 = h0e0P

3d0 = h0Pd0P2e0 = h0Pe0P

2d0 = h2d0P3d0 =

h2Pd0P2d0 = d2

0P3h2 = d0Ph2P

2d0 = d0Pd0P2h2 = gP 4h2 =

Ph2Pd20

22 (1) h20d0P

3e0 = h20e0P

3d0 = h20Pd0P

2e0 = h20Pe0P

2d0 =h0h2d0P

3d0 = h0h2Pd0P2d0 = h0d

20P

3h2 = h0d0Ph2P2d0 =

h0d0Pd0P2h2 = h0gP 4h2 = h0Ph2Pd2

0 = h22P

4e0 = h2e0P4h2 =

h2Ph2P3e0 = h2Pe0P

3h2 = h2P2h2P

2e0 = e0Ph2P3h2 =

e0P2h2

2 = Ph22P

2e0 = Ph2Pe0P2h2 = Pc0P

2i = iP 3c0

23 (1) P 4i

24 (1) h0P4i

25 (01) h20P

4i

(11) h1P5d0 = d0P


4h1 = P 2h1P3d0 =

P 2d0P3h1

26 (1) h30P

4i

27 (1) h40P

4i

28 (1) h50P

4i

34 ROBERT R. BRUNER

Stem 569 (1) h5Pe0

10 (10) gt

(01) Q1

11 (1) h0Q1 = h2x′

12 (1) h20Q1 = h0h2x

′

13 (10) d0v

(01) h30Q1 = h2

0h2x′ = h3

1x′ = h1Ph1B1

(11) e0u = rj

16 (1) d40 = d0e0Pe0 = d0gPd0 = e2

0Pd0

18 (1) h1P2u = Ph1Q = Ph1Pu = P 2h1u

19 (1) d0P2j = e0P

2i = iP 2e0 = jP 2d0 = Pd0Pj

20 (1) h0d0P2j = h0e0P

2i = h0iP2e0 = h0jP

2d0 = h0Pd0Pj =h2d0P

2i = h2iP2d0 = d0iP

2h2 = f0P3d0 = Ph2iPd0 = kP 3h2

21 (1) h20d0P

2j = h20e0P

2i = h20iP

2e0 = h20jP

2d0 = h20Pd0Pj =

h0h2d0P2i = h0h2iP

2d0 = h0d0iP2h2 = h0f0P

3d0 =h0Ph2iPd0 = h0kP 3h2 = h1d0P

3e0 = h1e0P3d0 = h1Pd0P

2e0 =h1Pe0P

2d0 = h22P

3j = h2Ph2P2j = h2jP

3h2 = h2P2h2Pj =

d0e0P3h1 = d0Ph1P

2e0 = d0Pe0P2h1 = e0Ph1P

2d0 =e0Pd0P

2h1 = Ph1Pd0Pe0 = Ph22Pj = Ph2jP

2h2

26 (1) h21P

5d0 = h1d0P5h1 = h1Ph1P

4d0 = h1Pd0P4h1 =

h1P2h1P

3d0 = h1P2d0P

3h1 = h3P6h1 = c0P

5c0 = d0Ph1P4h1 =

d0P2h1P

3h1 = Ph21P

3d0 = Ph1Pd0P3h1 = Ph1P

2h1P2d0 =

Pc0P4c0 = Pd0P

2h21 = P 2c0P

3c0

27 (1) P 6c0


Stem 577 (1) Q2

8 (10) h5j

(01) h0Q2

9 (10) h0h5j = h2h5i

(01) h20Q2

10 (1) h20h5j = h0h2h5i = h1h5Pe0 = h4v = h5e0Ph1

11 (1) h1Q1 = h2R1

12 (1) e0g2

15 (1) d20k = d0e0j = d0gi = e2

0i = lP e0 = mPd0

18 (1) iP j

19 (1) h0iP j = h21P

2u = h1Ph1Q = h1Ph1Pu = h1P2h1u = f0P

2i =Ph2

1u = Ph2i2 = rP 3h2 = qP 3h1

24 (1) P 5e0

25 (1) h0P5e0 = h2P

5d0 = d0P5h2 = Ph2P

4d0 = Pd0P4h2 =

P 2h2P3d0 = P 2d0P

3h2

26 (1) h20P

5e0 = h0h2P5d0 = h0d0P


4h2 =h0P

2h2P3d0 = h0P

2d0P3h2

27 (1) h30P

5e0 = h20h2P

5d0 = h20d0P

5h2 = h20Ph2P

4d0 = h20Pd0P

4h2 =h2

0P2h2P

3d0 = h20P

2d0P3h2 = h3

1P5d0 = h2

1d0P5h1 =

h21Ph1P

4d0 = h21Pd0P

4h1 = h21P

2h1P3d0 = h2

1P2d0P

3h1 =h1h3P

6h1 = h1c0P5c0 = h1d0Ph1P

4h1 = h1d0P2h1P

3h1 =h1Ph2

1P3d0 = h1Ph1Pd0P

3h1 = h1Ph1P2h1P

2d0 =h1Pc0P

4c0 = h1Pd0P2h2

1 = h1P2c0P

3c0 = h22P

6h2 =h2Ph2P

5h2 = h2P2h2P

4h2 = h2P3h2

2 = h3Ph1P5h1 =

h3P2h1P

4h1 = h3P3h2

1 = c20P


4h1 =c0P

2h1P3c0 = c0P

2c0P3h1 = d0Ph2

1P3h1 = d0Ph1P

2h21 =

Ph31P

2d0 = Ph21Pd0P

2h1 = Ph1Pc0P3c0 = Ph1P

2c20 =

Ph22P

4h2 = Ph2P2h2P

3h2 = Pc20P

3h1 = Pc0P2h1P

2c0 = P 2h32

28 (1) h1P6c0 = c0P


5h1 = P 2h1P4c0 =

P 2c0P4h1 = P 3h1P

3c0

29 (1) P 7h1

36 ROBERT R. BRUNER

Stem 586 (1) D2

7 (1) h0D2

8 (1) h20D2 = h1Q2

14 (1) d20r = e0z = im = jl = k2

17 (1) P 2v

20 (1) d20P

2d0 = d0Pd20 = e0P

3e0 = gP 3d0 = Pe0P2e0

21 (1) h0d20P

2d0 = h0d0Pd20 = h0e0P

3e0 = h0gP 3d0 = h0Pe0P2e0 =

h2d0P3e0 = h2e0P


2d0 = d0e0P3h2 =

d0Ph2P2e0 = d0Pe0P

2h2 = e0Ph2P2d0 = e0Pd0P

2h2 =Ph2Pd0Pe0

22 (1) h20d

20P

2d0 = h20d0Pd2

0 = h20e0P

3e0 = h20gP 3d0 = h2

0Pe0P2e0 =

h0h2d0P3e0 = h0h2e0P

3d0 = h0h2Pd0P2e0 = h0h2Pe0P

2d0 =h0d0e0P

3h2 = h0d0Ph2P2e0 = h0d0Pe0P

2h2 = h0e0Ph2P2d0 =

h0e0Pd0P2h2 = h0Ph2Pd0Pe0 = h2

2d0P3d0 = h2

2Pd0P2d0 =

h2d20P

3h2 = h2d0Ph2P2d0 = h2d0Pd0P

2h2 = h2gP 4h2 =h2Ph2Pd2

0 = h4P5h2 = c0P

3j = d20Ph2P

2h2 = d0Ph22Pd0 =

gPh2P3h2 = gP 2h2

2 = Pc0P2j = jP 3c0 = P 2c0Pj

23 (1) P 4j

24 (1) h0P4j = h2P

4i = iP 4h2 = P 2h2P2i

25 (1) h20P

4j = h0h2P4i = h0iP

4h2 = h0P2h2P

2i = h1P5e0 = e0P

5h1 =Ph1P

4e0 = Pe0P4h1 = P 2h1P

3e0 = P 2e0P3h1

30 (1) h1P7h1 = Ph1P

6h1 = P 2h1P5h1 = P 3h1P

4h1


Stem 5910 (1) B21

11 (1) h0B21 = h2Q1

12 (1) h20B21 = h0h2Q1 = h2

2x′ = Ph2B2

13 (1) d0w = e0v = gu = rk

16 (1) d30e0 = d0gPe0 = e2

0Pe0 = e0gPd0

19 (1) d0iPd0 = e0P2j = gP 2i = jP 2e0 = kP 2d0 = Pe0Pj

20 (1) h0d0iPd0 = h0e0P2j = h0gP 2i = h0jP

2e0 = h0kP 2d0 =h0Pe0Pj = h2d0P

2j = h2e0P2i = h2iP

2e0 = h2jP2d0 =

h2Pd0Pj = d0Ph2Pj = d0jP2h2 = e0iP

2h2 = f0P3e0 =

Ph2iPe0 = Ph2jPd0 = lP 3h2

21 (1) h20d0iPd0 = h2

0e0P2j = h2

0gP 2i = h20jP

2e0 = h20kP 2d0 =

h20Pe0Pj = h0h2d0P

2j = h0h2e0P2i = h0h2iP

2e0 = h0h2jP2d0 =

h0h2Pd0Pj = h0d0Ph2Pj = h0d0jP2h2 = h0e0iP

2h2 =h0f0P

3e0 = h0Ph2iPe0 = h0Ph2jPd0 = h0lP3h2 = h1d

20P

2d0 =h1d0Pd2

0 = h1e0P3e0 = h1gP 3d0 = h1Pe0P

2e0 = h22d0P

2i =h2

2iP2d0 = h2d0iP

2h2 = h2f0P3d0 = h2Ph2iPd0 = h2kP 3h2 =

d30P

2h1 = d20Ph1Pd0 = d0f0P

3h2 = d0gP 3h1 = d0Ph22i =

e20P

3h1 = e0Ph1P2e0 = e0Pe0P

2h1 = f0Ph2P2d0 =

f0Pd0P2h2 = gPh1P

2d0 = gPd0P2h1 = Ph1Pe2

0 = Ph2kP 2h2

29 (1) P 7h2

30 (1) h0P7h2

31 (1) h20P

7h2 = h21P

7h1 = h1Ph1P6h1 = h1P

2h1P5h1 =

h1P3h1P

4h1 = Ph21P

5h1 = Ph1P2h1P

4h1 = Ph1P3h2

1 =P 2h2

1P3h1

38 ROBERT R. BRUNER

Stem 607 (1) B3

8 (1) h0B3 = h2Q2 = h5k

9 (10) B4

(01) h20B3 = h0h2Q2 = h0h5k = h2h5j

10 (1) h0B4

11 (10) h3x′

(01) h20B4

(11) h1B21 = d0B1

12 (10) g3

(01) h30B4 = h0h3x

′ = xi

(11) r2

13 (1) h40B4 = h2

0h3x′ = h0xi = h0r

2

14 (1) h50B4 = h3

0h3x′ = h2

0xi = h20r

2 = h3ri

15 (1) d20l = d0e0k = d0gj = e2

0j = e0gi = mPe0

18 (1) d0i2 = rP 2d0 = jP j

24 (1) d0P4d0 = Pd0P

3d0 = P 2d20

25 (1) h0d0P4d0 = h0Pd0P

3d0 = h0P2d2

0 = h2P5e0 = e0P

5h2 =Ph2P

4e0 = Pe0P4h2 = P 2h2P

3e0 = P 2e0P3h2

26 (1) h20d0P

4d0 = h20Pd0P

3d0 = h20P

2d20 = h0h2P

5e0 = h0e0P5h2 =

h0Ph2P4e0 = h0Pe0P

4h2 = h0P2h2P

3e0 = h0P2e0P

3h2 =h2

2P5d0 = h2d0P


4h2 =h2P

2h2P3d0 = h2P

2d0P3h2 = d0Ph2P

4h2 = d0P2h2P

3h2 =Ph2

2P3d0 = Ph2Pd0P

3h2 = Ph2P2h2P

2d0 = Pd0P2h2

2


Stem 614 (1) D3

6 (01) A

(11) A′

7 (01) h0A = h2D2

(11) h0A′

8 (1) h20A = h0h2D2 = h1B3 = h4B1

9 (1) X1

10 (1) h0X1

11 (10) nr

(01) h20X1 = h3R1

12 (1) h30X1 = h0h3R1

13 (1) h40X1 = h2

0h3R1 = c0x′ = yi

14 (1) d0e0r = gz = jm = kl

17 (1) d0Pu = Pd0u

20 (1) d20P

2e0 = d0e0P2d0 = d0Pd0Pe0 = e0Pd2

0 = gP 3e0

23 (1) iP 3d0 = Pd0P2i

24 (1) h0iP3d0 = h0Pd0P

2i = h2P4j = Ph2P

3j = jP 4h2 = P 2h2P2j =

PjP 3h2

25 (1) h20iP

3d0 = h20Pd0P

2i = h0h2P4j = h0Ph2P

3j = h0jP4h2 =

h0P2h2P

2j = h0PjP 3h2 = h1d0P4d0 = h1Pd0P

3d0 = h1P2d2

0 =h2

2P4i = h2iP

4h2 = h2P2h2P

2i = d20P

4h1 = d0Ph1P3d0 =

d0Pd0P3h1 = d0P

2h1P2d0 = f0P

5h2 = gP 5h1 = Ph1Pd0P2d0 =

Ph22P

2i = Ph2iP3h2 = iP 2h2

2 = Pd20P

2h1

40 ROBERT R. BRUNER

Stem 622 (1) h2

5

3 (1) h0h25

4 (1) h20h

25

5 (100) H1

(010) h1D3

(001) h30h

25

6 (10) h5n

(01) h40h

25

7 (1) h50h

25

8 (100) x8,32

(010) x8,33

(001) h60h

25

9 (1) h70h

25 = h0x8,32 = h0x8,33

10 (100) x10,27

(010) x10,28

(001) h1X1

11 (10) h0x10,27

(01) h0x10,28 = h2B21 = d0B2

12 (10) h20x10,27

(01) h20x10,28 = h0h2B21 = h0d0B2 = h2

2Q1

13 (10) e0w = gv = rl

(01) h30x10,27

14 (1) h40x10,27 = h4Q

15 (10) Ph1x′

(01) h50x10,27 = h0h4Q

16 (10) d30g = d2

0e20 = e0gPe0 = g2Pd0 = iu

(01) h60x10,27 = h2

0h4Q

17 (1) h70x10,27 = h3

0h4Q

18 (1) h80x10,27 = h4

0h4Q

19 (01) h90x10,27 = h5

0h4Q

(11) d20Pj = d0iPe0 = d0jPd0 = e0iPd0 = gP 2j = kP 2e0 = lP 2d0

20 (1) h100 x10,27 = h6

0h4Q = h0d20Pj = h0d0iPe0 = h0d0jPd0 =

h0e0iPd0 = h0gP 2j = h0kP 2e0 = h0lP2d0 = h2d0iPd0 =

h2e0P2j = h2gP 2i = h2jP

2e0 = h2kP 2d0 = h2Pe0Pj =d20Ph2i = d0f0P

2d0 = d0kP 2h2 = e0Ph2Pj = e0jP2h2 =

f0Pd20 = giP 2h2 = Ph2jPe0 = Ph2kPd0 = mP 3h2

continued


Stem 62 continued21 (1) h11

0 x10,27 = h70h4Q = h2

0d20Pj = h2

0d0iPe0 = h20d0jPd0 =

h20e0iPd0 = h2

0gP 2j = h20kP 2e0 = h2

0lP2d0 = h0h2d0iPd0 =

h0h2e0P2j = h0h2gP 2i = h0h2jP

2e0 = h0h2kP 2d0 =h0h2Pe0Pj = h0d

20Ph2i = h0d0f0P

2d0 = h0d0kP 2h2 =h0e0Ph2Pj = h0e0jP

2h2 = h0f0Pd20 = h0giP 2h2 = h0Ph2jPe0 =

h0Ph2kPd0 = h0mP 3h2 = h1d20P

2e0 = h1d0e0P2d0 =

h1d0Pd0Pe0 = h1e0Pd20 = h1gP 3e0 = h2

2d0P2j = h2

2e0P2i =

h22iP

2e0 = h22jP

2d0 = h22Pd0Pj = h2d0Ph2Pj = h2d0jP

2h2 =h2e0iP

2h2 = h2f0P3e0 = h2Ph2iPe0 = h2Ph2jPd0 = h2lP

3h2 =d20e0P

2h1 = d20Ph1Pe0 = d0e0Ph1Pd0 = d0Ph2

2j = e0f0P3h2 =

e0gP 3h1 = e0Ph22i = f0Ph2P

2e0 = f0Pe0P2h2 = gPh1P

2e0 =gPe0P

2h1 = Ph2lP2h2 = rP 3c0 = Pc0i

2

22 (1) iP 2i

23 (1) h0iP2i

24 (1) h20iP

2i = h3P4i

25 (1) h30iP

2i = h0h3P4i

26 (1) h40iP

2i = h20h3P

4i

27 (1) h50iP

2i = h30h3P

4i = c0P5d0 = d0P

5c0 = Pc0P4d0 = Pd0P

4c0 =P 2c0P

3d0 = P 2d0P3c0

28 (1) P 6d0

29 (1) h0P6d0

30 (1) h20P

6d0 = h2P7h2 = Ph2P

6h2 = P 2h2P5h2 = P 3h2P

4h2

42 ROBERT R. BRUNER

Stem 631 (1) h6

2 (1) h0h6

3 (10) h1h25

(01) h20h6

4 (1) h30h6

5 (1) h40h6

6 (10) h1H1

(01) h50h6

7 (100) x7,33

(010) x7,34

(001) h60h6

8 (10) h0x7,33 = h0x7,34 = h2B3 = h4B2 = h5l

(01) h70h6

9 (100) h1x8,32

(010) h20x7,33 = h2

0x7,34 = h0h2B3 = h0h4B2 = h0h5l = h22Q2 =

h2h5k = h5d0f0

(001) h80h6

10 (10) h2B4

(01) h90h6

11 (100) h21X1 = h3Q1 = Ph1G

(010) h0h2B4 = h1x10,28 = e0B1

(110) h1x10,27

(001) h100 h6

12 (1) h110 h6

13 (1) h120 h6

14 (1) h130 h6

15 (10) d20m = d0e0l = d0gk = e2

0k = e0gj = g2i

(01) h140 h6

16 (10) h1Ph1x′ = B1P

2h1

(01) h150 h6

17 (1) h160 h6

18 (10) d0ij = e0i2 = rP 2e0 = kPj = Pd0z

(01) h170 h6

19 (1) h180 h6

20 (1) h190 h6

21 (10) P 3u

(01) h200 h6

22 (1) h210 h6

23 (1) h220 h6

continued


Stem 63 continued24 (10) d0P

4e0 = e0P4d0 = Pd0P

3e0 = Pe0P3d0 = P 2d0P

2e0

(01) h230 h6

25 (10) h0d0P4e0 = h0e0P


3d0 =h0P

2d0P2e0 = h2d0P

4d0 = h2Pd0P3d0 = h2P

2d20 = d2

0P4h2 =

d0Ph2P3d0 = d0Pd0P

3h2 = d0P2h2P

2d0 = gP 5h2 =Ph2Pd0P

2d0 = Pd20P

2h2

(01) h240 h6

26 (10) h20d0P

4e0 = h20e0P

4d0 = h20Pd0P

3e0 = h20Pe0P

3d0 =h2

0P2d0P

2e0 = h0h2d0P4d0 = h0h2Pd0P

3d0 = h0h2P2d2

0 =h0d

20P


3h2 = h0d0P2h2P

2d0 =h0gP 5h2 = h0Ph2Pd0P

2d0 = h0Pd20P

2h2 = h22P

5e0 =h2e0P

5h2 = h2Ph2P4e0 = h2Pe0P

4h2 = h2P2h2P

3e0 =h2P

2e0P3h2 = c0P

4i = e0Ph2P4h2 = e0P

2h2P3h2 = Ph2

2P3e0 =

Ph2Pe0P3h2 = Ph2P

2h2P2e0 = iP 4c0 = Pe0P

2h22 = P 2c0P

2i

(01) h250 h6

27 (1) h260 h6

28 (1) h270 h6

29 (10) h1P6d0 = d0P


5h1 = P 2h1P4d0 =

P 2d0P4h1 = P 3h1P

3d0

(01) h280 h6

30 (1) h290 h6

31 (1) h300 h6

32 (1) h310 h6

44 ROBERT R. BRUNER

Stem 642 (1) h1h6

4 (1) h21h

25

5 (1) h2D3

6 (1) A′′

7 (10) h2A

(01) h0A′′

(11) h2A′

8 (100) h3Q2

(010) h0h2A = h1x7,34 = h22D2

(001) h20A

′′ = h1x7,33

(011) h0h2A′ = gg2 = d2

1

9 (1) h0h3Q2

10 (10) x10,32

(01) h20h3Q2 = h2

1x8,32 = d1q

14 (10) PQ1

(01) d0gr = e20r = km = l2

15 (1) h0PQ1 = Ph2x′

16 (1) h20PQ1 = h0Ph2x

′

17 (10) d0Pv = Pd0v

(01) h30PQ1 = h2

0Ph2x′ = h2

1Ph1x′ = h1B1P

2h1 = e0Q = Ph21B1

(11) e0Pu = rPj = iz = Pe0u

20 (1) d30Pd0 = d0e0P

2e0 = d0gP 2d0 = d0Pe20 = e2

0P2d0 = e0Pd0Pe0 =

gPd20

22 (1) h1P3u = Ph1P

2u = P 2h1Q = P 2h1Pu = uP 3h1

23 (1) d0P3j = iP 3e0 = jP 3d0 = Pd0P

2j = Pe0P2i = PjP 2d0

24 (1) h0d0P3j = h0iP

3e0 = h0jP3d0 = h0Pd0P

2j = h0Pe0P2i =

h0PjP 2d0 = h2iP3d0 = h2Pd0P

2i = d0Ph2P2i = d0iP

3h2 =f0P

4d0 = Ph2iP2d0 = iPd0P

2h2 = kP 4h2

25 (1) h20d0P

3j = h20iP

3e0 = h20jP

3d0 = h20Pd0P

2j = h20Pe0P

2i =h2

0PjP 2d0 = h0h2iP3d0 = h0h2Pd0P

2i = h0d0Ph2P2i =

h0d0iP3h2 = h0f0P

4d0 = h0Ph2iP2d0 = h0iPd0P

2h2 =h0kP 4h2 = h1d0P

4e0 = h1e0P4d0 = h1Pd0P

3e0 = h1Pe0P3d0 =

h1P2d0P

2e0 = h22P

4j = h2Ph2P3j = h2jP

4h2 = h2P2h2P

2j =h2PjP 3h2 = d0e0P

4h1 = d0Ph1P3e0 = d0Pe0P

3h1 =d0P

2h1P2e0 = e0Ph1P

3d0 = e0Pd0P3h1 = e0P

2h1P2d0 =

Ph1Pd0P2e0 = Ph1Pe0P

2d0 = Ph22P

2j = Ph2jP3h2 =

Ph2P2h2Pj = jP 2h2

2 = Pd0Pe0P2h1

30 (1) h21P

6d0 = h1d0P6h1 = h1Ph1P

5d0 = h1Pd0P5h1 =

h1P2h1P

4d0 = h1P2d0P

4h1 = h1P3h1P

3d0 = h3P7h1 =

c0P6c0 = d0Ph1P

5h1 = d0P2h1P

4h1 = d0P3h2

1 = Ph21P

4d0 =Ph1Pd0P

4h1 = Ph1P2h1P

3d0 = Ph1P2d0P

3h1 = Pc0P5c0 =

Pd0P2h1P

3h1 = P 2h21P

2d0 = P 2c0P4c0 = P 3c2

0

31 (1) P 7c0


Stem 653 (10) h2h

25

(01) h21h6

4 (1) h0h2h25

5 (1) h20h2h

25 = h3

1h25

6 (1) h2H1

7 (10) h2h5n = h4C

(01) h3D2

8 (1) h0h3D2

9 (10) h2x8,33

(01) h20h3D2 = h1h3Q2

(11) h2x8,32

10 (1) B23

11 (10) h1x10,32

(01) h0B23 = h2x10,27 = h2x10,28 = e0B2

12 (10) h5Pj

(01) h20B23 = h0h2x10,27 = h0h2x10,28 = h0e0B2 = h2

2B21 = h2d0B2

13 (10) gw = rm

(01) R2

14 (1) h0R2

15 (1) h20R2 = h1PQ1 = Ph1Q1 = Ph2R1

16 (1) d20e0g = d0e

30 = g2Pe0 = iv = ju

19 (1) d30i = d0e0Pj = d0jPe0 = d0kPd0 = e0iPe0 = e0jPd0 = giPd0 =

lP 2e0 = mP 2d0

22 (1) iP 2j = jP 2i

23 (1) h0iP2j = h0jP

2i = h21P

3u = h1Ph1P2u = h1P

2h1Q =h1P

2h1Pu = h1uP 3h1 = h2iP2i = Ph2

1Q = Ph21Pu =

Ph1P2h1u = rP 4h2 = qP 4h1 = i2P 2h2

28 (1) P 6e0

29 (1) h0P6e0 = h2P

6d0 = d0P6h2 = Ph2P

5d0 = Pd0P5h2 =

P 2h2P4d0 = P 2d0P

4h2 = P 3h2P3d0

30 (1) h20P

6e0 = h0h2P6d0 = h0d0P


5h2 =h0P

2h2P4d0 = h0P

2d0P4h2 = h0P

3h2P3d0

continued

46 ROBERT R. BRUNER


0P6e0 = h2

0h2P6d0 = h2

0d0P6h2 = h2

0Ph2P5d0 = h2

0Pd0P5h2 =

h20P

2h2P4d0 = h2

0P2d0P

4h2 = h20P

3h2P3d0 = h3

1P6d0 =

h21d0P

6h1 = h21Ph1P

5d0 = h21Pd0P

5h1 = h21P

2h1P4d0 =

h21P

2d0P4h1 = h2

1P3h1P

3d0 = h1h3P7h1 = h1c0P

6c0 =h1d0Ph1P

5h1 = h1d0P2h1P

4h1 = h1d0P3h2

1 = h1Ph21P

4d0 =h1Ph1Pd0P

4h1 = h1Ph1P2h1P

3d0 = h1Ph1P2d0P

3h1 =h1Pc0P

5c0 = h1Pd0P2h1P

3h1 = h1P2h2

1P2d0 = h1P

2c0P4c0 =

h1P3c2

0 = h22P

7h2 = h2Ph2P6h2 = h2P

2h2P5h2 =

h2P3h2P

4h2 = h3Ph1P6h1 = h3P

2h1P5h1 = h3P

3h1P4h1 =

c20P


5h1 = c0P2h1P

4c0 =c0P

2c0P4h1 = c0P

3h1P3c0 = d0Ph2

1P4h1 = d0Ph1P

2h1P3h1 =

d0P2h3

1 = Ph31P

3d0 = Ph21Pd0P

3h1 = Ph21P

2h1P2d0 =

Ph1Pc0P4c0 = Ph1Pd0P

2h21 = Ph1P

2c0P3c0 = Ph2

2P5h2 =

Ph2P2h2P

4h2 = Ph2P3h2

2 = Pc20P

4h1 = Pc0P2h1P

3c0 =Pc0P

2c0P3h1 = P 2h1P

2c20 = P 2h2

2P3h2

32 (1) h1P7c0 = c0P


6h1 = P 2h1P5c0 =

P 2c0P5h1 = P 3h1P

4c0 = P 3c0P4h1

33 (1) P 8h1


Stem 662 (1) h2h6

3 (1) h0h2h6

4 (1) h20h2h6 = h3

1h6

6 (1) r1

7 (10) x7,40

(01) h0r1

8 (1) h0x7,40 = h2x7,34

10 (10) B5

(01) PD2

11 (01) h0PD2

(11) h0B5 = h1B23 = h22B4 = f0B2 = gB1

12 (10) gN = nm = rt

(01) h20PD2 = h2

1x10,32 = Ph1Q2

15 (1) d0e0m = d0gl = e20l = e0gk = g2j

18 (1) d0rPd0 = d0ik = d0j2 = e0ij = gi2 = lP j = Pe0z

21 (1) P 3v

24 (1) d20P

3d0 = d0Pd0P2d0 = e0P

4e0 = gP 4d0 = Pd30 = Pe0P

3e0 =P 2e2

0

25 (1) h0d20P

3d0 = h0d0Pd0P2d0 = h0e0P

4e0 = h0gP 4d0 = h0Pd30 =

h0Pe0P3e0 = h0P

2e20 = h2d0P

4e0 = h2e0P4d0 = h2Pd0P

3e0 =h2Pe0P

3d0 = h2P2d0P

2e0 = d0e0P4h2 = d0Ph2P

3e0 =d0Pe0P

3h2 = d0P2h2P

2e0 = e0Ph2P3d0 = e0Pd0P

3h2 =e0P

2h2P2d0 = Ph2Pd0P

2e0 = Ph2Pe0P2d0 = Pd0Pe0P

2h2

26 (1) h20d

20P

3d0 = h20d0Pd0P

2d0 = h20e0P

4e0 = h20gP 4d0 = h2

0Pd30 =

h20Pe0P

3e0 = h20P

2e20 = h0h2d0P

4e0 = h0h2e0P4d0 =

h0h2Pd0P3e0 = h0h2Pe0P

3d0 = h0h2P2d0P

2e0 =h0d0e0P


3h2 = h0d0P2h2P

2e0 =h0e0Ph2P

3d0 = h0e0Pd0P3h2 = h0e0P

2h2P2d0 =

h0Ph2Pd0P2e0 = h0Ph2Pe0P

2d0 = h0Pd0Pe0P2h2 =

h22d0P

4d0 = h22Pd0P

3d0 = h22P

2d20 = h2d

20P

4h2 =h2d0Ph2P

3d0 = h2d0Pd0P3h2 = h2d0P

2h2P2d0 = h2gP 5h2 =

h2Ph2Pd0P2d0 = h2Pd2

0P2h2 = h4P

6h2 = c0P4j =

d20Ph2P

3h2 = d20P

2h22 = d0Ph2

2P2d0 = d0Ph2Pd0P

2h2 =gPh2P

4h2 = gP 2h2P3h2 = Ph2

2Pd20 = Pc0P

3j = jP 4c0 =P 2c0P

2j = PjP 3c0

27 (1) P 5j

28 (1) h0P5j = Ph2P

4i = iP 5h2 = P 3h2P2i

29 (1) h20P


5h2 = h0P3h2P

2i = h1P6e0 =

e0P6h1 = Ph1P

5e0 = Pe0P5h1 = P 2h1P

4e0 = P 2e0P4h1 =

P 3h1P3e0

34 (1) h1P8h1 = Ph1P

7h1 = P 2h1P6h1 = P 3h1P

5h1 = P 4h21

48 ROBERT R. BRUNER

Stem 675 (10) n1

(01) Q3

6 (01) h0Q3

(11) h0n1 = h22D3 = h4D1

7 (1) h20Q3 = h2A

′′

8 (1) h1x7,40 = h22A

′ = h22A

9 (10) x9,39

(01) x9,40

10 (1) h0x9,40 = h3B4

11 (10) x11,35

(01) h20x9,40 = h0h3B4 = g2i = xr

12 (1) h30x9,40 = h2

0h3B4 = h0g2i = h0xr = h0x11,35 = h23x

′

14 (10) e0gr = lm

(01) d0x′

15 (1) h0d0x′ = h2PQ1 = Ph2Q1

16 (1) h20d0x

′ = h0h2PQ1 = h0Ph2Q1 = h2Ph2x′ = B2P

2h2

17 (1) d20u = d0ri = e0Pv = gPu = jz = Pd0w = Pe0v

20 (1) d30Pe0 = d2

0e0Pd0 = d0gP 2e0 = e20P

2e0 = e0gP 2d0 = e0Pe20 =

gPd0Pe0

23 (1) d20P

2i = d0iP2d0 = e0P

3j = iPd20 = jP 3e0 = kP 3d0 = Pe0P

2j =PjP 2e0

24 (1) h0d20P

2i = h0d0iP2d0 = h0e0P

3j = h0iPd20 = h0jP

3e0 =h0kP 3d0 = h0Pe0P

2j = h0PjP 2e0 = h2d0P3j = h2iP

3e0 =h2jP

3d0 = h2Pd0P2j = h2Pe0P

2i = h2PjP 2d0 = d0Ph2P2j =

d0jP3h2 = d0P

2h2Pj = e0Ph2P2i = e0iP

3h2 = f0P4e0 =

Ph2iP2e0 = Ph2jP

2d0 = Ph2Pd0Pj = iPe0P2h2 = jPd0P

2h2 =lP 4h2

25 (1) h20d

20P

2i = h20d0iP

2d0 = h20e0P

3j = h20iPd2

0 = h20jP

3e0 =h2

0kP 3d0 = h20Pe0P

2j = h20PjP 2e0 = h0h2d0P

3j = h0h2iP3e0 =

h0h2jP3d0 = h0h2Pd0P

2j = h0h2Pe0P2i = h0h2PjP 2d0 =

h0d0Ph2P2j = h0d0jP

3h2 = h0d0P2h2Pj = h0e0Ph2P

2i =h0e0iP

3h2 = h0f0P4e0 = h0Ph2iP

2e0 = h0Ph2jP2d0 =

h0Ph2Pd0Pj = h0iPe0P2h2 = h0jPd0P

2h2 = h0lP4h2 =

h1d20P


4e0 = h1gP 4d0 = h1Pd30 =

h1Pe0P3e0 = h1P

2e20 = h2

2iP3d0 = h2

2Pd0P2i = h2d0Ph2P

2i =h2d0iP

3h2 = h2f0P4d0 = h2Ph2iP

2d0 = h2iPd0P2h2 =

h2kP 4h2 = d30P

3h1 = d20Ph1P

2d0 = d20Pd0P

2h1 = d0f0P4h2 =

d0gP 4h1 = d0Ph1Pd20 = d0Ph2iP

2h2 = e20P

4h1 = e0Ph1P3e0 =

e0Pe0P3h1 = e0P

2h1P2e0 = f0Ph2P

3d0 = f0Pd0P3h2 =

f0P2h2P

2d0 = gPh1P3d0 = gPd0P

3h1 = gP 2h1P2d0 =

Ph1Pe0P2e0 = Ph2

2iPd0 = Ph2kP 3h2 = kP 2h22 = Pe2

0P2h1

continued


Stem 67 continued33 (1) P 8h2

34 (1) h0P8h2

35 (1) h20P

8h2 = h21P

8h1 = h1Ph1P7h1 = h1P

2h1P6h1 =

h1P3h1P

5h1 = h1P4h2

1 = Ph21P

6h1 = Ph1P2h1P

5h1 =Ph1P

3h1P4h1 = P 2h2

1P4h1 = P 2h1P

3h21

Stem 684 (1) d2

5 (1) h0d2 = h3D3

6 (1) h1Q3

7 (10) h22H1 = h3A

(11) h3A′

8 (10) G21

(01) h0h3A′

9 (1) h0G21

10 (10) h1x9,39 = h22x8,32 = h2

2x8,33 = f0C = d1t = e1r

(01) h20G21

(11) h3X1

11 (10) h2B23 = gB2

(01) h30G21 = h0h3X1

(11) h4x′

12 (10) h0h4x′ = h5d0i

(01) h40G21 = h2

0h3X1 = h23R1 = ry

(11) h0h2B23 = h0gB2 = h22x10,27 = h2

2x10,28 = h2e0B2 = c0B4 =Ph2Q2

13 (10) P 2D1

(01) h50G21 = h3

0h3X1 = h20h4x

′ = h0h23R1 = h0h5d0i = h0ry =

h2h5Pj = h5Ph2j

14 (1) h0P2D1 = h2R2 = d0R1

15 (1) h20P

2D1 = h0h2R2 = h0d0R1 = h1d0x′ = Ph1B21 = B1Pd0

16 (1) d20g

2 = d0e20g = e4

0 = iw = jv = ku

19 (1) d30j = d2

0e0i = d0gPj = d0kPe0 = d0lPd0 = e20Pj = e0jPe0 =

e0kPd0 = giPe0 = gjPd0 = mP 2e0

22 (1) rP 3d0 = i2Pd0 = jP 2j = kP 2i = Pj2

28 (1) d0P5d0 = Pd0P

4d0 = P 2d0P3d0

29 (1) h0d0P5d0 = h0Pd0P

4d0 = h0P2d0P

3d0 = h2P6e0 = e0P

6h2 =Ph2P

5e0 = Pe0P5h2 = P 2h2P

4e0 = P 2e0P4h2 = P 3h2P

3e0

30 (1) h20d0P

5d0 = h20Pd0P

4d0 = h20P

2d0P3d0 = h0h2P

6e0 =h0e0P

6h2 = h0Ph2P5e0 = h0Pe0P

5h2 = h0P2h2P

4e0 =h0P

2e0P4h2 = h0P

3h2P3e0 = h2

2P6d0 = h2d0P

6h2 =h2Ph2P

5d0 = h2Pd0P5h2 = h2P

2h2P4d0 = h2P

2d0P4h2 =

h2P3h2P

3d0 = d0Ph2P5h2 = d0P

2h2P4h2 = d0P

3h22 =

Ph22P

4d0 = Ph2Pd0P4h2 = Ph2P

2h2P3d0 = Ph2P

2d0P3h2 =

Pd0P2h2P

3h2 = P 2h22P

2d0

50 ROBERT R. BRUNER

Stem 693 (1) h2

2h6

4 (1) p′

5 (1) h0p′

6 (10) h3H1

(01) h20p

′

7 (1) h30p

′ = h21Q3 = h4G = c0D3

8 (10) h2x7,40

(01) PD3

9 (10) h1G21

(01) h0h2x7,40 = h22x7,34 = h3x8,33 = c0A

′ = c0A = c1C = e0D1 = e1n

(11) h3x8,32

10 (1) PA

11 (10) h2B5 = h4R1

(01) h0PA = h2PD2 = Ph2D2

(11) h3x10,27

13 (1) W1

15 (1) d0gm = e20m = e0gl = g2k = ru

18 (10) x18,20

(01) d20z = d0rPe0 = d0il = d0jk = e0rPd0 = e0ik = e0j

2 = gij =mPj

19 (1) h0x18,20

20 (1) h20x18,20

21 (10) d0P2u = Pd0Pu = uP 2d0

(01) h30x18,20

(11) rP 2i = i3

22 (1) h40x18,20 = h0rP

2i = h0i3

23 (1) h50x18,20 = h2

0rP2i = h2

0i3 = h3iP

2i

24 (01) h60x18,20 = h3

0rP2i = h3

0i3 = h0h3iP

2i

(11) d20P

3e0 = d0e0P3d0 = d0Pd0P

2e0 = d0Pe0P2d0 = e0Pd0P

2d0 =gP 4e0 = Pd2

0Pe0

25 (1) h70x18,20 = h4

0rP2i = h4

0i3 = h2

0h3iP2i = h0d

20P

3e0 =h0d0e0P

3d0 = h0d0Pd0P2e0 = h0d0Pe0P

2d0 = h0e0Pd0P2d0 =

h0gP 4e0 = h0Pd20Pe0 = h2d

20P


4e0 =h2gP 4d0 = h2Pd3

0 = h2Pe0P3e0 = h2P

2e20 = h2

3P4i = h4P

5d0 =d30P

3h2 = d20Ph2P

2d0 = d20Pd0P

2h2 = d0gP 4h2 = d0Ph2Pd20 =

e20P

4h2 = e0Ph2P3e0 = e0Pe0P

3h2 = e0P2h2P

2e0 =gPh2P

3d0 = gPd0P3h2 = gP 2h2P

2d0 = Ph2Pe0P2e0 =

Pe20P

2h2

continued



0x18,20 = h50rP

2i = h50i

3 = h30h3iP

2i = h20d

20P

3e0 =h2

0d0e0P3d0 = h2

0d0Pd0P2e0 = h2

0d0Pe0P2d0 = h2

0e0Pd0P2d0 =

h20gP 4e0 = h2

0Pd20Pe0 = h0h2d

20P

3d0 = h0h2d0Pd0P2d0 =

h0h2e0P4e0 = h0h2gP 4d0 = h0h2Pd3

0 = h0h2Pe0P3e0 =

h0h2P2e2

0 = h0h23P

4i = h0h4P5d0 = h0d

30P

3h2 = h0d20Ph2P

2d0 =h0d

20Pd0P

2h2 = h0d0gP 4h2 = h0d0Ph2Pd20 = h0e

20P

4h2 =h0e0Ph2P

3e0 = h0e0Pe0P3h2 = h0e0P

2h2P2e0 = h0gPh2P

3d0 =h0gPd0P

3h2 = h0gP 2h2P2d0 = h0Ph2Pe0P

2e0 = h0Pe20P

2h2 =h2

2d0P4e0 = h2

2e0P4d0 = h2

2Pd0P3e0 = h2

2Pe0P3d0 =

h22P

2d0P2e0 = h2d0e0P


3h2 =h2d0P

2h2P2e0 = h2e0Ph2P

3d0 = h2e0Pd0P3h2 =

h2e0P2h2P

2d0 = h2Ph2Pd0P2e0 = h2Ph2Pe0P

2d0 =h2Pd0Pe0P

2h2 = c0iP3d0 = c0Pd0P

2i = d0e0Ph2P3h2 =

d0e0P2h2

2 = d0Ph22P

2e0 = d0Ph2Pe0P2h2 = d0Pc0P

2i =d0iP

3c0 = e0Ph22P

2d0 = e0Ph2Pd0P2h2 = Ph2

2Pd0Pe0 =Pc0iP

2d0 = iPd0P2c0 = kP 4c0

27 (1) d0P4i = iP 4d0 = P 2d0P

2i

28 (1) h0d0P4i = h0iP

4d0 = h0P2d0P

2i = h2P5j = Ph2P

4j = jP 5h2 =P 2h2P

3j = PjP 4h2 = P 3h2P2j

29 (1) h20d0P

4i = h20iP

4d0 = h20P

2d0P2i = h0h2P

5j = h0Ph2P4j =

h0jP5h2 = h0P

2h2P3j = h0PjP 4h2 = h0P

3h2P2j =

h1d0P5d0 = h1Pd0P

4d0 = h1P2d0P

3d0 = h2Ph2P4i =

h2iP5h2 = h2P

3h2P2i = d2

0P5h1 = d0Ph1P

4d0 = d0Pd0P4h1 =

d0P2h1P

3d0 = d0P2d0P

3h1 = f0P6h2 = gP 6h1 =

Ph1Pd0P3d0 = Ph1P

2d20 = Ph2iP

4h2 = Ph2P2h2P

2i =iP 2h2P

3h2 = Pd20P

3h1 = Pd0P2h1P

2d0

52 ROBERT R. BRUNER

Stem 702 (1) h3h6

3 (1) h0h3h6

4 (01) h20h3h6

(11) p1

5 (10) h1p′ = h2

5c0

(01) h30h3h6

6 (1) h2Q3

7 (10) h1h3H1

(01) h0h2Q3

8 (1) h3x7,33 = d1e1

9 (1) h1PD3 = D3Ph1

10 (1) h21G21 = h1h3x8,32 = h2x9,39 = gC = d1y = e1q

12 (1) h2x11,35

14 (010) d0Q1

(110) g2r = m2

(001) h1W1 = Ph1X1

(011) e0x′

15 (1) h0d0Q1 = h0e0x′ = h2d0x

′ = Ph2B21 = B2Pd0

16 (1) h20d0Q1 = h2

0e0x′ = h0h2d0x

′ = h0Ph2B21 = h0B2Pd0 =h2

2PQ1 = h2Ph2Q1

17 (10) R1

(01) d20v = d0e0u = d0rj = e0ri = gPv = kz = Pe0w

18 (1) h0R1

19 (10) h1x18,20 = P 2h1x′

(01) h20R1

20 (10) d50 = d2

0e0Pe0 = d20gPd0 = d0e

20Pd0 = e0gP 2e0 = g2P 2d0 =

gPe20 = iPu

(01) h30R1 = iQ

21 (1) h40R1 = h0iQ

22 (1) h50R1 = h2

0iQ

23 (01) h60R1 = h3

0iQ

(11) d20P

2j = d0e0P2i = d0iP

2e0 = d0jP2d0 = d0Pd0Pj = e0iP

2d0 =gP 3j = iPd0Pe0 = jPd2

0 = kP 3e0 = lP 3d0

24 (1) h70R1 = h4

0iQ = h0d20P

2j = h0d0e0P2i = h0d0iP

2e0 =h0d0jP

2d0 = h0d0Pd0Pj = h0e0iP2d0 = h0gP 3j = h0iPd0Pe0 =

h0jPd20 = h0kP 3e0 = h0lP

3d0 = h2d20P

2i = h2d0iP2d0 =

h2e0P3j = h2iPd2

0 = h2jP3e0 = h2kP 3d0 = h2Pe0P

2j =h2PjP 2e0 = d2

0iP2h2 = d0f0P

3d0 = d0Ph2iPd0 = d0kP 3h2 =e0Ph2P

2j = e0jP3h2 = e0P

2h2Pj = f0Pd0P2d0 = gPh2P

2i =giP 3h2 = Ph2jP

2e0 = Ph2kP 2d0 = Ph2Pe0Pj = jPe0P2h2 =

kPd0P2h2 = mP 4h2

continued



0R1 = h50iQ = h2

0d20P

2j = h20d0e0P

2i = h20d0iP

2e0 =h2

0d0jP2d0 = h2

0d0Pd0Pj = h20e0iP

2d0 = h20gP 3j = h2

0iPd0Pe0 =h2

0jPd20 = h2

0kP 3e0 = h20lP

3d0 = h0h2d20P

2i = h0h2d0iP2d0 =

h0h2e0P3j = h0h2iPd2

0 = h0h2jP3e0 = h0h2kP 3d0 =

h0h2Pe0P2j = h0h2PjP 2e0 = h0d

20iP

2h2 = h0d0f0P3d0 =

h0d0Ph2iPd0 = h0d0kP 3h2 = h0e0Ph2P2j = h0e0jP

3h2 =h0e0P

2h2Pj = h0f0Pd0P2d0 = h0gPh2P

2i = h0giP 3h2 =h0Ph2jP

2e0 = h0Ph2kP 2d0 = h0Ph2Pe0Pj = h0jPe0P2h2 =

h0kPd0P2h2 = h0mP 4h2 = h1d

20P

3e0 = h1d0e0P3d0 =

h1d0Pd0P2e0 = h1d0Pe0P

2d0 = h1e0Pd0P2d0 = h1gP 4e0 =

h1Pd20Pe0 = h2

2d0P3j = h2

2iP3e0 = h2

2jP3d0 = h2

2Pd0P2j =

h22Pe0P

2i = h22PjP 2d0 = h2d0Ph2P

2j = h2d0jP3h2 =

h2d0P2h2Pj = h2e0Ph2P

2i = h2e0iP3h2 = h2f0P

4e0 =h2Ph2iP

2e0 = h2Ph2jP2d0 = h2Ph2Pd0Pj = h2iPe0P

2h2 =h2jPd0P

2h2 = h2lP4h2 = c0iP

2i = d20e0P

3h1 = d20Ph1P

2e0 =d20Pe0P

2h1 = d0e0Ph1P2d0 = d0e0Pd0P

2h1 = d0Ph1Pd0Pe0 =d0Ph2

2Pj = d0Ph2jP2h2 = e0f0P

4h2 = e0gP 4h1 = e0Ph1Pd20 =

e0Ph2iP2h2 = f0Ph2P

3e0 = f0Pe0P3h2 = f0P

2h2P2e0 =

gPh1P3e0 = gPe0P

3h1 = gP 2h1P2e0 = Ph2

2iPe0 = Ph22jPd0 =

Ph2lP3h2 = rP 4c0 = i2P 2c0 = lP 2h2

2

32 (1) P 7d0

33 (1) h0P7d0

34 (1) h20P

7d0 = h2P8h2 = Ph2P

7h2 = P 2h2P6h2 = P 3h2P

5h2 = P 4h22

54 ROBERT R. BRUNER

Stem 713 (1) h1h3h6

4 (1) h6c0

5 (1) h1p1 = h2d2

6 (10) x6,47

(01) h21p

′ = h1h25c0

7 (1) h0x6,47 = h3A′′

9 (1) h2G21 = h23Q2

10 (1) h0h2G21 = h0h23Q2 = py

11 (1) h4Q1 = d0Q2

12 (10) x12,37

(01) h0h4Q1 = h0d0Q2 = h22B23 = h2h4x

′ = h2gB2 = h5d0j = h5e0i =Ph2B3

13 (100) g2n = tm

(010) x13,34

(001) x13,35

14 (10) h0x13,34

(01) h0x13,35 = f0x′ = Ph2B4 = iB2

(11) h2P2D1 = e0R1

15 (10) h20x13,34 = h2

1W1 = h1Ph1X1 = h3PQ1 = qu = GP 2h1

(01) h20x13,35 = h0f0x

′ = h0Ph2B4 = h0iB2 = h1e0x′ = Ph1x10,28 =

B1Pe0

(11) h0h2P2D1 = h0e0R1 = h1d0Q1 = h2

2R2 = h2d0R1 = Ph1x10,27

16 (1) d0e0g2 = e3

0g = rz = jw = kv = lu

19 (1) d30k = d2

0e0j = d20gi = d0e

20i = d0lP e0 = d0mPd0 = e0gPj =

e0kPe0 = e0lPd0 = gjPe0 = gkPd0

20 (1) h21x18,20 = h1P

2h1x′ = Ph2

1x′ = B1P

3h1

22 (1) d0iP j = rP 3e0 = i2Pe0 = ijPd0 = kP 2j = lP 2i = zP 2d0

25 (1) P 4u

28 (1) d0P5e0 = e0P


4d0 = P 2d0P3e0 =

P 2e0P3d0

29 (1) h0d0P5e0 = h0e0P


4d0 =h0P

2d0P3e0 = h0P

2e0P3d0 = h2d0P

5d0 = h2Pd0P4d0 =

h2P2d0P

3d0 = d20P


4h2 =d0P

2h2P3d0 = d0P

2d0P3h2 = gP 6h2 = Ph2Pd0P

3d0 =Ph2P

2d20 = Pd2

0P3h2 = Pd0P

2h2P2d0

continued



0d0P5e0 = h2

0e0P5d0 = h2

0Pd0P4e0 = h2

0Pe0P4d0 =

h20P

2d0P3e0 = h2

0P2e0P

3d0 = h0h2d0P5d0 = h0h2Pd0P

4d0 =h0h2P

2d0P3d0 = h0d

20P


4h2 =h0d0P

2h2P3d0 = h0d0P

2d0P3h2 = h0gP 6h2 = h0Ph2Pd0P

3d0 =h0Ph2P

2d20 = h0Pd2

0P3h2 = h0Pd0P

2h2P2d0 = h2

2P6e0 =

h2e0P6h2 = h2Ph2P

5e0 = h2Pe0P5h2 = h2P

2h2P4e0 =

h2P2e0P

4h2 = h2P3h2P

3e0 = e0Ph2P5h2 = e0P

2h2P4h2 =

e0P3h2

2 = Ph22P

4e0 = Ph2Pe0P4h2 = Ph2P

2h2P3e0 =

Ph2P2e0P

3h2 = Pc0P4i = iP 5c0 = Pe0P

2h2P3h2 = P 2h2

2P2e0 =

P 3c0P2i

31 (1) P 6i

32 (1) h0P6i

33 (01) h20P

6i

(11) h1P7d0 = d0P


6h1 = P 2h1P5d0 =

P 2d0P5h1 = P 3h1P

4d0 = P 3d0P4h1

34 (1) h30P

6i

35 (1) h40P

6i

36 (1) h50P

6i

56 ROBERT R. BRUNER

Stem 724 (1) h2

1h3h6 = h32h6

5 (1) h1h6c0

6 (1) h6Ph1

8 (10) h23D2

(11) h4Q2

9 (1) h0h23D2 = h0h4Q2 = h2

2x7,40 = gD1

10 (1) d0D2

11 (1) h0d0D2 = h2PA = Ph2A

12 (1) h20d0D2 = h0h2PA = h0Ph2A = h1h4Q1 = h1d0Q2 = h2

2B5 =h2

2PD2 = h2h4R1 = h2Ph2D2 = g2d1 = Ph1x7,33 = Ph1x7,34 = t2

13 (1) h1x12,37 = c0x10,32

15 (1) e0gm = g2l = rv

18 (10) P 2Q1

(01) d30r = d0e0z = d0im = d0jl = d0k

2 = e0rPe0 = e0il = e0jk =grPd0 = gik = gj2

19 (1) h0P2Q1 = h2x18,20 = P 2h2x

′

20 (1) h20P

2Q1 = h0h2x18,20 = h0P2h2x

′

21 (10) d0P2v = Pd0Pv = vP 2d0

(01) h30P

2Q1 = h20h2x18,20 = h2

0P2h2x

′ = h31x18,20 = h2

1P2h1x

′ =h1Ph2

1x′ = h1B1P

3h1 = Ph1B1P2h1 = Pe0Q

(11) e0P2u = rP 2j = i2j = Pe0Pu = uP 2e0

24 (1) d30P

2d0 = d20Pd2

0 = d0e0P3e0 = d0gP 3d0 = d0Pe0P

2e0 =e20P

3d0 = e0Pd0P2e0 = e0Pe0P

2d0 = gPd0P2d0 = Pd0Pe2

0

26 (1) h1P4u = Ph1P

3u = P 2h1P2u = uP 4h1 = P 3h1Q = P 3h1Pu

27 (1) d0P4j = e0P

4i = iP 4e0 = jP 4d0 = Pd0P3j = PjP 3d0 =

P 2d0P2j = P 2e0P

2i

28 (1) h0d0P4j = h0e0P

4i = h0iP4e0 = h0jP

4d0 = h0Pd0P3j =

h0PjP 3d0 = h0P2d0P

2j = h0P2e0P

2i = h2d0P4i = h2iP

4d0 =h2P

2d0P2i = d0iP

4h2 = d0P2h2P

2i = f0P5d0 = Ph2iP

3d0 =Ph2Pd0P

2i = iPd0P3h2 = iP 2h2P

2d0 = kP 5h2

continued



0d0P4j = h2

0e0P4i = h2

0iP4e0 = h2

0jP4d0 = h2

0Pd0P3j =

h20PjP 3d0 = h2

0P2d0P

2j = h20P

2e0P2i = h0h2d0P

4i =h0h2iP

4d0 = h0h2P2d0P

2i = h0d0iP4h2 = h0d0P

2h2P2i =

h0f0P5d0 = h0Ph2iP

3d0 = h0Ph2Pd0P2i = h0iPd0P

3h2 =h0iP

2h2P2d0 = h0kP 5h2 = h1d0P

5e0 = h1e0P5d0 =

h1Pd0P4e0 = h1Pe0P

4d0 = h1P2d0P

3e0 = h1P2e0P

3d0 =h2

2P5j = h2Ph2P

4j = h2jP5h2 = h2P

2h2P3j = h2PjP 4h2 =

h2P3h2P

2j = d0e0P5h1 = d0Ph1P

4e0 = d0Pe0P4h1 =

d0P2h1P

3e0 = d0P2e0P


4h1 =e0P

2h1P3d0 = e0P

2d0P3h1 = Ph1Pd0P

3e0 = Ph1Pe0P3d0 =

Ph1P2d0P

2e0 = Ph22P

3j = Ph2jP4h2 = Ph2P

2h2P2j =

Ph2PjP 3h2 = jP 2h2P3h2 = Pd0Pe0P

3h1 = Pd0P2h1P

2e0 =Pe0P

2h1P2d0 = P 2h2

2Pj

34 (1) h21P

7d0 = h1d0P7h1 = h1Ph1P

6d0 = h1Pd0P6h1 =

h1P2h1P

5d0 = h1P2d0P

5h1 = h1P3h1P

4d0 = h1P3d0P

4h1 =h3P

8h1 = c0P7c0 = d0Ph1P

6h1 = d0P2h1P

5h1 = d0P3h1P

4h1 =Ph2

1P5d0 = Ph1Pd0P

5h1 = Ph1P2h1P

4d0 = Ph1P2d0P

4h1 =Ph1P

3h1P3d0 = Pc0P

6c0 = Pd0P2h1P

4h1 = Pd0P3h2

1 =P 2h2

1P3d0 = P 2h1P

2d0P3h1 = P 2c0P

5c0 = P 3c0P4c0

35 (1) P 8c0

58 ROBERT R. BRUNER

Stem 737 (100) h4D2

(010) h22Q3 = h3r1 = h2

5Ph2

(001) h1h6Ph1

8 (1) h0h4D2

9 (1) h20h4D2 = h1h4Q2

14 (1) d0B21 = e0Q1 = gx′

15 (1) h0d0B21 = h0e0Q1 = h0gx′ = h2d0Q1 = h2e0x′ = Ph2x10,27 =

Ph2x10,28 = B2Pe0

16 (1) h20d0B21 = h2

0e0Q1 = h20gx′ = h0h2d0Q1 = h0h2e0x

′ =h0Ph2x10,27 = h0Ph2x10,28 = h0B2Pe0 = h2

2d0x′ = h2Ph2B21 =

h2B2Pd0 = c0R2 = d0Ph2B2

17 (10) PR2

(01) d20w = d0e0v = d0gu = d0rk = e2

0u = e0rj = gri = lz

18 (1) h0PR2 = h2R1

19 (1) h20PR2 = h0h2R1 = h1P

2Q1 = Ph1PQ1 = P 2h1Q1 = P 2h2R1

20 (1) d40e0 = d2

0gPe0 = d0e20Pe0 = d0e0gPd0 = e3

0Pd0 = g2P 2e0 =iPv = jPu = uPj

23 (1) d20iPd0 = d0e0P

2j = d0gP 2i = d0jP2e0 = d0kP 2d0 = d0Pe0Pj =

e20P

2i = e0iP2e0 = e0jP

2d0 = e0Pd0Pj = giP 2d0 = iPe20 =

jPd0Pe0 = kPd20 = lP 3e0 = mP 3d0

26 (1) iP 3j = PjP 2i

27 (1) h0iP3j = h0PjP 2i = h2

1P4u = h1Ph1P

3u = h1P2h1P

2u =h1uP 4h1 = h1P

3h1Q = h1P3h1Pu = f0P

4i = Ph21P

2u =Ph1P

2h1Q = Ph1P2h1Pu = Ph1uP 3h1 = Ph2iP

2i = rP 5h2 =qP 5h1 = i2P 3h2 = P 2h2

1u

32 (1) P 7e0

33 (1) h0P7e0 = h2P

7d0 = d0P7h2 = Ph2P

6d0 = Pd0P6h2 =

P 2h2P5d0 = P 2d0P

5h2 = P 3h2P4d0 = P 3d0P

4h2

34 (1) h20P

7e0 = h0h2P7d0 = h0d0P


6h2 =h0P

2h2P5d0 = h0P

2d0P5h2 = h0P

3h2P4d0 = h0P

3d0P4h2

continued



0P7e0 = h2

0h2P7d0 = h2

0d0P7h2 = h2

0Ph2P6d0 = h2

0Pd0P6h2 =

h20P

2h2P5d0 = h2

0P2d0P

5h2 = h20P

3h2P4d0 = h2

0P3d0P

4h2 =h3

1P7d0 = h2

1d0P7h1 = h2

1Ph1P6d0 = h2

1Pd0P6h1 =

h21P

2h1P5d0 = h2

1P2d0P

5h1 = h21P

3h1P4d0 = h2

1P3d0P

4h1 =h1h3P

8h1 = h1c0P7c0 = h1d0Ph1P

6h1 = h1d0P2h1P

5h1 =h1d0P

3h1P4h1 = h1Ph2

1P5d0 = h1Ph1Pd0P

5h1 =h1Ph1P

2h1P4d0 = h1Ph1P

2d0P4h1 = h1Ph1P

3h1P3d0 =

h1Pc0P6c0 = h1Pd0P

2h1P4h1 = h1Pd0P

3h21 = h1P

2h21P

3d0 =h1P

2h1P2d0P

3h1 = h1P2c0P

5c0 = h1P3c0P

4c0 = h22P

8h2 =h2Ph2P

7h2 = h2P2h2P

6h2 = h2P3h2P

5h2 = h2P4h2

2 =h3Ph1P

7h1 = h3P2h1P

6h1 = h3P3h1P

5h1 = h3P4h2

1 =c20P


6h1 = c0P2h1P

5c0 =c0P

2c0P5h1 = c0P

3h1P4c0 = c0P

3c0P4h1 = d0Ph2

1P5h1 =

d0Ph1P2h1P

4h1 = d0Ph1P3h2

1 = d0P2h2

1P3h1 = Ph3

1P4d0 =

Ph21Pd0P

4h1 = Ph21P

2h1P3d0 = Ph2

1P2d0P

3h1 =Ph1Pc0P

5c0 = Ph1Pd0P2h1P

3h1 = Ph1P2h2

1P2d0 =

Ph1P2c0P

4c0 = Ph1P3c2

0 = Ph22P

6h2 = Ph2P2h2P

5h2 =Ph2P

3h2P4h2 = Pc2

0P5h1 = Pc0P

2h1P4c0 = Pc0P

2c0P4h1 =

Pc0P3h1P

3c0 = Pd0P2h3

1 = P 2h1P2c0P

3c0 = P 2h22P

4h2 =P 2h2P

3h22 = P 2c2

0P3h1

36 (1) h1P8c0 = c0P


7h1 = P 2h1P6c0 =

P 2c0P6h1 = P 3h1P

5c0 = P 3c0P5h1 = P 4h1P

4c0

37 (1) P 9h1

60 ROBERT R. BRUNER

Stem 746 (10) h3n1

(01) h6Ph2

7 (1) h0h6Ph2

8 (10) x8,51

(01) h20h6Ph2 = h2

1h6Ph1

9 (1) h0x8,51

10 (1) h20x8,51 = h3x9,40 = g2r = x2

11 (1) h30x8,51 = h0h3x9,40 = h0g2r = h0x

2 = h23B4 = h4B21 = d0B3 =

e0Q2

12 (1) h40x8,51 = h2

0h3x9,40 = h20g2r = h2

0x2 = h0h

23B4 = h0h4B21 =

h0d0B3 = h0e0Q2 = h2h4Q1 = h2d0Q2 = h3g2i = h3xr =h3x11,35 = h5d0k = h5e0j = h5gi = Ph2x7,33 = Ph2x7,34

13 (1) d0B4

14 (10) gR1

(01) h0d0B4 = h2x13,35 = f0Q1 = jB2

(11) h2x13,34

15 (1) h20d0B4 = h0h2x13,35 = h0f0Q1 = h0gR1 = h0jB2 = h1d0B21 =

h1e0Q1 = h1gx′ = h22P

2D1 = h2e0R1 = h2f0x′ = h2Ph2B4 =

h2iB2 = d20B1 = Ph1B23

16 (1) d0g3 = d0r

2 = e20g

2 = kw = lv = mu

19 (1) d30l = d2

0e0k = d20gj = d0e

20j = d0e0gi = d0mPe0 = e3

0i = e0lP e0 =e0mPd0 = g2Pj = gkPe0 = glPd0

22 (1) d20i

2 = d0rP2d0 = d0jP j = e0iP j = rPd2

0 = ijPe0 = ikPd0 =j2Pd0 = lP 2j = mP 2i = zP 2e0

25 (1) P 4v

28 (1) d20P

4d0 = d0Pd0P3d0 = d0P

2d20 = e0P

5e0 = gP 5d0 = Pd20P

2d0 =Pe0P

4e0 = P 2e0P3e0

29 (1) h0d20P

4d0 = h0d0Pd0P3d0 = h0d0P

2d20 = h0e0P

5e0 = h0gP 5d0 =h0Pd2

0P2d0 = h0Pe0P

4e0 = h0P2e0P

3e0 = h2d0P5e0 =

h2e0P5d0 = h2Pd0P

4e0 = h2Pe0P4d0 = h2P

2d0P3e0 =

h2P2e0P

3d0 = d0e0P5h2 = d0Ph2P

4e0 = d0Pe0P4h2 =

d0P2h2P

3e0 = d0P2e0P


4h2 =e0P

2h2P3d0 = e0P

2d0P3h2 = Ph2Pd0P

3e0 = Ph2Pe0P3d0 =

Ph2P2d0P

2e0 = Pd0Pe0P3h2 = Pd0P

2h2P2e0 = Pe0P

2h2P2d0

continued



0d20P

4d0 = h20d0Pd0P

3d0 = h20d0P

2d20 = h2

0e0P5e0 = h2

0gP 5d0 =h2

0Pd20P

2d0 = h20Pe0P

4e0 = h20P

2e0P3e0 = h0h2d0P

5e0 =h0h2e0P

5d0 = h0h2Pd0P4e0 = h0h2Pe0P

4d0 = h0h2P2d0P

3e0 =h0h2P

2e0P3d0 = h0d0e0P


4h2 =h0d0P

2h2P3e0 = h0d0P

2e0P3h2 = h0e0Ph2P

4d0 =h0e0Pd0P

4h2 = h0e0P2h2P

3d0 = h0e0P2d0P

3h2 =h0Ph2Pd0P

3e0 = h0Ph2Pe0P3d0 = h0Ph2P

2d0P2e0 =

h0Pd0Pe0P3h2 = h0Pd0P

2h2P2e0 = h0Pe0P

2h2P2d0 =

h22d0P

5d0 = h22Pd0P

4d0 = h22P

2d0P3d0 = h2d

20P

5h2 =h2d0Ph2P


2h2P3d0 =

h2d0P2d0P

3h2 = h2gP 6h2 = h2Ph2Pd0P3d0 = h2Ph2P

2d20 =

h2Pd20P

3h2 = h2Pd0P2h2P

2d0 = h4P7h2 = c0P

5j =d20Ph2P

4h2 = d20P

2h2P3h2 = d0Ph2

2P3d0 = d0Ph2Pd0P

3h2 =d0Ph2P

2h2P2d0 = d0Pd0P

2h22 = gPh2P

5h2 = gP 2h2P4h2 =

gP 3h22 = Ph2

2Pd0P2d0 = Ph2Pd2

0P2h2 = Pc0P

4j = jP 5c0 =P 2c0P

3j = PjP 4c0 = P 3c0P2j

31 (1) P 6j

32 (1) h0P6j = h2P

6i = iP 6h2 = P 2h2P4i = P 2iP 4h2

33 (1) h20P

6j = h0h2P6i = h0iP

6h2 = h0P2h2P

4i = h0P2iP 4h2 =

h1P7e0 = e0P


6h1 = P 2h1P5e0 =

P 2e0P5h1 = P 3h1P

4e0 = P 3e0P4h1

38 (1) h1P9h1 = Ph1P

8h1 = P 2h1P7h1 = P 3h1P

6h1 = P 4h1P5h1

62 ROBERT R. BRUNER

Stem 755 (1) h3d2 = h5g2

6 (1) h0h3d2 = h0h5g2 = h23D3

7 (1) x7,53

8 (01) h0x7,53 = h23A

′

(11) h4B3 = c0Q3 = d0D3

9 (01) h20x7,53 = h0h

23A

′ = h1x8,51 = e1x = g2n

(11) h3G21

10 (1) h0h3G21 = d0A = e0D2

11 (1) h20h3G21 = h0d0A = h0e0D2 = h2d0D2 = h2

3X1 = f0Q2 =Ph2A

′′ = xy

15 (1) g2m = rw

18 (10) Pd0x′

(01) d20e0r = d0gz = d0jm = d0kl = e2

0z = e0im = e0jl = e0k2 =

grPe0 = gil = gjk

19 (1) h0Pd0x′ = h2P

2Q1 = Ph2PQ1 = P 2h2Q1

20 (1) h20Pd0x

′ = h0h2P2Q1 = h0Ph2PQ1 = h0P

2h2Q1 = h22x18,20 =

h2P2h2x

′ = Ph22x

′ = B2P3h2

21 (1) d20Pu = d0Pd0u = e0P

2v = gP 2u = riPd0 = i2k = ij2 =Pe0Pv = vP 2e0 = wP 2d0 = zPj

24 (1) d30P

2e0 = d20e0P

2d0 = d20Pd0Pe0 = d0e0Pd2

0 = d0gP 3e0 =e20P

3e0 = e0gP 3d0 = e0Pe0P2e0 = gPd0P

2e0 = gPe0P2d0 = Pe3

0

27 (1) d0iP3d0 = d0Pd0P

2i = e0P4j = gP 4i = iPd0P

2d0 = jP 4e0 =kP 4d0 = Pe0P

3j = PjP 3e0 = P 2e0P2j

28 (1) h0d0iP3d0 = h0d0Pd0P

2i = h0e0P4j = h0gP 4i = h0iPd0P

2d0 =h0jP

4e0 = h0kP 4d0 = h0Pe0P3j = h0PjP 3e0 = h0P

2e0P2j =

h2d0P4j = h2e0P

4i = h2iP4e0 = h2jP

4d0 = h2Pd0P3j =

h2PjP 3d0 = h2P2d0P

2j = h2P2e0P

2i = d0Ph2P3j = d0jP

4h2 =d0P

2h2P2j = d0PjP 3h2 = e0iP

4h2 = e0P2h2P

2i = f0P5e0 =

Ph2iP3e0 = Ph2jP

3d0 = Ph2Pd0P2j = Ph2Pe0P

2i =Ph2PjP 2d0 = iPe0P

3h2 = iP 2h2P2e0 = jPd0P

3h2 =jP 2h2P

2d0 = lP 5h2 = Pd0P2h2Pj

continued



0d0iP3d0 = h2

0d0Pd0P2i = h2

0e0P4j = h2

0gP 4i =h2

0iPd0P2d0 = h2

0jP4e0 = h2

0kP 4d0 = h20Pe0P

3j = h20PjP 3e0 =

h20P

2e0P2j = h0h2d0P

4j = h0h2e0P4i = h0h2iP

4e0 =h0h2jP

4d0 = h0h2Pd0P3j = h0h2PjP 3d0 = h0h2P

2d0P2j =

h0h2P2e0P

2i = h0d0Ph2P3j = h0d0jP

4h2 = h0d0P2h2P

2j =h0d0PjP 3h2 = h0e0iP

4h2 = h0e0P2h2P

2i = h0f0P5e0 =

h0Ph2iP3e0 = h0Ph2jP

3d0 = h0Ph2Pd0P2j = h0Ph2Pe0P

2i =h0Ph2PjP 2d0 = h0iPe0P

3h2 = h0iP2h2P

2e0 = h0jPd0P3h2 =

h0jP2h2P

2d0 = h0lP5h2 = h0Pd0P

2h2Pj = h1d20P

4d0 =h1d0Pd0P

3d0 = h1d0P2d2

0 = h1e0P5e0 = h1gP 5d0 =

h1Pd20P

2d0 = h1Pe0P4e0 = h1P

2e0P3e0 = h2

2d0P4i = h2

2iP4d0 =

h22P

2d0P2i = h2d0iP

4h2 = h2d0P2h2P

2i = h2f0P5d0 =

h2Ph2iP3d0 = h2Ph2Pd0P

2i = h2iPd0P3h2 = h2iP

2h2P2d0 =

h2kP 5h2 = d30P

4h1 = d20Ph1P

3d0 = d20Pd0P

3h1 = d20P

2h1P2d0 =

d0f0P5h2 = d0gP 5h1 = d0Ph1Pd0P

2d0 = d0Ph22P

2i =d0Ph2iP

3h2 = d0iP2h2

2 = d0Pd20P

2h1 = e20P

5h1 = e0Ph1P4e0 =

e0Pe0P4h1 = e0P

2h1P3e0 = e0P

2e0P3h1 = f0Ph2P

4d0 =f0Pd0P

4h2 = f0P2h2P

3d0 = f0P2d0P

3h2 = gPh1P4d0 =

gPd0P4h1 = gP 2h1P

3d0 = gP 2d0P3h1 = Ph1Pd3

0 =Ph1Pe0P

3e0 = Ph1P2e2

0 = Ph22iP

2d0 = Ph2iPd0P2h2 =

Ph2kP 4h2 = kP 2h2P3h2 = Pe2

0P3h1 = Pe0P

2h1P2e0

37 (1) P 9h2

38 (1) h0P9h2

39 (1) h20P

9h2 = h21P

9h1 = h1Ph1P8h1 = h1P

2h1P7h1 =

h1P3h1P

6h1 = h1P4h1P

5h1 = Ph21P

7h1 = Ph1P2h1P

6h1 =Ph1P

3h1P5h1 = Ph1P

4h21 = P 2h2

1P5h1 = P 2h1P

3h1P4h1 =

P 3h31

64 ROBERT R. BRUNER

Stem 765 (1) h4D3

6 (1) x6,53

7 (10) h23H1 = h4A

′

(01) h0x6,53

(11) h4A

8 (10) h1x7,53 = d1g2 = e21

(01) h20x6,53 = h0h4A = h2h4D2

9 (10) x9,51

(01) h30x6,53 = h2

0h4A = h0h2h4D2 = h1h4B3 = h1c0Q3 = h1d0D3 =h3PD3 = h2

4B1

10 (1) h0x9,51 = h1h3G21 = h23x8,32 = c1Q2 = f0D2 = e1y = g2q =

Ph1Q3

14 (01) d0x10,27 = d0x10,28 = e0B21 = gQ1

(11) g2t = nw = rN

15 (1) h0d0x10,27 = h0d0x10,28 = h0e0B21 = h0gQ1 = h2d0B21 =h2e0Q1 = h2gx′ = d2

0B2 = Ph2B23

16 (1) x16,32

17 (010) d0e0w = d0gv = d0rl = e20v = e0gu = e0rk = grj = mz

(110) ix′

(001) h0x16,32

18 (10) h0ix′

(01) h20x16,32

(11) h2PR2 = Ph2R2 = Pd0R1

19 (10) h20ix

′

(01) h30x16,32 = h3x18,20

(11) h0h2PR2 = h0Ph2R2 = h0Pd0R1 = h1Pd0x′ = h2

2R1 =d0Ph1x

′ = B1P2d0 = P 2h1B21

20 (10) d40g = d3

0e20 = d0e0gPe0 = d0g

2Pd0 = d0iu = e30Pe0 = e2

0gPd0 =jPv = kPu = vPj

(01) h40x16,32 = h3

0ix′ = h0h3x18,20 = xP 2i

(11) ri2

21 (1) h50x16,32 = h4

0ix′ = h2

0h3x18,20 = h0xP 2i = h0ri2

22 (1) h60x16,32 = h5

0ix′ = h3

0h3x18,20 = h20xP 2i = h2

0ri2 = h3rP

2i = h3i3

23 (1) d30Pj = d2

0iPe0 = d20jPd0 = d0e0iPd0 = d0gP 2j = d0kP 2e0 =

d0lP2d0 = e2

0P2j = e0gP 2i = e0jP

2e0 = e0kP 2d0 = e0Pe0Pj =giP 2e0 = gjP 2d0 = gPd0Pj = jPe2

0 = kPd0Pe0 = lPd20 =

mP 3e0

26 (1) d0iP2i = rP 4d0 = i2P 2d0 = jP 3j = PjP 2j

continued



6d0 = Pd0P5d0 = P 2d0P

4d0 = P 3d20

33 (1) h0d0P6d0 = h0Pd0P

5d0 = h0P2d0P

4d0 = h0P3d2

0 = h2P7e0 =

e0P7h2 = Ph2P

6e0 = Pe0P6h2 = P 2h2P

5e0 = P 2e0P5h2 =

P 3h2P4e0 = P 3e0P

4h2

34 (1) h20d0P

6d0 = h20Pd0P

5d0 = h20P

2d0P4d0 = h2

0P3d2

0 = h0h2P7e0 =

h0e0P7h2 = h0Ph2P

6e0 = h0Pe0P6h2 = h0P

2h2P5e0 =

h0P2e0P

5h2 = h0P3h2P

4e0 = h0P3e0P

4h2 = h22P

7d0 =h2d0P


6h2 = h2P2h2P

5d0 =h2P

2d0P5h2 = h2P

3h2P4d0 = h2P

3d0P4h2 = d0Ph2P

6h2 =d0P

2h2P5h2 = d0P

3h2P4h2 = Ph2

2P5d0 = Ph2Pd0P

5h2 =Ph2P

2h2P4d0 = Ph2P

2d0P4h2 = Ph2P

3h2P3d0 =

Pd0P2h2P

4h2 = Pd0P3h2

2 = P 2h22P

3d0 = P 2h2P2d0P

3h2

66 ROBERT R. BRUNER

Stem 773 (1) h2

3h6

4 (1) h0h23h6

5 (1) h6d0

6 (10) h1h4D3

(01) h0h6d0

7 (0100) x7,57

(0010) h1x6,53

(1010) m1

(0001) h20h6d0 = h2h6Ph2

8 (100) x8,57

(001) h0x7,57

(011) h0m1 = pg2

9 (01) h20x7,57

(11) h20m1 = h0pg2 = h2

1x7,53 = h1d1g2 = h1e21 = h2x8,51 = h2

3x7,33 =h3d1e1 = h4x8,33 = h5N = f1x

10 (1) h30x7,57

11 (10) gQ2

(01) h40x7,57 = h4x10,27

12 (10) P 2D3

(01) h50x7,57 = h0h4x10,27

13 (10) e0B4

(01) h60x7,57 = h2

0h4x10,27

14 (10) h0e0B4 = h2d0B4 = f0B21 = kB2

(01) h70x7,57 = h3

0h4x10,27

15 (1) h20e0B4 = h0h2d0B4 = h0f0B21 = h0kB2 = h1d0x10,27 =

h1d0x10,28 = h1e0B21 = h1gQ1 = h22x13,35 = h2f0Q1 = h2gR1 =

h2jB2 = d0e0B1 = Ph2B5 = Ph2PD2 = D2P2h2

16 (10) x16,33

(01) e0g3 = e0r

2 = lw = mv

17 (10) h1x16,32

(01) h0x16,33 = iR1

18 (1) h20x16,33 = h0iR1 = h3R1

19 (10) d30m = d2

0e0l = d20gk = d0e

20k = d0e0gj = d0g

2i = e30j = e2

0gi =e0mPe0 = glPe0 = gmPd0 = rPu

(01) h30x16,33 = h2

0iR1 = h0h3R1 = rQ

20 (1) h40x16,33 = h3

0iR1 = h20h3R1 = h0rQ

21 (1) h50x16,33 = h4

0iR1 = h30h3R1 = h2

0rQ = h3iQ = c0x18,20 = yP 2i =x′P 2c0

22 (1) d20ij = d0e0i

2 = d0rP2e0 = d0kPj = d0Pd0z = e0rP

2d0 =e0jP j = giP j = rPd0Pe0 = ikPe0 = ilPd0 = j2Pe0 = jkPd0 =mP 2j

continued



3u = Pd0P2u = uP 3d0 = P 2d0Pu

28 (1) d20P

4e0 = d0e0P4d0 = d0Pd0P

3e0 = d0Pe0P3d0 = d0P

2d0P2e0 =

e0Pd0P3d0 = e0P

2d20 = gP 5e0 = Pd2

0P2e0 = Pd0Pe0P

2d0

31 (1) iP 5d0 = Pd0P4i = P 2iP 3d0

32 (1) h0iP5d0 = h0Pd0P

4i = h0P2iP 3d0 = h2P

6j = Ph2P5j =

jP 6h2 = P 2h2P4j = PjP 5h2 = P 3h2P

3j = P 2jP 4h2

33 (1) h20iP

5d0 = h20Pd0P

4i = h20P

2iP 3d0 = h0h2P6j = h0Ph2P

5j =h0jP

6h2 = h0P2h2P

4j = h0PjP 5h2 = h0P3h2P

3j =h0P

2jP 4h2 = h1d0P6d0 = h1Pd0P

5d0 = h1P2d0P

4d0 =h1P

3d20 = h2

2P6i = h2iP

6h2 = h2P2h2P

4i = h2P2iP 4h2 =

d20P


5h1 = d0P2h1P

4d0 =d0P

2d0P4h1 = d0P

3h1P3d0 = f0P

7h2 = gP 7h1 =Ph1Pd0P

4d0 = Ph1P2d0P

3d0 = Ph22P

4i = Ph2iP5h2 =

Ph2P3h2P

2i = iP 2h2P4h2 = iP 3h2

2 = Pd20P

4h1 =Pd0P

2h1P3d0 = Pd0P

2d0P3h1 = P 2h1P

2d20 = P 2h2

2P2i

68 ROBERT R. BRUNER

Stem 782 (1) h4h6

3 (1) h0h4h6

4 (1) h20h4h6

5 (1) h30h4h6

6 (010) h1h6d0

(110) t1(001) h4

0h4h6

7 (10) h0t1 = h3x6,47

(01) h50h4h6

8 (100) h4x7,33 = h4x7,34

(001) h60h4h6

(011) h20t1 = h0h3x6,47 = h1m1 = h1x7,57 = h2

3A′′ = c2x = e0D3 = e1f1

(111) h21x6,53

9 (10) x9,55

(01) h70h4h6

10 (01) e0A′ = e0A = gD2

(11) P 2h25

11 (1) h0P2h2

5

12 (1) h20P

2h25

13 (10) h1P2D3 = e0X1 = f0B4 = D3P

2h1 = Ph1PD3 = rB2 = qB1

(01) h30P

2h25

18 (010) d20gr = d0e

20r = d0km = d0l

2 = e0gz = e0jm = e0kl = gim =gjl = gk2

(110) d0PQ1 = Pd0Q1

(001) h21x16,32 = Ph1W1 = P 2h1X1

(011) u2

(111) Pe0x′

19 (1) h0d0PQ1 = h0Pd0Q1 = h0Pe0x′ = h2Pd0x

′ = d0Ph2x′ =

B2P2d0 = P 2h2B21

20 (1) h20d0PQ1 = h2

0Pd0Q1 = h20Pe0x

′ = h0h2Pd0x′ = h0d0Ph2x

′ =h0B2P

2d0 = h0P2h2B21 = h2

2P2Q1 = h2Ph2PQ1 =

h2P2h2Q1 = c0R1 = Ph2

2Q1

21 (1) d20Pv = d0e0Pu = d0rPj = d0iz = d0Pd0v = d0Pe0u = e0Pd0u =

gP 2v = riPe0 = rjPd0 = i2l = ijk = j3 = wP 2e0

23 (1) Ph1x18,20 = x′P 3h1

24 (1) d40Pd0 = d2

0e0P2e0 = d2

0gP 2d0 = d20Pe2

0 = d0e20P

2d0 =d0e0Pd0Pe0 = d0gPd2

0 = e20Pd2

0 = e0gP 3e0 = g2P 3d0 =gPe0P

2e0 = iP 2u = uP 2i

27 (1) d20P

3j = d0iP3e0 = d0jP

3d0 = d0Pd0P2j = d0Pe0P

2i =d0PjP 2d0 = e0iP

3d0 = e0Pd0P2i = gP 4j = iPd0P

2e0 =iPe0P

2d0 = jPd0P2d0 = kP 4e0 = lP 4d0 = Pd2

0Pj

continued


Stem 78 continued30 (1) iP 4i = P 2i2

31 (1) h0iP4i = h0P

2i2

32 (1) h20iP

4i = h20P

2i2 = h3P6i

33 (1) h30iP

4i = h30P

2i2 = h0h3P6i

34 (1) h40iP

4i = h40P

2i2 = h20h3P

6i

35 (1) h50iP

4i = h50P

2i2 = h30h3P

6i = c0P7d0 = d0P

7c0 = Pc0P6d0 =

Pd0P6c0 = P 2c0P

5d0 = P 2d0P5c0 = P 3c0P

4d0 = P 3d0P4c0

36 (1) P 8d0

37 (1) h0P8d0

38 (1) h20P

8d0 = h2P9h2 = Ph2P

8h2 = P 2h2P7h2 = P 3h2P

6h2 =P 4h2P

5h2

70 ROBERT R. BRUNER

Stem 793 (1) h1h4h6

5 (1) x1

6 (1) h0x1 = h2h4D3 = h25e0

7 (01) h21h6d0 = h3h6Ph1 = h6c

20

(11) h2x6,53 = h4A′′

8 (10) h6Pc0

(01) h0h2x6,53 = h0h4A′′ = h2h4A

9 (1) h20h2x6,53 = h2

0h4A′′ = h0h2h4A = h3

1x6,53 = h1h4x7,33 =h1h4x7,34 = h2

2h4D2 = h33D2 = c0x6,47 = c2y = e0H1 = d2Ph2 =

p1Ph1

10 (1) h1x9,55 = h2x9,51 = f0A′ = f0A

11 (1) h1P2h2

5 = h4x10,32

13 (1) x13,42

14 (1) d0B23 = e0x10,27 = e0x10,28 = gB21

15 (1) h0d0B23 = h0e0x10,27 = h0e0x10,28 = h0gB21 = h2d0x10,27 =h2d0x10,28 = h2e0B21 = h2gQ1 = h4PQ1 = d0e0B2 = Q2Pd0

16 (1) x16,35

17 (010) d0gw = d0rm = e20w = e0gv = e0rl = g2u = grk

(110) d0R2

(001) h0x16,35 = h2x16,32

(111) iQ1 = jx′

18 (10) h0d0R2 = Ph2P2D1 = Pe0R1

(01) h20x16,35 = h0h2x16,32

(11) h0iQ1 = h0jx′ = h2ix

′ = P 2h2B4

19 (10) h20d0R2 = h0Ph2P

2D1 = h0Pe0R1 = h1d0PQ1 = h1Pd0Q1 =h2

2PR2 = h2Ph2R2 = h2Pd0R1 = d0Ph1Q1 = d0Ph2R1 =P 2h1x10,27

(01) h30x16,35 = h2

0h2x16,32 = h31x16,32 = h1Ph1W1 = h1P

2h1X1 =h1u

2 = h3P2Q1 = Ph2

1X1 = qQ = qPu = GP 3h1

(11) h20iQ1 = h2

0jx′ = h0h2ix

′ = h0P2h2B4 = h1Pe0x

′ = e0Ph1x′ =

B1P2e0 = P 2h1x10,28

20 (1) d30e0g = d2

0e30 = d0g

2Pe0 = d0iv = d0ju = e20gPe0 = e0g

2Pd0 =e0iu = rij = kPv = lPu = wPj

23 (1) d40i = d2

0e0Pj = d20jPe0 = d2

0kPd0 = d0e0iPe0 = d0e0jPd0 =d0giPd0 = d0lP

2e0 = d0mP 2d0 = e20iPd0 = e0gP 2j = e0kP 2e0 =

e0lP2d0 = g2P 2i = gjP 2e0 = gkP 2d0 = gPe0Pj = kPe2

0 =lPd0Pe0 = mPd2

0

24 (1) h1Ph1x18,20 = h1x′P 3h1 = Ph1P

2h1x′ = B1P

4h1

continued


Stem 79 continued26 (1) d0iP

2j = d0jP2i = e0iP

2i = rP 4e0 = i2P 2e0 = ijP 2d0 =iPd0Pj = kP 3j = zP 3d0

29 (01) P 5u

(11) P 4Q

30 (1) h0P4Q

31 (1) h20P

4Q

32 (01) h30P

4Q

(11) d0P6e0 = e0P


5d0 = P 2d0P4e0 =

P 2e0P4d0 = P 3d0P

3e0

33 (01) h40P

4Q

(11) h0d0P6e0 = h0e0P


5d0 =h0P

2d0P4e0 = h0P

2e0P4d0 = h0P

3d0P3e0 = h2d0P

6d0 =h2Pd0P

5d0 = h2P2d0P

4d0 = h2P3d2

0 = d20P

6h2 = d0Ph2P5d0 =

d0Pd0P5h2 = d0P

2h2P4d0 = d0P

2d0P4h2 = d0P

3h2P3d0 =

gP 7h2 = Ph2Pd0P4d0 = Ph2P

2d0P3d0 = Pd2

0P4h2 =

Pd0P2h2P

3d0 = Pd0P2d0P

3h2 = P 2h2P2d2

0

34 (01) h50P

4Q

(11) h20d0P

6e0 = h20e0P

6d0 = h20Pd0P

5e0 = h20Pe0P

5d0 =h2

0P2d0P

4e0 = h20P

2e0P4d0 = h2

0P3d0P

3e0 = h0h2d0P6d0 =

h0h2Pd0P5d0 = h0h2P

2d0P4d0 = h0h2P

3d20 = h0d

20P

6h2 =h0d0Ph2P


2h2P4d0 =

h0d0P2d0P

4h2 = h0d0P3h2P

3d0 = h0gP 7h2 = h0Ph2Pd0P4d0 =

h0Ph2P2d0P

3d0 = h0Pd20P

4h2 = h0Pd0P2h2P

3d0 =h0Pd0P

2d0P3h2 = h0P

2h2P2d2

0 = h22P

7e0 = h2e0P7h2 =

h2Ph2P6e0 = h2Pe0P

6h2 = h2P2h2P

5e0 = h2P2e0P

5h2 =h2P

3h2P4e0 = h2P

3e0P4h2 = c0P

6i = e0Ph2P6h2 =

e0P2h2P

5h2 = e0P3h2P

4h2 = Ph22P

5e0 = Ph2Pe0P5h2 =

Ph2P2h2P

4e0 = Ph2P2e0P

4h2 = Ph2P3h2P

3e0 = iP 6c0 =Pe0P

2h2P4h2 = Pe0P

3h22 = P 2h2

2P3e0 = P 2h2P

2e0P3h2 =

P 2c0P4i = P 2iP 4c0

35 (1) h60P

4Q

36 (1) h70P

4Q

37 (10) h1P8d0 = d0P


7h1 = P 2h1P6d0 =

P 2d0P6h1 = P 3h1P

5d0 = P 3d0P5h1 = P 4h1P

4d0

(01) h80P

4Q

38 (1) h90P

4Q

39 (1) h100 P 4Q

72 ROBERT R. BRUNER

Stem 804 (01) h2

1h4h6

(11) e2

5 (10) h6e0

(01) h0e2

6 (01) h20e2 = h1x1

(11) h0h6e0 = h2h6d0

7 (1) h20h6e0 = h0h2h6d0

8 (1) h30h6e0 = h2

0h2h6d0 = h31h6d0 = h1h3h6Ph1 = h1h6c

20 = h2

2h6Ph2

9 (10) h2x8,57 = c1A′ = c1A = f0H1

(01) h1h6Pc0 = h6c0Ph1

10 (1) h6P2h1

12 (1) x12,44

13 (1) gB4

14 (10) x14,42

(01) h0gB4 = h2e0B4 = h4R2 = d0B5 = d0PD2 = f0x10,27 =f0x10,28 = D2Pd0 = iQ2 = lB2

15 (1) h20gB4 = h0h2e0B4 = h0h4R2 = h0d0B5 = h0d0PD2 =

h0f0x10,27 = h0f0x10,28 = h0D2Pd0 = h0iQ2 = h0lB2 =h1d0B23 = h1e0x10,27 = h1e0x10,28 = h1gB21 = h2

2d0B4 =h2f0B21 = h2kB2 = d0f0B2 = d0gB1 = e2

0B1 = Ph2PA = AP 2h2

16 (10) g4 = gr2 = mw

(01) x16,37

17 (1) h0x16,37 = h1x16,35 = h2x16,33 = jR1

19 (1) d20e0m = d2

0gl = d0e20l = d0e0gk = d0g

2j = e30k = e2

0gj = e0g2i =

gmPe0 = rPv = uz

22 (10) P 3Q1

(01) d20rPd0 = d2

0ik = d20j

2 = d0e0ij = d0gi2 = d0lP j = d0Pe0z =e20i

2 = e0rP2e0 = e0kPj = e0Pd0z = grP 2d0 = gjPj = rPe2

0 =ilPe0 = imPd0 = jkPe0 = jlPd0 = k2Pd0

23 (1) h0P3Q1 = Ph2x18,20 = x′P 3h2

24 (1) h20P

3Q1 = h0Ph2x18,20 = h0x′P 3h2

25 (10) d0P3v = Pd0P

2v = vP 3d0 = P 2d0Pv

(01) h30P

3Q1 = h20Ph2x18,20 = h2

0x′P 3h2 = h2

1Ph1x18,20 =h2

1x′P 3h1 = h1Ph1P

2h1x′ = h1B1P

4h1 = Ph31x

′ = Ph1B1P3h1 =

B1P2h2

1 = P 2e0Q

(11) e0P3u = rP 3j = i2Pj = Pe0P

2u = uP 3e0 = zP 2i = P 2e0Pu

28 (1) d30P

3d0 = d20Pd0P

2d0 = d0e0P4e0 = d0gP 4d0 = d0Pd3

0 =d0Pe0P

3e0 = d0P2e2

0 = e20P

4d0 = e0Pd0P3e0 = e0Pe0P

3d0 =e0P

2d0P2e0 = gPd0P

3d0 = gP 2d20 = Pd0Pe0P

2e0 = Pe20P

2d0

continued


Stem 80 continued30 (1) h1P

4Q = h1P5u = Ph1P

4u = P 2h1P3u = uP 5h1 = P 3h1P

2u =QP 4h1 = PuP 4h1

31 (1) d0P5j = iP 5e0 = jP 5d0 = Pd0P

4j = Pe0P4i = PjP 4d0 =

P 2d0P3j = P 2iP 3e0 = P 2jP 3d0

32 (1) h0d0P5j = h0iP

5e0 = h0jP5d0 = h0Pd0P

4j = h0Pe0P4i =

h0PjP 4d0 = h0P2d0P

3j = h0P2iP 3e0 = h0P

2jP 3d0 =h2iP

5d0 = h2Pd0P4i = h2P

2iP 3d0 = d0Ph2P4i = d0iP

5h2 =d0P

3h2P2i = f0P

6d0 = Ph2iP4d0 = Ph2P

2d0P2i = iPd0P

4h2 =iP 2h2P

3d0 = iP 2d0P3h2 = kP 6h2 = Pd0P

2h2P2i

33 (1) h20d0P

5j = h20iP

5e0 = h20jP

5d0 = h20Pd0P

4j = h20Pe0P

4i =h2

0PjP 4d0 = h20P

2d0P3j = h2

0P2iP 3e0 = h2

0P2jP 3d0 =

h0h2iP5d0 = h0h2Pd0P

4i = h0h2P2iP 3d0 = h0d0Ph2P

4i =h0d0iP

5h2 = h0d0P3h2P

2i = h0f0P6d0 = h0Ph2iP

4d0 =h0Ph2P

2d0P2i = h0iPd0P

4h2 = h0iP2h2P

3d0 = h0iP2d0P

3h2 =h0kP 6h2 = h0Pd0P

2h2P2i = h1d0P

6e0 = h1e0P6d0 =

h1Pd0P5e0 = h1Pe0P

5d0 = h1P2d0P

4e0 = h1P2e0P

4d0 =h1P

3d0P3e0 = h2

2P6j = h2Ph2P

5j = h2jP6h2 = h2P

2h2P4j =

h2PjP 5h2 = h2P3h2P

3j = h2P2jP 4h2 = d0e0P

6h1 =d0Ph1P

5e0 = d0Pe0P5h1 = d0P

2h1P4e0 = d0P

2e0P4h1 =

d0P3h1P

3e0 = e0Ph1P5d0 = e0Pd0P

5h1 = e0P2h1P

4d0 =e0P

2d0P4h1 = e0P

3h1P3d0 = Ph1Pd0P

4e0 = Ph1Pe0P4d0 =

Ph1P2d0P

3e0 = Ph1P2e0P

3d0 = Ph22P

4j = Ph2jP5h2 =

Ph2P2h2P

3j = Ph2PjP 4h2 = Ph2P3h2P

2j = jP 2h2P4h2 =

jP 3h22 = Pd0Pe0P

4h1 = Pd0P2h1P

3e0 = Pd0P2e0P

3h1 =Pe0P

2h1P3d0 = Pe0P

2d0P3h1 = P 2h1P

2d0P2e0 = P 2h2

2P2j =

P 2h2PjP 3h2

38 (1) h21P

8d0 = h1d0P8h1 = h1Ph1P

7d0 = h1Pd0P7h1 =

h1P2h1P

6d0 = h1P2d0P

6h1 = h1P3h1P

5d0 = h1P3d0P

5h1 =h1P

4h1P4d0 = h3P

9h1 = c0P8c0 = d0Ph1P

7h1 = d0P2h1P

6h1 =d0P

3h1P5h1 = d0P

4h21 = Ph2

1P6d0 = Ph1Pd0P

6h1 =Ph1P

2h1P5d0 = Ph1P

2d0P5h1 = Ph1P

3h1P4d0 =

Ph1P3d0P

4h1 = Pc0P7c0 = Pd0P

2h1P5h1 = Pd0P

3h1P4h1 =

P 2h21P

4d0 = P 2h1P2d0P

4h1 = P 2h1P3h1P

3d0 = P 2c0P6c0 =

P 2d0P3h2

1 = P 3c0P5c0 = P 4c2

0

39 (1) P 9c0

74 ROBERT R. BRUNER

Stem 813 (1) h2h4h6

4 (1) h0h2h4h6

5 (10) h6f0

(01) h20h2h4h6 = h3

1h4h6

6 (1) h0h6f0 = h1h6e0

7 (1) h2t1 = h23n1 = h4r1 = c2f1

8 (1) h4x7,40 = c1H1 = gD3

9 (1) h3x8,51 = d0Q3 = g2x

10 (10) gA′

(01) h0h3x8,51 = h0d0Q3 = h0g2x = h2x9,55 = e0A′′

(11) gA

11 (10) h1h6P2h1 = h6Ph2

1

(01) h0gA′ = h0gA = h2e0A′ = h2e0A = h2gD2 = h4B5 = h4PD2 =

c1x8,32 = c1x8,33 = f0x7,34 = nC

12 (1) x12,45

13 (1) h0x12,45 = h1x12,44

15 (10) gnr = tw = mN

(01) h1x14,42

18 (01) d0e0gr = d0lm = e30r = e0km = e0l

2 = g2z = gjm = gkl = uv

(11) d20x

′ = e0PQ1 = Pd0B21 = Pe0Q1

19 (1) h0d20x

′ = h0e0PQ1 = h0Pd0B21 = h0Pe0Q1 = h2d0PQ1 =h2Pd0Q1 = h2Pe0x

′ = d0Ph2Q1 = e0Ph2x′ = B2P

2e0 =P 2h2x10,27 = P 2h2x10,28

20 (1) h20d

20x

′ = h20e0PQ1 = h2

0Pd0B21 = h20Pe0Q1 = h0h2d0PQ1 =

h0h2Pd0Q1 = h0h2Pe0x′ = h0d0Ph2Q1 = h0e0Ph2x

′ =h0B2P

2e0 = h0P2h2x10,27 = h0P

2h2x10,28 = h22Pd0x

′ =h2d0Ph2x

′ = h2B2P2d0 = h2P

2h2B21 = c0PR2 = d0B2P2h2 =

Ph22B21 = Ph2B2Pd0 = Pc0R2

21 (10) P 2R2

(01) d30u = d2

0ri = d0e0Pv = d0gPu = d0jz = d0Pd0w = d0Pe0v =e20Pu = e0rPj = e0iz = e0Pd0v = e0Pe0u = gPd0u = rjPe0 =

rkPd0 = i2m = ijl = ik2 = j2k

22 (1) h0P2R2 = Ph2R1

23 (1) h20P

2R2 = h0Ph2R1 = h1P3Q1 = Ph1P

2Q1 = P 2h1PQ1 =R1P

3h2 = Q1 P 3h1

24 (1) d40Pe0 = d3

0e0Pd0 = d20gP 2e0 = d0e

20P

2e0 = d0e0gP 2d0 =d0e0Pe2

0 = d0gPd0Pe0 = e30P

2d0 = e20Pd0Pe0 = e0gPd2

0 =g2P 3e0 = iP 2v = jP 2u = uP 2j = vP 2i = PjPu

continued


Stem 81 continued27 (1) d3

0P2i = d2

0iP2d0 = d0e0P

3j = d0iPd20 = d0jP

3e0 = d0kP 3d0 =d0Pe0P

2j = d0PjP 2e0 = e0iP3e0 = e0jP

3d0 = e0Pd0P2j =

e0Pe0P2i = e0PjP 2d0 = giP 3d0 = gPd0P

2i = iPe0P2e0 =

jPd0P2e0 = jPe0P

2d0 = kPd0P2d0 = lP 4e0 = mP 4d0 =

Pd0Pe0Pj

30 (1) iP 4j = jP 4i = P 2iP 2j

31 (1) h0iP4j = h0jP

4i = h0P2iP 2j = h2

1P4Q = h2

1P5u =

h1Ph1P4u = h1P

2h1P3u = h1uP 5h1 = h1P

3h1P2u =

h1QP 4h1 = h1PuP 4h1 = h2iP4i = h2P

2i2 = Ph21P

3u =Ph1P

2h1P2u = Ph1uP 4h1 = Ph1P

3h1Q = Ph1P3h1Pu =

rP 6h2 = qP 6h1 = i2P 4h2 = iP 2h2P2i = P 2h2

1Q = P 2h21Pu =

P 2h1uP 3h1

36 (1) P 8e0

37 (1) h0P8e0 = h2P

8d0 = d0P8h2 = Ph2P

7d0 = Pd0P7h2 =

P 2h2P6d0 = P 2d0P

6h2 = P 3h2P5d0 = P 3d0P

5h2 = P 4h2P4d0

38 (1) h20P

8e0 = h0h2P8d0 = h0d0P


7h2 =h0P

2h2P6d0 = h0P

2d0P6h2 = h0P

3h2P5d0 = h0P

3d0P5h2 =

h0P4h2P

4d0

continued

76 ROBERT R. BRUNER


0P8e0 = h2

0h2P8d0 = h2

0d0P8h2 = h2

0Ph2P7d0 = h2

0Pd0P7h2 =

h20P

2h2P6d0 = h2

0P2d0P

6h2 = h20P

3h2P5d0 = h2

0P3d0P

5h2 =h2

0P4h2P

4d0 = h31P

8d0 = h21d0P

8h1 = h21Ph1P

7d0 =h2

1Pd0P7h1 = h2

1P2h1P

6d0 = h21P

2d0P6h1 = h2

1P3h1P

5d0 =h2

1P3d0P

5h1 = h21P

4h1P4d0 = h1h3P

9h1 = h1c0P8c0 =

h1d0Ph1P7h1 = h1d0P

2h1P6h1 = h1d0P

3h1P5h1 = h1d0P

4h21 =

h1Ph21P

6d0 = h1Ph1Pd0P6h1 = h1Ph1P

2h1P5d0 =

h1Ph1P2d0P

5h1 = h1Ph1P3h1P

4d0 = h1Ph1P3d0P

4h1 =h1Pc0P

7c0 = h1Pd0P2h1P

5h1 = h1Pd0P3h1P

4h1 =h1P

2h21P

4d0 = h1P2h1P

2d0P4h1 = h1P

2h1P3h1P

3d0 =h1P

2c0P6c0 = h1P

2d0P3h2

1 = h1P3c0P

5c0 = h1P4c2

0 = h22P

9h2 =h2Ph2P

8h2 = h2P2h2P

7h2 = h2P3h2P

6h2 = h2P4h2P

5h2 =h3Ph1P

8h1 = h3P2h1P

7h1 = h3P3h1P

6h1 = h3P4h1P

5h1 =c20P


7h1 = c0P2h1P

6c0 =c0P

2c0P6h1 = c0P

3h1P5c0 = c0P

3c0P5h1 = c0P

4h1P4c0 =

d0Ph21P

6h1 = d0Ph1P2h1P

5h1 = d0Ph1P3h1P

4h1 =d0P

2h21P

4h1 = d0P2h1P

3h21 = Ph3

1P5d0 = Ph2

1Pd0P5h1 =

Ph21P

2h1P4d0 = Ph2

1P2d0P

4h1 = Ph21P

3h1P3d0 =

Ph1Pc0P6c0 = Ph1Pd0P

2h1P4h1 = Ph1Pd0P

3h21 =

Ph1P2h2

1P3d0 = Ph1P

2h1P2d0P

3h1 = Ph1P2c0P

5c0 =Ph1P

3c0P4c0 = Ph2

2P7h2 = Ph2P

2h2P6h2 = Ph2P

3h2P5h2 =

Ph2P4h2

2 = Pc20P

6h1 = Pc0P2h1P

5c0 = Pc0P2c0P

5h1 =Pc0P

3h1P4c0 = Pc0P

3c0P4h1 = Pd0P

2h21P

3h1 = P 2h31P

2d0 =P 2h1P

2c0P4c0 = P 2h1P

3c20 = P 2h2

2P5h2 = P 2h2P

3h2P4h2 =

P 2c20P

4h1 = P 2c0P3h1P

3c0 = P 3h32


Stem 824 (1) h6c1

6 (10) h4Q3

(01) h2x1 = h23d2 = h3h5g2 = h4n1 = h2

5g = c22

7 (10) h0h4Q3

(01) h0h2x1 = h0h23d2 = h0h3h5g2 = h0h4n1 = h0h

25g = h0c

22 =

h22h4D3 = h2h

25e0 = h3

3D3 = h24D1

8 (10) e1g2

(01) h20h4Q3 = h2

2x6,53 = h2h4A′′ = d0d2

(11) h3x7,53

9 (1) gH1

10 (1) h6P2h2

11 (1) h0h6P2h2

12 (10) gx8,33

(01) h20h6P

2h2 = h21h6P

2h1 = h1h6Ph21

14 (01) e0B23 = gx10,27 = gx10,28

(11) h2x13,42

16 (1) x16,38

17 (010) iB21 = jQ1 = kx′ = Pd0B4

(001) h0x16,38 = h2x16,35

(011) d0P2D1 = e0R2

(111) e0gw = e0rm = g2v = grl

18 (10) h0d0P2D1 = h0e0R2 = h2d0R2 = d2

0R1

(01) h20x16,38 = h0h2x16,35 = h2

2x16,32 = Ph2x13,34

(11) h0iB21 = h0jQ1 = h0kx′ = h0Pd0B4 = h2iQ1 = h2jx′ =

f0PQ1 = Ph2x13,35 = B2Pj

19 (1) h20d0P

2D1 = h20e0R2 = h2

0iB21 = h20jQ1 = h2

0kx′ = h20Pd0B4 =

h0h2d0R2 = h0h2iQ1 = h0h2jx′ = h0d

20R1 = h0f0PQ1 =

h0Ph2x13,35 = h0B2Pj = h1d20x

′ = h1e0PQ1 = h1Pd0B21 =h1Pe0Q1 = h2

2ix′ = h2Ph2P

2D1 = h2Pe0R1 = h2P2h2B4 =

d0Ph1B21 = d0B1Pd0 = e0Ph1Q1 = e0Ph2R1 = f0Ph2x′ =

gPh1x′ = Ph2

2B4 = Ph2iB2 = P 2h1B23

20 (1) d30g

2 = d20e

20g = d0e

40 = d0iw = d0jv = d0ku = e0g

2Pe0 = e0iv =e0ju = g3Pd0 = giu = r2Pd0 = rik = rj2 = lPv = mPu = z2

23 (1) d40j = d3

0e0i = d20gPj = d2

0kPe0 = d20lPd0 = d0e

20Pj = d0e0jPe0 =

d0e0kPd0 = d0giPe0 = d0gjPd0 = d0mP 2e0 = e20iPe0 =

e20jPd0 = e0giPd0 = e0lP

2e0 = e0mP 2d0 = g2P 2j = gkP 2e0 =glP 2d0 = lP e2

0 = mPd0Pe0

26 (1) d0rP3d0 = d0i

2Pd0 = d0jP2j = d0kP 2i = d0Pj2 = e0iP

2j =e0jP

2i = giP 2i = rPd0P2d0 = ijP 2e0 = ikP 2d0 = iPe0Pj =

j2P 2d0 = jPd0Pj = lP 3j = zP 3e0

continued

78 ROBERT R. BRUNER

Stem 82 continued29 (1) P 5v

32 (1) d20P

5d0 = d0Pd0P4d0 = d0P

2d0P3d0 = e0P

6e0 = gP 6d0 =Pd2

0P3d0 = Pd0P

2d20 = Pe0P

5e0 = P 2e0P4e0 = P 3e2

0

33 (1) h0d20P


2d0P3d0 = h0e0P

6e0 =h0gP 6d0 = h0Pd2

0P3d0 = h0Pd0P

2d20 = h0Pe0P

5e0 =h0P

2e0P4e0 = h0P

3e20 = h2d0P

6e0 = h2e0P6d0 = h2Pd0P

5e0 =h2Pe0P

5d0 = h2P2d0P

4e0 = h2P2e0P

4d0 = h2P3d0P

3e0 =d0e0P

6h2 = d0Ph2P5e0 = d0Pe0P

5h2 = d0P2h2P

4e0 =d0P

2e0P4h2 = d0P

3h2P3e0 = e0Ph2P

5d0 = e0Pd0P5h2 =

e0P2h2P

4d0 = e0P2d0P

4h2 = e0P3h2P

3d0 = Ph2Pd0P4e0 =

Ph2Pe0P4d0 = Ph2P

2d0P3e0 = Ph2P

2e0P3d0 = Pd0Pe0P

4h2 =Pd0P

2h2P3e0 = Pd0P

2e0P3h2 = Pe0P

2h2P3d0 =

Pe0P2d0P

3h2 = P 2h2P2d0P

2e0

34 (1) h20d

20P

5d0 = h20d0Pd0P

4d0 = h20d0P

2d0P3d0 = h2

0e0P6e0 =

h20gP 6d0 = h2

0Pd20P

3d0 = h20Pd0P

2d20 = h2

0Pe0P5e0 =

h20P

2e0P4e0 = h2

0P3e2

0 = h0h2d0P6e0 = h0h2e0P

6d0 =h0h2Pd0P

5e0 = h0h2Pe0P5d0 = h0h2P

2d0P4e0 =

h0h2P2e0P

4d0 = h0h2P3d0P

3e0 = h0d0e0P6h2 =

h0d0Ph2P5e0 = h0d0Pe0P

5h2 = h0d0P2h2P

4e0 =h0d0P

2e0P4h2 = h0d0P

3h2P3e0 = h0e0Ph2P

5d0 =h0e0Pd0P

5h2 = h0e0P2h2P

4d0 = h0e0P2d0P

4h2 =h0e0P

3h2P3d0 = h0Ph2Pd0P

4e0 = h0Ph2Pe0P4d0 =

h0Ph2P2d0P

3e0 = h0Ph2P2e0P

3d0 = h0Pd0Pe0P4h2 =

h0Pd0P2h2P

3e0 = h0Pd0P2e0P

3h2 = h0Pe0P2h2P

3d0 =h0Pe0P

2d0P3h2 = h0P

2h2P2d0P

2e0 = h22d0P

6d0 =h2

2Pd0P5d0 = h2

2P2d0P

4d0 = h22P

3d20 = h2d

20P

6h2 =h2d0Ph2P


2h2P4d0 =

h2d0P2d0P

4h2 = h2d0P3h2P

3d0 = h2gP 7h2 = h2Ph2Pd0P4d0 =

h2Ph2P2d0P

3d0 = h2Pd20P

4h2 = h2Pd0P2h2P

3d0 =h2Pd0P

2d0P3h2 = h2P

2h2P2d2

0 = h4P8h2 = c0P

6j =d20Ph2P

5h2 = d20P

2h2P4h2 = d2

0P3h2

2 = d0Ph22P

4d0 =d0Ph2Pd0P

4h2 = d0Ph2P2h2P

3d0 = d0Ph2P2d0P

3h2 =d0Pd0P

2h2P3h2 = d0P

2h22P

2d0 = gPh2P6h2 = gP 2h2P

5h2 =gP 3h2P

4h2 = Ph22Pd0P

3d0 = Ph22P

2d20 = Ph2Pd2

0P3h2 =

Ph2Pd0P2h2P

2d0 = Pc0P5j = jP 6c0 = Pd2

0P2h2

2 = P 2c0P4j =

PjP 5c0 = P 3c0P3j = P 2jP 4c0

35 (1) P 7j

36 (1) h0P7j = Ph2P

6i = iP 7h2 = P 3h2P4i = P 2iP 5h2

37 (1) h20P


7h2 = h0P3h2P

4i = h0P2iP 5h2 =

h1P8e0 = e0P


7h1 = P 2h1P6e0 =

P 2e0P6h1 = P 3h1P

5e0 = P 3e0P5h1 = P 4h1P

4e0


Stem 835 (10) h6g

(01) h2e2 = h4d2

6 (1) h0h6g = h2h6e0

7 (10) h1h4Q3 = h3x6,53

(01) h20h6g = h0h2h6e0 = h2

2h6d0

10 (1) h1gH1 = h22x8,57 = h2c1A

′ = h2c1A = h2f0H1 = h3x9,51 = nD1

11 (1) e0x7,40 = gx7,34

13 (1) h2x12,44

15 (1) x15,41

16 (10) rx′ = iB4

(01) h0x15,41

17 (10) h0rx′ = h0iB4 = h3x16,32

(01) h20x15,41

(11) h1x16,38 = h2x16,37 = d0W1 = f0R2 = kR1

18 (1) h30x15,41 = h2

0rx′ = h2

0iB4 = h0h3x16,32 = h3ix′

19 (10) d20gm = d0e

20m = d0e0gl = d0g

2k = d0ru = e30l = e2

0gk = e0g2j =

g3i = vz

(01) h40x15,41 = h3

0rx′ = h3

0iB4 = h20h3x16,32 = h0h3ix

′ = g2P2i = xi2

(11) r2i

20 (1) h50x15,41 = h4

0rx′ = h4

0iB4 = h30h3x16,32 = h2

0h3ix′ = h0g2P

2i =h0xi2 = h0r

2i = h23x18,20

22 (10) x′P 2d0

(01) d30z = d2

0rPe0 = d20il = d2

0jk = d0e0rPd0 = d0e0ik = d0e0j2 =

d0gij = d0mPj = e20ij = e0gi2 = e0lP j = e0Pe0z = grP 2e0 =

gkPj = gPd0z = imPe0 = jlPe0 = jmPd0 = k2Pe0 = klPd0

(11) d0x18,20

23 (1) h0d0x18,20 = h0x′P 2d0 = h2P

3Q1 = Ph2P2Q1 = P 2h2PQ1 =

Q1 P 3h2

24 (1) h20d0x18,20 = h2

0x′P 2d0 = h0h2P

3Q1 = h0Ph2P2Q1 =

h0P2h2PQ1 = h0Q1 P 3h2 = h2Ph2x18,20 = h2x

′P 3h2 =Ph2P

2h2x′ = B2P

4h2

25 (1) d20P

2u = d0rP2i = d0i

3 = d0Pd0Pu = d0uP 2d0 = e0P3v =

gP 3u = riP 2d0 = ijP j = Pd20u = Pe0P

2v = vP 3e0 = wP 3d0 =zP 2j = P 2e0Pv

28 (1) d30P

3e0 = d20e0P

3d0 = d20Pd0P

2e0 = d20Pe0P

2d0 =d0e0Pd0P

2d0 = d0gP 4e0 = d0Pd20Pe0 = e2

0P4e0 = e0gP 4d0 =

e0Pd30 = e0Pe0P

3e0 = e0P2e2

0 = gPd0P3e0 = gPe0P

3d0 =gP 2d0P

2e0 = Pe20P

2e0

continued

80 ROBERT R. BRUNER


0P4i = d0iP

4d0 = d0P2d0P

2i = e0P5j = iPd0P

3d0 = iP 2d20 =

jP 5e0 = kP 5d0 = Pd20P

2i = Pe0P4j = PjP 4e0 = P 2e0P

3j =P 2jP 3e0

32 (1) h0d20P

4i = h0d0iP4d0 = h0d0P

2d0P2i = h0e0P

5j =h0iPd0P

3d0 = h0iP2d2

0 = h0jP5e0 = h0kP 5d0 = h0Pd2

0P2i =

h0Pe0P4j = h0PjP 4e0 = h0P

2e0P3j = h0P

2jP 3e0 = h2d0P5j =

h2iP5e0 = h2jP

5d0 = h2Pd0P4j = h2Pe0P

4i = h2PjP 4d0 =h2P

2d0P3j = h2P

2iP 3e0 = h2P2jP 3d0 = d0Ph2P

4j =d0jP

5h2 = d0P2h2P

3j = d0PjP 4h2 = d0P3h2P

2j = e0Ph2P4i =

e0iP5h2 = e0P

3h2P2i = f0P

6e0 = Ph2iP4e0 = Ph2jP

4d0 =Ph2Pd0P

3j = Ph2PjP 3d0 = Ph2P2d0P

2j = Ph2P2e0P

2i =iPe0P

4h2 = iP 2h2P3e0 = iP 2e0P

3h2 = jPd0P4h2 =

jP 2h2P3d0 = jP 2d0P

3h2 = lP 6h2 = Pd0P2h2P

2j =Pd0PjP 3h2 = Pe0P

2h2P2i = P 2h2PjP 2d0

continued



0d20P

4i = h20d0iP

4d0 = h20d0P

2d0P2i = h2

0e0P5j =

h20iPd0P

3d0 = h20iP

2d20 = h2

0jP5e0 = h2

0kP 5d0 = h20Pd2

0P2i =

h20Pe0P

4j = h20PjP 4e0 = h2

0P2e0P

3j = h20P

2jP 3e0 =h0h2d0P

5j = h0h2iP5e0 = h0h2jP

5d0 = h0h2Pd0P4j =

h0h2Pe0P4i = h0h2PjP 4d0 = h0h2P

2d0P3j = h0h2P

2iP 3e0 =h0h2P

2jP 3d0 = h0d0Ph2P4j = h0d0jP

5h2 = h0d0P2h2P

3j =h0d0PjP 4h2 = h0d0P

3h2P2j = h0e0Ph2P

4i = h0e0iP5h2 =

h0e0P3h2P

2i = h0f0P6e0 = h0Ph2iP

4e0 = h0Ph2jP4d0 =

h0Ph2Pd0P3j = h0Ph2PjP 3d0 = h0Ph2P

2d0P2j =

h0Ph2P2e0P

2i = h0iPe0P4h2 = h0iP

2h2P3e0 = h0iP

2e0P3h2 =

h0jPd0P4h2 = h0jP

2h2P3d0 = h0jP

2d0P3h2 = h0lP

6h2 =h0Pd0P

2h2P2j = h0Pd0PjP 3h2 = h0Pe0P

2h2P2i =

h0P2h2PjP 2d0 = h1d

20P


2d0P3d0 =

h1e0P6e0 = h1gP 6d0 = h1Pd2

0P3d0 = h1Pd0P

2d20 =

h1Pe0P5e0 = h1P

2e0P4e0 = h1P

3e20 = h2

2iP5d0 =

h22Pd0P

4i = h22P

2iP 3d0 = h2d0Ph2P4i = h2d0iP

5h2 =h2d0P

3h2P2i = h2f0P

6d0 = h2Ph2iP4d0 = h2Ph2P

2d0P2i =

h2iPd0P4h2 = h2iP

2h2P3d0 = h2iP

2d0P3h2 = h2kP 6h2 =

h2Pd0P2h2P

2i = d30P

5h1 = d20Ph1P

4d0 = d20Pd0P

4h1 =d20P

2h1P3d0 = d2

0P2d0P

3h1 = d0f0P6h2 = d0gP 6h1 =

d0Ph1Pd0P3d0 = d0Ph1P

2d20 = d0Ph2iP

4h2 = d0Ph2P2h2P

2i =d0iP

2h2P3h2 = d0Pd2

0P3h1 = d0Pd0P

2h1P2d0 = e2

0P6h1 =

e0Ph1P5e0 = e0Pe0P

5h1 = e0P2h1P

4e0 = e0P2e0P

4h1 =e0P

3h1P3e0 = f0Ph2P

5d0 = f0Pd0P5h2 = f0P

2h2P4d0 =

f0P2d0P

4h2 = f0P3h2P

3d0 = gPh1P5d0 = gPd0P

5h1 =gP 2h1P

4d0 = gP 2d0P4h1 = gP 3h1P

3d0 = Ph1Pd20P

2d0 =Ph1Pe0P

4e0 = Ph1P2e0P

3e0 = Ph22iP

3d0 = Ph22Pd0P

2i =Ph2iPd0P

3h2 = Ph2iP2h2P

2d0 = Ph2kP 5h2 = iPd0P2h2

2 =kP 2h2P

4h2 = kP 3h22 = Pd3

0P2h1 = Pe2

0P4h1 = Pe0P

2h1P3e0 =

Pe0P2e0P

3h1 = P 2h1P2e2

0

82 ROBERT R. BRUNER

Stem 844 (10) f2

(01) h22h4h6 = h3

3h6

5 (1) h0f2 = h4p′

6 (01) h20f2 = h0h4p

′

(11) h1h6g = h2h6f0

7 (1) h30f2 = h2

0h4p′

8 (1) h40f2 = h3

0h4p′ = h2

1h4Q3 = h1h3x6,53 = h3m1 = h3x7,57 = h24G =

h4c0D3 = d0p1 = f1g2

9 (1) h2h4x7,40 = h2c1H1 = h2gD3 = h3x8,57 = h4PD3 = c0x6,53 =e0Q3 = d1D1

10 (1) Px6,53

14 (1) x14,46

15 (10) x15,42

(01) x15,43

16 (1) h0x15,42 = rR1 = iX1

17 (1) h20x15,42 = h0rR1 = h0iX1 = h3x16,33

18 (001) h30x15,42 = h2

0rR1 = h20iX1 = h0h3x16,33 = h3iR1 = xQ

(011) d20Q1 = d0e0x

′ = gPQ1 = Pd0x10,27 = Pd0x10,28 = Pe0B21

(111) d0g2r = d0m

2 = e20gr = e0lm = gkm = gl2 = uw = v2

19 (10) h4x18,20 = c0x16,32

(01) h40x15,42 = h3

0rR1 = h30iX1 = h2

0h3x16,33 = h0h3iR1 = h0xQ =h2

3R1

(11) h0d20Q1 = h0d0e0x

′ = h0gPQ1 = h0Pd0x10,27 = h0Pd0x10,28 =h0Pe0B21 = h2d

20x

′ = h2e0PQ1 = h2Pd0B21 = h2Pe0Q1 =d0Ph2B21 = d0B2Pd0 = e0Ph2Q1 = gPh2x

′ = P 2h2B23

20 (1) h50x15,42 = h4

0rR1 = h40iX1 = h3

0h3x16,33 = h20h3iR1 = h2

0d20Q1 =

h20d0e0x

′ = h20gPQ1 = h2

0xQ = h20Pd0x10,27 = h2

0Pd0x10,28 =h2

0Pe0B21 = h0h2d20x

′ = h0h2e0PQ1 = h0h2Pd0B21 =h0h2Pe0Q1 = h0h

23R1 = h0d0Ph2B21 = h0d0B2Pd0 =

h0e0Ph2Q1 = h0gPh2x′ = h0P

2h2B23 = h22d0PQ1 =

h22Pd0Q1 = h2

2Pe0x′ = h2d0Ph2Q1 = h2e0Ph2x

′ = h2B2P2e0 =

h2P2h2x10,27 = h2P

2h2x10,28 = h3rQ = c0ix′ = e0B2P

2h2 =Ph2

2x10,27 = Ph22x10,28 = Ph2B2Pe0 = yi2 = Pc0P

2D1 =Q2P

3h2 = B4P2c0

21 (10) d0R1

(01) d30v = d2

0e0u = d20rj = d0e0ri = d0gPv = d0kz = d0Pe0w =

e20Pv = e0gPu = e0jz = e0Pd0w = e0Pe0v = grPj = giz =

gPd0v = gPe0u = rkPe0 = rlPd0 = ijm = ikl = j2l = jk2

22 (1) h0d0R1 = h2P2R2 = Ph2PR2 = P 2h2R2 = R1P

2d0

continued



0d0R1 = h0h2P2R2 = h0Ph2PR2 = h0P

2h2R2 = h0R1P2d0 =

h1d0x18,20 = h1x′P 2d0 = h2Ph2R1 = d0P

2h1x′ = Ph1Pd0x

′ =B1P

3d0 = B21P3h1

24 (1) d60 = d3

0e0Pe0 = d30gPd0 = d2

0e20Pd0 = d0e0gP 2e0 = d0g

2P 2d0 =d0gPe2

0 = d0iPu = e30P

2e0 = e20gP 2d0 = e2

0Pe20 = e0gPd0Pe0 =

g2Pd20 = iPd0u = jP 2v = kP 2u = vP 2j = wP 2i = PjPv

27 (1) d30P

2j = d20e0P

2i = d20iP

2e0 = d20jP

2d0 = d20Pd0Pj =

d0e0iP2d0 = d0gP 3j = d0iPd0Pe0 = d0jPd2

0 = d0kP 3e0 =d0lP

3d0 = e20P

3j = e0iPd20 = e0jP

3e0 = e0kP 3d0 = e0Pe0P2j =

e0PjP 2e0 = giP 3e0 = gjP 3d0 = gPd0P2j = gPe0P

2i =gPjP 2d0 = jPe0P

2e0 = kPd0P2e0 = kPe0P

2d0 = lPd0P2d0 =

mP 4e0 = Pe20Pj

30 (1) rP 5d0 = i2P 3d0 = iPd0P2i = jP 4j = kP 4i = PjP 3j = P 2j2

36 (1) d0P7d0 = Pd0P

6d0 = P 2d0P5d0 = P 3d0P

4d0

37 (1) h0d0P7d0 = h0Pd0P

6d0 = h0P2d0P

5d0 = h0P3d0P

4d0 =h2P

8e0 = e0P8h2 = Ph2P

7e0 = Pe0P7h2 = P 2h2P

6e0 =P 2e0P

6h2 = P 3h2P5e0 = P 3e0P

5h2 = P 4h2P4e0

38 (1) h20d0P

7d0 = h20Pd0P

6d0 = h20P

2d0P5d0 = h2

0P3d0P

4d0 =h0h2P

8e0 = h0e0P8h2 = h0Ph2P

7e0 = h0Pe0P7h2 =

h0P2h2P

6e0 = h0P2e0P

6h2 = h0P3h2P

5e0 = h0P3e0P

5h2 =h0P

4h2P4e0 = h2

2P8d0 = h2d0P

8h2 = h2Ph2P7d0 =

h2Pd0P7h2 = h2P

2h2P6d0 = h2P

2d0P6h2 = h2P

3h2P5d0 =

h2P3d0P

5h2 = h2P4h2P

4d0 = d0Ph2P7h2 = d0P

2h2P6h2 =

d0P3h2P

5h2 = d0P4h2

2 = Ph22P

6d0 = Ph2Pd0P6h2 =

Ph2P2h2P

5d0 = Ph2P2d0P

5h2 = Ph2P3h2P

4d0 =Ph2P

3d0P4h2 = Pd0P

2h2P5h2 = Pd0P

3h2P4h2 = P 2h2

2P4d0 =

P 2h2P2d0P

4h2 = P 2h2P3h2P

3d0 = P 2d0P3h2

2

84 ROBERT R. BRUNER

Stem 853 (1) c3

4 (1) h0c3

5 (010) h1f2 = h4p1

(110) h2h6c1

(001) h20c3

6 (10) x6,68

(01) h30c3

7 (1) h40c3 = h0x6,68 = h2h4Q3 = h3t1 = c2g2

8 (1) h50c3 = h2

0x6,68 = h0h2h4Q3 = h0h3t1 = h0c2g2 = h23x6,47 = e0d2

9 (1) h6Pd0

10 (1) h0h6Pd0

11 (10) h1Px6,53 = h5R1 = Ph1x6,53

(01) h20h6Pd0 = h2h6P

2h2 = h6Ph22

13 (1) x13,46

14 (10) gB23

(01) h0x13,46

15 (10) h1x14,46 = h22x13,42 = f0x11,35 = nR1

(01) h20x13,46

16 (100) x16,42

(001) h30x13,46

(011) h1x15,42 = h1x15,43 = qx′ = B1u

17 (100) g2w = grm

(010) d0x13,35 = ix10,28 = jB21 = kQ1 = lx′ = Pe0B4

(001) h40x13,46 = h2x16,38 = d0x13,34

(011) e0P2D1 = gR2 = ix10,27

18 (10) h0d0x13,35 = h0ix10,28 = h0jB21 = h0kQ1 = h0lx′ = h0Pe0B4 =

h2iB21 = h2jQ1 = h2kx′ = h2Pd0B4 = h4R1 = d0f0x′ =

d0Ph2B4 = d0iB2

(01) h50x13,46 = h0h2x16,38 = h0d0x13,34 = h2

2x16,35

(11) h0e0P2D1 = h0gR2 = h0ix10,27 = h2d0P

2D1 = h2e0R2 = d0e0R1

19 (1) h20d0x13,35 = h2

0e0P2D1 = h2

0gR2 = h20ix10,27 = h2

0ix10,28 =h2

0jB21 = h20kQ1 = h2

0lx′ = h2

0Pe0B4 = h0h2d0P2D1 =

h0h2e0R2 = h0h2iB21 = h0h2jQ1 = h0h2kx′ = h0h2Pd0B4 =h0h4R1 = h0d0e0R1 = h0d0f0x

′ = h0d0Ph2B4 = h0d0iB2 =h1d

20Q1 = h1d0e0x

′ = h1gPQ1 = h1Pd0x10,27 = h1Pd0x10,28 =h1Pe0B21 = h2

2d0R2 = h22iQ1 = h2

2jx′ = h2d

20R1 =

h2f0PQ1 = h2Ph2x13,35 = h2B2Pj = c0x16,33 = d0Ph1x10,27 =d0Ph1x10,28 = d0B1Pe0 = e0Ph1B21 = e0B1Pd0 = f0Ph2Q1 =gPh1Q1 = gPh2R1 = Ph2jB2 = D2P

3h2 = P 2h2B5 =P 2h2PD2

continued



0e0g2 = d0e

30g = d0rz = d0jw = d0kv = d0lu = e5

0 = e0iw =e0jv = e0ku = g3Pe0 = giv = gju = r2Pe0 = ril = rjk = mPv

21 (1) Ph1x16,32

23 (1) d40k = d3

0e0j = d30gi = d2

0e20i = d2

0lP e0 = d20mPd0 = d0e0gPj =

d0e0kPe0 = d0e0lPd0 = d0gjPe0 = d0gkPd0 = e30Pj = e2

0jPe0 =e20kPd0 = e0giPe0 = e0gjPd0 = e0mP 2e0 = g2iPd0 = glP 2e0 =

gmP 2d0 = rP 2u = i2u = mPe20

26 (10) P 4x′

(01) d20iP j = d0rP

3e0 = d0i2Pe0 = d0ijPd0 = d0kP 2j = d0lP

2i =d0zP 2d0 = e0rP

3d0 = e0i2Pd0 = e0jP

2j = e0kP 2i = e0Pj2 =giP 2j = gjP 2i = rPd0P

2e0 = rPe0P2d0 = ikP 2e0 = ilP 2d0 =

j2P 2e0 = jkP 2d0 = jPe0Pj = kPd0Pj = mP 3j = Pd20z

27 (1) h0P4x′

28 (1) h20P

4x′

29 (10) d0P4u = Pd0P

3u = uP 4d0 = P 2d0P2u = PuP 3d0

(01) h30P

4x′

(11) rP 4i = i2P 2i

30 (1) h40P

4x′ = h0rP4i = h0i

2P 2i

31 (1) h50P

4x′ = h20rP

4i = h20i

2P 2i = h3iP4i = h3P

2i2

32 (01) h60P

4x′ = h30rP

4i = h30i

2P 2i = h0h3iP4i = h0h3P

2i2

(11) d20P

5e0 = d0e0P5d0 = d0Pd0P

4e0 = d0Pe0P4d0 = d0P

2d0P3e0 =

d0P2e0P

3d0 = e0Pd0P4d0 = e0P

2d0P3d0 = gP 6e0 = Pd2

0P3e0 =

Pd0Pe0P3d0 = Pd0P

2d0P2e0 = Pe0P

2d20

33 (1) h70P

4x′ = h40rP

4i = h40i

2P 2i = h20h3iP

4i = h20h3P

2i2 =h0d

20P

5e0 = h0d0e0P5d0 = h0d0Pd0P

4e0 = h0d0Pe0P4d0 =

h0d0P2d0P

3e0 = h0d0P2e0P

3d0 = h0e0Pd0P4d0 =

h0e0P2d0P

3d0 = h0gP 6e0 = h0Pd20P

3e0 = h0Pd0Pe0P3d0 =

h0Pd0P2d0P

2e0 = h0Pe0P2d2

0 = h2d20P

5d0 = h2d0Pd0P4d0 =

h2d0P2d0P

3d0 = h2e0P6e0 = h2gP 6d0 = h2Pd2

0P3d0 =

h2Pd0P2d2

0 = h2Pe0P5e0 = h2P

2e0P4e0 = h2P

3e20 = h2

3P6i =

h4P7d0 = d3

0P5h2 = d2

0Ph2P4d0 = d2

0Pd0P4h2 = d2

0P2h2P

3d0 =d20P

2d0P3h2 = d0gP 6h2 = d0Ph2Pd0P

3d0 = d0Ph2P2d2

0 =d0Pd2

0P3h2 = d0Pd0P

2h2P2d0 = e2

0P6h2 = e0Ph2P

5e0 =e0Pe0P

5h2 = e0P2h2P

4e0 = e0P2e0P

4h2 = e0P3h2P

3e0 =gPh2P

5d0 = gPd0P5h2 = gP 2h2P

4d0 = gP 2d0P4h2 =

gP 3h2P3d0 = Ph2Pd2

0P2d0 = Ph2Pe0P

4e0 = Ph2P2e0P

3e0 =Pd3

0P2h2 = Pe2

0P4h2 = Pe0P

2h2P3e0 = Pe0P

2e0P3h2 =

P 2h2P2e2

0

continued

86 ROBERT R. BRUNER


0P4x′ = h5

0rP4i = h5

0i2P 2i = h3

0h3iP4i = h3

0h3P2i2 =

h20d

20P

5e0 = h20d0e0P

5d0 = h20d0Pd0P

4e0 = h20d0Pe0P

4d0 =h2

0d0P2d0P

3e0 = h20d0P

2e0P3d0 = h2

0e0Pd0P4d0 =

h20e0P

2d0P3d0 = h2

0gP 6e0 = h20Pd2

0P3e0 = h2

0Pd0Pe0P3d0 =

h20Pd0P

2d0P2e0 = h2

0Pe0P2d2

0 = h0h2d20P

5d0 =h0h2d0Pd0P

4d0 = h0h2d0P2d0P

3d0 = h0h2e0P6e0 =

h0h2gP 6d0 = h0h2Pd20P

3d0 = h0h2Pd0P2d2

0 = h0h2Pe0P5e0 =

h0h2P2e0P

4e0 = h0h2P3e2

0 = h0h23P

6i = h0h4P7d0 =

h0d30P

5h2 = h0d20Ph2P

4d0 = h0d20Pd0P

4h2 = h0d20P

2h2P3d0 =

h0d20P

2d0P3h2 = h0d0gP 6h2 = h0d0Ph2Pd0P

3d0 =h0d0Ph2P

2d20 = h0d0Pd2

0P3h2 = h0d0Pd0P

2h2P2d0 =

h0e20P

6h2 = h0e0Ph2P5e0 = h0e0Pe0P

5h2 = h0e0P2h2P

4e0 =h0e0P

2e0P4h2 = h0e0P

3h2P3e0 = h0gPh2P

5d0 =h0gPd0P

5h2 = h0gP 2h2P4d0 = h0gP 2d0P

4h2 = h0gP 3h2P3d0 =

h0Ph2Pd20P

2d0 = h0Ph2Pe0P4e0 = h0Ph2P

2e0P3e0 =

h0Pd30P

2h2 = h0Pe20P

4h2 = h0Pe0P2h2P

3e0 =h0Pe0P

2e0P3h2 = h0P

2h2P2e2

0 = h22d0P

6e0 = h22e0P

6d0 =h2

2Pd0P5e0 = h2

2Pe0P5d0 = h2

2P2d0P

4e0 = h22P

2e0P4d0 =

h22P

3d0P3e0 = h2d0e0P


5h2 =h2d0P

2h2P4e0 = h2d0P

2e0P4h2 = h2d0P

3h2P3e0 =

h2e0Ph2P5d0 = h2e0Pd0P

5h2 = h2e0P2h2P

4d0 =h2e0P

2d0P4h2 = h2e0P

3h2P3d0 = h2Ph2Pd0P

4e0 =h2Ph2Pe0P

4d0 = h2Ph2P2d0P

3e0 = h2Ph2P2e0P

3d0 =h2Pd0Pe0P

4h2 = h2Pd0P2h2P

3e0 = h2Pd0P2e0P

3h2 =h2Pe0P

2h2P3d0 = h2Pe0P

2d0P3h2 = h2P

2h2P2d0P

2e0 =c0iP

5d0 = c0Pd0P4i = c0P

2iP 3d0 = d0e0Ph2P5h2 =

d0e0P2h2P

4h2 = d0e0P3h2

2 = d0Ph22P

4e0 = d0Ph2Pe0P4h2 =

d0Ph2P2h2P

3e0 = d0Ph2P2e0P

3h2 = d0Pc0P4i = d0iP

5c0 =d0Pe0P

2h2P3h2 = d0P

2h22P

2e0 = d0P3c0P

2i = e0Ph22P

4d0 =e0Ph2Pd0P

4h2 = e0Ph2P2h2P

3d0 = e0Ph2P2d0P

3h2 =e0Pd0P

2h2P3h2 = e0P

2h22P

2d0 = Ph22Pd0P

3e0 =Ph2

2Pe0P3d0 = Ph2

2P2d0P

2e0 = Ph2Pd0Pe0P3h2 =

Ph2Pd0P2h2P

2e0 = Ph2Pe0P2h2P

2d0 = Pc0iP4d0 =

Pc0P2d0P

2i = iPd0P4c0 = iP 2c0P

3d0 = iP 2d0P3c0 = kP 6c0 =

Pd0Pe0P2h2

2 = Pd0P2c0P

2i

continued



6i = iP 6d0 = P 2d0P4i = P 2iP 4d0

36 (1) h0d0P6i = h0iP

6d0 = h0P2d0P

4i = h0P2iP 4d0 = h2P

7j =Ph2P

6j = jP 7h2 = P 2h2P5j = PjP 6h2 = P 3h2P

4j =P 2jP 5h2 = P 4h2P

3j

37 (1) h20d0P

6i = h20iP

6d0 = h20P

2d0P4i = h2

0P2iP 4d0 =

h0h2P7j = h0Ph2P

6j = h0jP7h2 = h0P

2h2P5j =

h0PjP 6h2 = h0P3h2P

4j = h0P2jP 5h2 = h0P

4h2P3j =

h1d0P7d0 = h1Pd0P

6d0 = h1P2d0P

5d0 = h1P3d0P

4d0 =h2Ph2P

6i = h2iP7h2 = h2P

3h2P4i = h2P

2iP 5h2 =d20P


6h1 = d0P2h1P

5d0 =d0P

2d0P5h1 = d0P

3h1P4d0 = d0P

3d0P4h1 = f0P

8h2 = gP 8h1 =Ph1Pd0P

5d0 = Ph1P2d0P

4d0 = Ph1P3d2

0 = Ph2iP6h2 =

Ph2P2h2P

4i = Ph2P2iP 4h2 = iP 2h2P

5h2 = iP 3h2P4h2 =

Pd20P

5h1 = Pd0P2h1P

4d0 = Pd0P2d0P

4h1 = Pd0P3h1P

3d0 =P 2h1P

2d0P3d0 = P 2h2P

3h2P2i = P 2d2

0P3h1

88 ROBERT R. BRUNER

Stem 864 (1) h1c3

5 (1) h4h6c0

6 (10) h2h6g

(01) h21f2 = h1h4p1 = h2

2e2 = h2h4d2

7 (10) h1x6,68 = h4x6,47

(01) h0h2h6g = h22h6e0

8 (1) h6i

9 (1) h0h6i

10 (10) h1h6Pd0 = h6d0Ph1

(01) h20h6i

11 (10) gx7,40

(01) h30h6i

12 (10) x12,48

(01) h40h6i

13 (1) h50h6i

14 (10) P 3h25

(01) h1x13,46 = h22x12,44 = h3x13,42 = h4x13,34 = c1x11,35 = gB5 =

d1R1

15 (1) h0P3h2

5

16 (100) g2N = gnm = grt

(010) rQ1 = jB4

(001) h20P

3h25 = h2x15,41

17 (10) h1x16,42 = f0P2D1 = lR1

(01) h30P

3h25 = h0h2x15,41 = e0W1

(11) h0rQ1 = h0jB4 = h21x15,42 = h2

1x15,43 = h1qx′ = h1B1u =

h2rx′ = h2iB4 = h3x16,35 = D3P

3h1 = Ph1P2D3 = Pe0X1 =

PD3P2h1

19 (1) d0e0gm = d0g2l = d0rv = e3

0m = e20gl = e0g

2k = e0ru = g3j =r2j = wz

22 (100) d0P2Q1 = Pd0PQ1 = Q1 P 2d0

(010) uPu

(110) e0x18,20

(001) h1Ph1x16,32 = P 2h1W1 = uQ = X1P3h1

(101) x′P 2e0

(011) d40r = d2

0e0z = d20im = d2

0jl = d20k

2 = d0e0rPe0 = d0e0il =d0e0jk = d0grPd0 = d0gik = d0gj2 = e2

0rPd0 = e20ik = e2

0j2 =

e0gij = e0mPj = g2i2 = glP j = gPe0z = jmPe0 = klPe0 =kmPd0 = l2Pd0

continued


Stem 86 continued23 (1) h0d0P

2Q1 = h0e0x18,20 = h0Pd0PQ1 = h0x′P 2e0 =

h0Q1 P 2d0 = h2d0x18,20 = h2x′P 2d0 = d0P

2h2x′ = Ph2Pd0x

′ =B2P

3d0 = B21P3h2

24 (1) h20d0P

2Q1 = h20e0x18,20 = h2

0Pd0PQ1 = h20x

′P 2e0 =h2

0Q1 P 2d0 = h0h2d0x18,20 = h0h2x′P 2d0 = h0d0P

2h2x′ =

h0Ph2Pd0x′ = h0B2P

3d0 = h0B21P3h2 = h2

2P3Q1 =

h2Ph2P2Q1 = h2P

2h2PQ1 = h2Q1 P 3h2 = Ph22PQ1 =

Ph2P2h2Q1 = Pc0R1

25 (10) x25,24

(01) d20P

2v = d0e0P2u = d0rP

2j = d0i2j = d0Pd0Pv = d0Pe0Pu =

d0uP 2e0 = d0vP 2d0 = e0rP2i = e0i

3 = e0Pd0Pu = e0uP 2d0 =gP 3v = riP 2e0 = rjP 2d0 = rPd0Pj = ikPj = iPd0z = j2Pj =Pd2

0v = Pd0Pe0u = wP 3e0

26 (1) h0x25,24

27 (01) h20x25,24

(11) h1P4x′ = P 2h1x18,20 = x′P 4h1

28 (10) d40P

2d0 = d30Pd2

0 = d20e0P

3e0 = d20gP 3d0 = d2

0Pe0P2e0 =

d0e20P

3d0 = d0e0Pd0P2e0 = d0e0Pe0P

2d0 = d0gPd0P2d0 =

d0Pd0Pe20 = e2

0Pd0P2d0 = e0gP 4e0 = e0Pd2

0Pe0 = g2P 4d0 =gPd3

0 = gPe0P3e0 = gP 2e2

0 = iP 3u = PuP 2i

(01) h30x25,24 = QP 2i

29 (1) h40x25,24 = h0QP 2i

30 (1) h50x25,24 = h2

0QP 2i = h3P4Q

31 (01) h60x25,24 = h3

0QP 2i = h0h3P4Q

(11) d20P

4j = d0e0P4i = d0iP

4e0 = d0jP4d0 = d0Pd0P

3j =d0PjP 3d0 = d0P

2d0P2j = d0P

2e0P2i = e0iP

4d0 = e0P2d0P

2i =gP 5j = iPd0P

3e0 = iPe0P3d0 = iP 2d0P

2e0 = jPd0P3d0 =

jP 2d20 = kP 5e0 = lP 5d0 = Pd2

0P2j = Pd0Pe0P

2i = Pd0PjP 2d0

32 (1) h70x25,24 = h4

0QP 2i = h20h3P

4Q = h0d20P

4j = h0d0e0P4i =

h0d0iP4e0 = h0d0jP

4d0 = h0d0Pd0P3j = h0d0PjP 3d0 =

h0d0P2d0P

2j = h0d0P2e0P

2i = h0e0iP4d0 = h0e0P

2d0P2i =

h0gP 5j = h0iPd0P3e0 = h0iPe0P

3d0 = h0iP2d0P

2e0 =h0jPd0P

3d0 = h0jP2d2

0 = h0kP 5e0 = h0lP5d0 = h0Pd2

0P2j =

h0Pd0Pe0P2i = h0Pd0PjP 2d0 = h2d

20P

4i = h2d0iP4d0 =

h2d0P2d0P

2i = h2e0P5j = h2iPd0P

3d0 = h2iP2d2

0 =h2jP

5e0 = h2kP 5d0 = h2Pd20P

2i = h2Pe0P4j = h2PjP 4e0 =

h2P2e0P

3j = h2P2jP 3e0 = d2

0iP4h2 = d2

0P2h2P

2i = d0f0P5d0 =

d0Ph2iP3d0 = d0Ph2Pd0P

2i = d0iPd0P3h2 = d0iP

2h2P2d0 =

d0kP 5h2 = e0Ph2P4j = e0jP

5h2 = e0P2h2P

3j = e0PjP 4h2 =(continued)

90 ROBERT R. BRUNER

Stem 86 continued32 (1) (continued) = e0P

3h2P2j = f0Pd0P

4d0 = f0P2d0P

3d0 =gPh2P

4i = giP 5h2 = gP 3h2P2i = Ph2iPd0P

2d0 = Ph2jP4e0 =

Ph2kP 4d0 = Ph2Pe0P3j = Ph2PjP 3e0 = Ph2P

2e0P2j =

iPd20P

2h2 = jPe0P4h2 = jP 2h2P

3e0 = jP 2e0P3h2 =

kPd0P4h2 = kP 2h2P

3d0 = kP 2d0P3h2 = mP 6h2 =

Pe0P2h2P

2j = Pe0PjP 3h2 = P 2h2PjP 2e0

33 (1) h80x25,24 = h5

0QP 2i = h30h3P

4Q = h20d

20P

4j = h20d0e0P

4i =h2

0d0iP4e0 = h2

0d0jP4d0 = h2

0d0Pd0P3j = h2

0d0PjP 3d0 =h2

0d0P2d0P

2j = h20d0P

2e0P2i = h2

0e0iP4d0 = h2

0e0P2d0P

2i =h2

0gP 5j = h20iPd0P

3e0 = h20iPe0P

3d0 = h20iP

2d0P2e0 =

h20jPd0P

3d0 = h20jP

2d20 = h2

0kP 5e0 = h20lP

5d0 =h2

0Pd20P

2j = h20Pd0Pe0P

2i = h20Pd0PjP 2d0 = h0h2d

20P

4i =h0h2d0iP

4d0 = h0h2d0P2d0P

2i = h0h2e0P5j = h0h2iPd0P

3d0 =h0h2iP

2d20 = h0h2jP

5e0 = h0h2kP 5d0 = h0h2Pd20P

2i =h0h2Pe0P

4j = h0h2PjP 4e0 = h0h2P2e0P

3j = h0h2P2jP 3e0 =

h0d20iP

4h2 = h0d20P

2h2P2i = h0d0f0P

5d0 = h0d0Ph2iP3d0 =

h0d0Ph2Pd0P2i = h0d0iPd0P

3h2 = h0d0iP2h2P

2d0 =h0d0kP 5h2 = h0e0Ph2P

4j = h0e0jP5h2 = h0e0P

2h2P3j =

h0e0PjP 4h2 = h0e0P3h2P

2j = h0f0Pd0P4d0 = h0f0P

2d0P3d0 =

h0gPh2P4i = h0giP 5h2 = h0gP 3h2P

2i = h0Ph2iPd0P2d0 =

h0Ph2jP4e0 = h0Ph2kP 4d0 = h0Ph2Pe0P

3j = h0Ph2PjP 3e0 =h0Ph2P

2e0P2j = h0iPd2

0P2h2 = h0jPe0P

4h2 = h0jP2h2P

3e0 =h0jP

2e0P3h2 = h0kPd0P

4h2 = h0kP 2h2P3d0 = h0kP 2d0P

3h2 =h0mP 6h2 = h0Pe0P

2h2P2j = h0Pe0PjP 3h2 = h0P

2h2PjP 2e0 =h1d

20P


4e0 = h1d0Pe0P4d0 =

h1d0P2d0P

3e0 = h1d0P2e0P

3d0 = h1e0Pd0P4d0 =

h1e0P2d0P

3d0 = h1gP 6e0 = h1Pd20P

3e0 = h1Pd0Pe0P3d0 =

h1Pd0P2d0P

2e0 = h1Pe0P2d2

0 = h22d0P

5j = h22iP

5e0 =h2

2jP5d0 = h2

2Pd0P4j = h2

2Pe0P4i = h2

2PjP 4d0 =h2

2P2d0P

3j = h22P

2iP 3e0 = h22P

2jP 3d0 = h2d0Ph2P4j =

h2d0jP5h2 = h2d0P

2h2P3j = h2d0PjP 4h2 = h2d0P

3h2P2j =

h2e0Ph2P4i = h2e0iP

5h2 = h2e0P3h2P

2i = h2f0P6e0 =


4d0 = h2Ph2Pd0P3j = h2Ph2PjP 3d0 =

h2Ph2P2d0P

2j = h2Ph2P2e0P

2i = h2iPe0P4h2 =

h2iP2h2P

3e0 = h2iP2e0P

3h2 = h2jPd0P4h2 = h2jP

2h2P3d0 =

h2jP2d0P

3h2 = h2lP6h2 = h2Pd0P

2h2P2j = h2Pd0PjP 3h2 =

h2Pe0P2h2P

2i = h2P2h2PjP 2d0 = c0iP

4i = c0P2i2 =

d20e0P

5h1 = d20Ph1P

4e0 = d20Pe0P

4h1 = d20P

2h1P3e0 =

d20P

2e0P3h1 = d0e0Ph1P

4d0 = d0e0Pd0P4h1 = d0e0P

2h1P3d0 =

d0e0P2d0P

3h1 = d0Ph1Pd0P3e0 = (continued)


Stem 86 continued33 (1) (continued) = d0Ph1Pe0P

3d0 = d0Ph1P2d0P

2e0 =d0Ph2

2P3j = d0Ph2jP

4h2 = d0Ph2P2h2P

2j = d0Ph2PjP 3h2 =d0jP

2h2P3h2 = d0Pd0Pe0P

3h1 = d0Pd0P2h1P

2e0 =d0Pe0P

2h1P2d0 = d0P

2h22Pj = e0f0P

6h2 = e0gP 6h1 =e0Ph1Pd0P

3d0 = e0Ph1P2d2

0 = e0Ph2iP4h2 = e0Ph2P

2h2P2i =

e0iP2h2P

3h2 = e0Pd20P

3h1 = e0Pd0P2h1P

2d0 = f0Ph2P5e0 =

f0Pe0P5h2 = f0P

2h2P4e0 = f0P

2e0P4h2 = f0P

3h2P3e0 =

gPh1P5e0 = gPe0P

5h1 = gP 2h1P4e0 = gP 2e0P

4h1 =gP 3h1P

3e0 = Ph1Pd20P

2e0 = Ph1Pd0Pe0P2d0 = Ph2

2iP3e0 =

Ph22jP

3d0 = Ph22Pd0P

2j = Ph22Pe0P

2i = Ph22PjP 2d0 =

Ph2iPe0P3h2 = Ph2iP

2h2P2e0 = Ph2jPd0P

3h2 =Ph2jP

2h2P2d0 = Ph2lP

5h2 = Ph2Pd0P2h2Pj = rP 6c0 =

i2P 4c0 = iPe0P2h2

2 = iP 2c0P2i = jPd0P

2h22 = lP 2h2P

4h2 =lP 3h2

2 = Pd20Pe0P

2h1

92 ROBERT R. BRUNER

Stem 875 (1) h2

1c3 = h2f2 = h3e2

6 (1) h1h4h6c0 = h3h6e0

7 (1) x7,74

9 (1) h24Q2 = gQ3

10 (1) x10,60

11 (1) h21h6Pd0 = h1h6d0Ph1 = h3h6P

2h1 = h6c0Pc0

12 (1) h6P2c0

13 (10) gx9,39 = rQ2

(01) h1x12,48 = h3x12,44

15 (10) x15,47

(01) h1P3h2

5 = h2x14,46 = h3x14,42 = gx11,35

17 (1) x17,50

18 (10) e0g2r = e0m

2 = glm = vw

(01) d20B21 = d0e0Q1 = d0gx′ = e2

0x′ = Pd0B23 = Pe0x10,27 =

Pe0x10,28

19 (1) h0d20B21 = h0d0e0Q1 = h0d0gx′ = h0e

20x

′ = h0Pd0B23 =h0Pe0x10,27 = h0Pe0x10,28 = h2d

20Q1 = h2d0e0x

′ = h2gPQ1 =h2Pd0x10,27 = h2Pd0x10,28 = h2Pe0B21 = h4P

2Q1 =c0x16,35 = d0Ph2x10,27 = d0Ph2x10,28 = d0B2Pe0 = e0Ph2B21 =e0B2Pd0 = gPh2Q1 = Q2P

2d0

20 (1) Px16,35

21 (100) d0PR2 = e0R1 = Pd0R2

(010) d30w = d2

0e0v = d20gu = d2

0rk = d0e20u = d0e0rj = d0gri = d0lz =

e20ri = e0gPv = e0kz = e0Pe0w = g2Pu = gjz = gPd0w =

gPe0v = rlPe0 = rmPd0 = ikm = il2 = j2m = jkl = k3

(001) h0Px16,35 = Ph2x16,32

(101) iPQ1 = x′Pj

22 (10) h0iPQ1 = h0x′Pj = f0x18,20 = Ph2ix

′ = B2P2i = B4P

3h2

(01) h20Px16,35 = h0Ph2x16,32

(11) h0d0PR2 = h0e0R1 = h0Pd0R2 = h2d0R1 = P 2h2P2D1 =

R1P2e0

continued



0iPQ1 = h20x

′Pj = h0f0x18,20 = h0Ph2ix′ = h0B2P

2i =h0B4P

3h2 = h1e0x18,20 = h1x′P 2e0 = e0P

2h1x′ = Ph1Pe0x

′ =B1P

3e0 = x10,28P3h1

(01) h30Px16,35 = h2

0Ph2x16,32 = h21Ph1x16,32 = h1P

2h1W1 = h1uQ =h1uPu = h1X1P

3h1 = h3P3Q1 = Ph2

1W1 = Ph1P2h1X1 =

Ph1u2 = qP 2u = GP 4h1

(11) h20d0PR2 = h2

0e0R1 = h20Pd0R2 = h0h2d0R1 = h0P

2h2P2D1 =

h0R1P2e0 = h1d0P

2Q1 = h1Pd0PQ1 = h1Q1 P 2d0 = h22P

2R2 =h2Ph2PR2 = h2P

2h2R2 = h2R1P2d0 = d0Ph1PQ1 =

d0P2h1Q1 = d0P

2h2R1 = Ph1Pd0Q1 = Ph22R2 = Ph2Pd0R1 =

x10,27P3h1

24 (1) d50e0 = d3

0gPe0 = d20e

20Pe0 = d2

0e0gPd0 = d0e30Pd0 = d0g

2P 2e0 =d0iPv = d0jPu = d0uPj = e2

0gP 2e0 = e0g2P 2d0 = e0gPe2

0 =e0iPu = g2Pd0Pe0 = riP j = i2z = iPd0v = iPe0u = jPd0u =kP 2v = lP 2u = wP 2j

27 (1) d30iPd0 = d2

0e0P2j = d2

0gP 2i = d20jP

2e0 = d20kP 2d0 = d2

0Pe0Pj =d0e

20P

2i = d0e0iP2e0 = d0e0jP

2d0 = d0e0Pd0Pj = d0giP 2d0 =d0iPe2

0 = d0jPd0Pe0 = d0kPd20 = d0lP

3e0 = d0mP 3d0 =e20iP

2d0 = e0gP 3j = e0iPd0Pe0 = e0jPd20 = e0kP 3e0 =

e0lP3d0 = giPd2

0 = gjP 3e0 = gkP 3d0 = gPe0P2j = gPjP 2e0 =

kPe0P2e0 = lPd0P

2e0 = lP e0P2d0 = mPd0P

2d0

28 (1) h21P

4x′ = h1P2h1x18,20 = h1x

′P 4h1 = Ph21x18,20 = Ph1x

′P 3h1 =B1P

5h1 = P 2h21x

′

30 (1) d0iP3j = d0PjP 2i = rP 5e0 = i2P 3e0 = ijP 3d0 = iPd0P

2j =iPe0P

2i = iP jP 2d0 = jPd0P2i = kP 4j = lP 4i = zP 4d0

33 (1) P 6u

36 (1) d0P7e0 = e0P


6d0 = P 2d0P5e0 =

P 2e0P5d0 = P 3d0P

4e0 = P 3e0P4d0

37 (1) h0d0P7e0 = h0e0P


6d0 =h0P

2d0P5e0 = h0P

2e0P5d0 = h0P

3d0P4e0 = h0P

3e0P4d0 =

h2d0P7d0 = h2Pd0P

6d0 = h2P2d0P

5d0 = h2P3d0P

4d0 =d20P


6h2 = d0P2h2P

5d0 =d0P

2d0P5h2 = d0P

3h2P4d0 = d0P

3d0P4h2 = gP 8h2 =

Ph2Pd0P5d0 = Ph2P

2d0P4d0 = Ph2P

3d20 = Pd2

0P5h2 =

Pd0P2h2P

4d0 = Pd0P2d0P

4h2 = Pd0P3h2P

3d0 =P 2h2P

2d0P3d0 = P 2d2

0P3h2

continued

94 ROBERT R. BRUNER


0d0P7e0 = h2

0e0P7d0 = h2

0Pd0P6e0 = h2

0Pe0P6d0 =

h20P

2d0P5e0 = h2

0P2e0P

5d0 = h20P

3d0P4e0 = h2

0P3e0P

4d0 =h0h2d0P

7d0 = h0h2Pd0P6d0 = h0h2P

2d0P5d0 =

h0h2P3d0P

4d0 = h0d20P


6h2 =h0d0P

2h2P5d0 = h0d0P

2d0P5h2 = h0d0P

3h2P4d0 =

h0d0P3d0P

4h2 = h0gP 8h2 = h0Ph2Pd0P5d0 =

h0Ph2P2d0P

4d0 = h0Ph2P3d2

0 = h0Pd20P

5h2 =h0Pd0P

2h2P4d0 = h0Pd0P

2d0P4h2 = h0Pd0P

3h2P3d0 =

h0P2h2P

2d0P3d0 = h0P

2d20P

3h2 = h22P

8e0 = h2e0P8h2 =

h2Ph2P7e0 = h2Pe0P

7h2 = h2P2h2P

6e0 = h2P2e0P

6h2 =h2P

3h2P5e0 = h2P

3e0P5h2 = h2P

4h2P4e0 = e0Ph2P

7h2 =e0P

2h2P6h2 = e0P

3h2P5h2 = e0P

4h22 = Ph2

2P6e0 =

Ph2Pe0P6h2 = Ph2P

2h2P5e0 = Ph2P

2e0P5h2 =

Ph2P3h2P

4e0 = Ph2P3e0P

4h2 = Pc0P6i = iP 7c0 =

Pe0P2h2P

5h2 = Pe0P3h2P

4h2 = P 2h22P

4e0 = P 2h2P2e0P

4h2 =P 2h2P

3h2P3e0 = P 2e0P

3h22 = P 3c0P

4i = P 2iP 5c0

39 (1) P 8i


Stem 888 (10) g2

2

(01) h1x7,74

(11) h24D2 = h5Q2

9 (10) h6Pe0

(01) h0h24D2 = h0h5Q2 = h0g

22

10 (1) h0h6Pe0 = h2h6Pd0 = h6d0Ph2

11 (1) h20h6Pe0 = h0h2h6Pd0 = h0h6d0Ph2

12 (100) x12,51

(001) h30h6Pe0 = h2

0h2h6Pd0 = h20h6d0Ph2 = h3

1h6Pd0 = h21h6d0Ph1 =

h1h3h6P2h1 = h1h6c0Pc0 = h2

2h6P2h2 = h2h6Ph2

2 = h3h6Ph21 =

h6c20Ph1 = d0x8,51

(011) gG21 = nQ2 = rD2

13 (10) h1h6P2c0 = h6c0P

2h1 = h6Ph1Pc0

(01) h0x12,51 = h3x12,45

14 (10) h6P3h1

(01) h20x12,51 = h0h3x12,45 = h2

1x12,48 = h1h3x12,44 = d1Q1

16 (1) x16,48

17 (1) d20B4 = e0x13,35 = gP 2D1 = iB23 = jx10,27 = jx10,28 = kB21 =

lQ1 = mx′

18 (10) h1x17,50

(01) h0d20B4 = h0e0x13,35 = h0gP 2D1 = h0iB23 = h0jx10,27 =

h0jx10,28 = h0kB21 = h0lQ1 = h0mx′ = h2d0x13,35 =h2e0P

2D1 = h2gR2 = h2ix10,27 = h2ix10,28 = h2jB21 =h2kQ1 = h2lx

′ = h2Pe0B4 = h4PR2 = d0f0Q1 = d0gR1 =d0jB2 = e2

0R1 = e0f0x′ = e0Ph2B4 = e0iB2 = D2P

2d0 =Pd0B5 = Pd0PD2

19 (1) h20d

20B4 = h2

0e0x13,35 = h20gP 2D1 = h2

0iB23 = h20jx10,27 =

h20jx10,28 = h2

0kB21 = h20lQ1 = h2

0mx′ = h0h2d0x13,35 =h0h2e0P

2D1 = h0h2gR2 = h0h2ix10,27 = h0h2ix10,28 =h0h2jB21 = h0h2kQ1 = h0h2lx

′ = h0h2Pe0B4 = h0h4PR2 =h0d0f0Q1 = h0d0gR1 = h0d0jB2 = h0e

20R1 = h0e0f0x

′ =h0e0Ph2B4 = h0e0iB2 = h0D2P

2d0 = h0Pd0B5 = h0Pd0PD2 =h1d

20B21 = h1d0e0Q1 = h1d0gx′ = h1e

20x

′ = h1Pd0B23 =h1Pe0x10,27 = h1Pe0x10,28 = h2

2d0P2D1 = h2

2e0R2 = h22iB21 =

h22jQ1 = h2

2kx′ = h22Pd0B4 = h2h4R1 = h2d0e0R1 = h2d0f0x

′ =h2d0Ph2B4 = h2d0iB2 = c0x16,37 = d3

0B1 = d0Ph1B23 =e0Ph1x10,27 = e0Ph1x10,28 = e0B1Pe0 = f0Ph2B21 = f0B2Pd0 =gPh1B21 = gB1Pd0 = Ph2kB2 = AP 3h2 = P 2h2PA

continued

96 ROBERT R. BRUNER

Stem 88 continued20 (10) iR2

(01) d20g

3 = d20r

2 = d0e20g

2 = d0kw = d0lv = d0mu = e40g = e0rz =

e0jw = e0kv = e0lu = giw = gjv = gku = rim = rjl = rk2

21 (1) h0iR2 = h1Px16,35 = f0R1 = Ph1x16,35 = Ph2x16,33 = R1Pj

23 (1) d40l = d3

0e0k = d30gj = d2

0e20j = d2

0e0gi = d20mPe0 = d0e

30i =

d0e0lP e0 = d0e0mPd0 = d0g2Pj = d0gkPe0 = d0glPd0 =

e20gPj = e2

0kPe0 = e20lPd0 = e0gjPe0 = e0gkPd0 = g2iPe0 =

g2jPd0 = gmP 2e0 = rP 2v = i2v = iju = zPu

26 (01) d30i

2 = d20rP

2d0 = d20jP j = d0e0iP j = d0rPd2

0 = d0ijPe0 =d0ikPd0 = d0j

2Pd0 = d0lP2j = d0mP 2i = d0zP 2e0 = e0rP

3e0 =e0i

2Pe0 = e0ijPd0 = e0kP 2j = e0lP2i = e0zP 2d0 = grP 3d0 =

gi2Pd0 = gjP 2j = gkP 2i = gPj2 = rPe0P2e0 = ilP 2e0 =

imP 2d0 = jkP 2e0 = jlP 2d0 = k2P 2d0 = kPe0Pj = lPd0Pj =Pd0Pe0z

(11) P 4Q1

27 (1) h0P4Q1 = h2P

4x′ = P 2h2x18,20 = x′P 4h2

28 (1) h20P

4Q1 = h0h2P4x′ = h0P

2h2x18,20 = h0x′P 4h2

29 (10) d0P4v = Pd0P

3v = vP 4d0 = P 2d0P2v = PvP 3d0

(01) h30P

4Q1 = h20h2P

4x′ = h20P

2h2x18,20 = h20x

′P 4h2 = h31P

4x′ =h2

1P2h1x18,20 = h2

1x′P 4h1 = h1Ph2

1x18,20 = h1Ph1x′P 3h1 =

h1B1P5h1 = h1P

2h21x

′ = Ph21P

2h1x′ = Ph1B1P

4h1 =B1P

2h1P3h1 = QP 3e0

(11) e0P4u = rP 4j = i2P 2j = ijP 2i = Pe0P

3u = uP 4e0 =P 2e0P

2u = PuP 3e0

32 (1) d30P

4d0 = d20Pd0P

3d0 = d20P

2d20 = d0e0P

5e0 = d0gP 5d0 =d0Pd2

0P2d0 = d0Pe0P

4e0 = d0P2e0P

3e0 = e20P

5d0 =e0Pd0P

4e0 = e0Pe0P4d0 = e0P

2d0P3e0 = e0P

2e0P3d0 =

gPd0P4d0 = gP 2d0P

3d0 = Pd40 = Pd0Pe0P

3e0 = Pd0P2e2

0 =Pe2

0P3d0 = Pe0P

2d0P2e0

34 (1) h1P6u = Ph1P

4Q = Ph1P5u = P 2h1P

4u = uP 6h1 =P 3h1P

3u = QP 5h1 = PuP 5h1 = P 4h1P2u

35 (1) d0P6j = e0P

6i = iP 6e0 = jP 6d0 = Pd0P5j = PjP 5d0 =

P 2d0P4j = P 2e0P

4i = P 2iP 4e0 = P 2jP 4d0 = P 3d0P3j

36 (1) h0d0P6j = h0e0P

6i = h0iP6e0 = h0jP

6d0 = h0Pd0P5j =

h0PjP 5d0 = h0P2d0P

4j = h0P2e0P

4i = h0P2iP 4e0 =

h0P2jP 4d0 = h0P

3d0P3j = h2d0P

6i = h2iP6d0 = h2P

2d0P4i =

h2P2iP 4d0 = d0iP

6h2 = d0P2h2P

4i = d0P2iP 4h2 =

f0P7d0 = Ph2iP

5d0 = Ph2Pd0P4i = Ph2P

2iP 3d0 =iPd0P

5h2 = iP 2h2P4d0 = iP 2d0P

4h2 = iP 3h2P3d0 = kP 7h2 =

Pd0P3h2P

2i = P 2h2P2d0P

2i

continued



0d0P6j = h2

0e0P6i = h2

0iP6e0 = h2

0jP6d0 = h2

0Pd0P5j =

h20PjP 5d0 = h2

0P2d0P

4j = h20P

2e0P4i = h2

0P2iP 4e0 =

h20P

2jP 4d0 = h20P

3d0P3j = h0h2d0P

6i = h0h2iP6d0 =

h0h2P2d0P

4i = h0h2P2iP 4d0 = h0d0iP

6h2 = h0d0P2h2P

4i =h0d0P

2iP 4h2 = h0f0P7d0 = h0Ph2iP

5d0 = h0Ph2Pd0P4i =

h0Ph2P2iP 3d0 = h0iPd0P

5h2 = h0iP2h2P

4d0 = h0iP2d0P

4h2 =h0iP

3h2P3d0 = h0kP 7h2 = h0Pd0P

3h2P2i = h0P

2h2P2d0P

2i =h1d0P

7e0 = h1e0P7d0 = h1Pd0P

6e0 = h1Pe0P6d0 =

h1P2d0P

5e0 = h1P2e0P

5d0 = h1P3d0P

4e0 = h1P3e0P

4d0 =h2

2P7j = h2Ph2P

6j = h2jP7h2 = h2P

2h2P5j = h2PjP 6h2 =

h2P3h2P

4j = h2P2jP 5h2 = h2P

4h2P3j = d0e0P

7h1 =d0Ph1P

6e0 = d0Pe0P6h1 = d0P

2h1P5e0 = d0P

2e0P5h1 =

d0P3h1P

4e0 = d0P3e0P


6h1 =e0P

2h1P5d0 = e0P

2d0P5h1 = e0P

3h1P4d0 = e0P

3d0P4h1 =

Ph1Pd0P5e0 = Ph1Pe0P

5d0 = Ph1P2d0P

4e0 = Ph1P2e0P

4d0 =Ph1P

3d0P3e0 = Ph2

2P5j = Ph2jP

6h2 = Ph2P2h2P

4j =Ph2PjP 5h2 = Ph2P

3h2P3j = Ph2P

2jP 4h2 = jP 2h2P5h2 =

jP 3h2P4h2 = Pd0Pe0P

5h1 = Pd0P2h1P

4e0 = Pd0P2e0P

4h1 =Pd0P

3h1P3e0 = Pe0P

2h1P4d0 = Pe0P

2d0P4h1 =

Pe0P3h1P

3d0 = P 2h1P2d0P

3e0 = P 2h1P2e0P

3d0 = P 2h22P

3j =P 2h2PjP 4h2 = P 2h2P

3h2P2j = PjP 3h2

2 = P 2d0P2e0P

3h1

98 ROBERT R. BRUNER

Stem 897 (1) h2

2h6g = h4h6Ph2 = h5D2

8 (1) h6j

9 (1) h0h6j = h2h6i

10 (1) h20h6j = h0h2h6i = h1h6Pe0 = h6e0Ph1

11 (1) x11,59

12 (1) h0x11,59

13 (1) h20x11,59 = h1x12,51 = h2x12,48 = qQ2

15 (1) h1h6P3h1 = h6Ph1P

2h1

16 (1) rB21 = kB4

18 (1) x18,50

19 (10) d0g2m = d0rw = e2

0gm = e0g2l = e0rv = g3k = gru = r2k

(01) h0x18,50 = h21x17,50 = Ph1x14,42

22 (10) d0Pd0x′ = e0P

2Q1 = Pe0PQ1 = Q1 P 2e0 = B21P2d0

(01) d30e0r = d2

0gz = d20jm = d2

0kl = d0e20z = d0e0im = d0e0jl =

d0e0k2 = d0grPe0 = d0gil = d0gjk = e2

0rPe0 = e20il = e2

0jk =e0grPd0 = e0gik = e0gj2 = g2ij = gmPj = kmPe0 = l2Pe0 =lmPd0 = uPv = vPu

(11) gx18,20

23 (1) h0d0Pd0x′ = h0e0P

2Q1 = h0gx18,20 = h0Pe0PQ1 =h0Q1 P 2e0 = h0B21P

2d0 = h2d0P2Q1 = h2e0x18,20 =

h2Pd0PQ1 = h2x′P 2e0 = h2Q1 P 2d0 = d0Ph2PQ1 =

d0P2h2Q1 = e0P

2h2x′ = Ph2Pd0Q1 = Ph2Pe0x

′ = B2P3e0 =

x10,27P3h2 = x10,28P

3h2

24 (1) h20d0Pd0x

′ = h20e0P

2Q1 = h20gx18,20 = h2

0Pe0PQ1 =h2

0Q1 P 2e0 = h20B21P

2d0 = h0h2d0P2Q1 = h0h2e0x18,20 =

h0h2Pd0PQ1 = h0h2x′P 2e0 = h0h2Q1 P 2d0 = h0d0Ph2PQ1 =

h0d0P2h2Q1 = h0e0P

2h2x′ = h0Ph2Pd0Q1 = h0Ph2Pe0x

′ =h0B2P

3e0 = h0x10,27P3h2 = h0x10,28P

3h2 = h22d0x18,20 =

h22x

′P 2d0 = h2d0P2h2x

′ = h2Ph2Pd0x′ = h2B2P

3d0 =h2B21P

3h2 = c0P2R2 = d0Ph2

2x′ = d0B2P

3h2 = Ph2B2P2d0 =

Ph2P2h2B21 = Pc0PR2 = B2Pd0P

2h2 = P 2c0R2

25 (01) d30Pu = d2

0Pd0u = d0e0P2v = d0gP 2u = d0riPd0 = d0i

2k =d0ij

2 = d0Pe0Pv = d0vP 2e0 = d0wP 2d0 = d0zPj = e20P

2u =e0rP

2j = e0i2j = e0Pd0Pv = e0Pe0Pu = e0uP 2e0 = e0vP 2d0 =

grP 2i = gi3 = gPd0Pu = guP 2d0 = rjP 2e0 = rkP 2d0 =rPe0Pj = ilP j = iPe0z = jkPj = jPd0z = Pd2

0w = Pd0Pe0v =Pe2

0u

(11) P 3R2

26 (1) h0P3R2 = h2x25,24 = P 2h2R1

continued



0P3R2 = h0h2x25,24 = h0P

2h2R1 = h1P4Q1 = Ph1P

3Q1 =P 2h1P

2Q1 = R1P4h2 = Q1 P 4h1 = P 3h1PQ1

28 (1) d40P

2e0 = d30e0P

2d0 = d30Pd0Pe0 = d2

0e0Pd20 = d2

0gP 3e0 =d0e

20P

3e0 = d0e0gP 3d0 = d0e0Pe0P2e0 = d0gPd0P

2e0 =d0gPe0P

2d0 = d0Pe30 = e3

0P3d0 = e2

0Pd0P2e0 = e2

0Pe0P2d0 =

e0gPd0P2d0 = e0Pd0Pe2

0 = g2P 4e0 = gPd20Pe0 = iP 3v = jP 3u =

uP 3j = PjP 2u = PuP 2j = PvP 2i

31 (1) d20iP

3d0 = d20Pd0P

2i = d0e0P4j = d0gP 4i = d0iPd0P

2d0 =d0jP

4e0 = d0kP 4d0 = d0Pe0P3j = d0PjP 3e0 = d0P

2e0P2j =

e20P

4i = e0iP4e0 = e0jP

4d0 = e0Pd0P3j = e0PjP 3d0 =

e0P2d0P

2j = e0P2e0P

2i = giP 4d0 = gP 2d0P2i = iPd3

0 =iPe0P

3e0 = iP 2e20 = jPd0P

3e0 = jPe0P3d0 = jP 2d0P

2e0 =kPd0P

3d0 = kP 2d20 = lP 5e0 = mP 5d0 = Pd0Pe0P

2j =Pd0PjP 2e0 = Pe2

0P2i = Pe0PjP 2d0

34 (1) iP 5j = PjP 4i = P 2iP 3j

35 (1) h0iP5j = h0PjP 4i = h0P

2iP 3j = h21P

6u = h1Ph1P4Q =

h1Ph1P5u = h1P

2h1P4u = h1uP 6h1 = h1P

3h1P3u =

h1QP 5h1 = h1PuP 5h1 = h1P4h1P

2u = f0P6i = Ph2

1P4u =

Ph1P2h1P

3u = Ph1uP 5h1 = Ph1P3h1P

2u = Ph1QP 4h1 =Ph1PuP 4h1 = Ph2iP

4i = Ph2P2i2 = rP 7h2 = qP 7h1 =

i2P 5h2 = iP 3h2P2i = P 2h2

1P2u = P 2h1uP 4h1 = P 2h1P

3h1Q =P 2h1P

3h1Pu = uP 3h21

100 ROBERT R. BRUNER

Stem 9010 (1) x10,63

11 (1) h0x10,63 = pQ2

12 (1) x12,55

13 (1) h0x12,55

14 (10) h6P3h2

(01) h20x12,55

15 (010) h0h6P3h2

(001) h30x12,55 = xx′

(101) rB4

16 (01) h40x12,55 = h0xx′ = h0rB4 = h3x15,41 = ix9,40

(11) h20h6P

3h2 = h21h6P

3h1 = h1h6Ph1P2h1 = h6Ph3

1

17 (10) x17,52

(01) h50x12,55 = h2

0xx′ = h20rB4 = h0h3x15,41 = h0ix9,40 = h3rx

′ =h3iB4

18 (100) g3r = gm2 = w2

(001) h60x12,55 = h3

0xx′ = h30rB4 = h2

0h3x15,41 = h20ix9,40 = h0h3rx

′ =h0h3iB4 = h2

3x16,32 = g2i2 = xri = ix11,35

(101) r3

(011) d20x10,27 = d2

0x10,28 = d0e0B21 = d0gQ1 = e20Q1 = e0gx′ =

Pe0B23

19 (1) h70x12,55 = h4

0xx′ = h40rB4 = h3

0h3x15,41 = h30ix9,40 = h2

0h3rx′ =

h20h3iB4 = h0h

23x16,32 = h0d

20x10,27 = h0d

20x10,28 = h0d0e0B21 =

h0d0gQ1 = h0e20Q1 = h0e0gx′ = h0g2i

2 = h0xri = h0r3 =

h0ix11,35 = h0Pe0B23 = h1x18,50 = h2d20B21 = h2d0e0Q1 =

h2d0gx′ = h2e20x

′ = h2Pd0B23 = h2Pe0x10,27 = h2Pe0x10,28 =h2

3ix′ = h4Pd0x

′ = c0x16,38 = d30B2 = d0Ph2B23 = e0Ph2x10,27 =

e0Ph2x10,28 = e0B2Pe0 = gPh2B21 = gB2Pd0 = Q2P2e0 =

B3P2d0

20 (1) d0x16,32

21 (100) e0PR2 = gR1 = Pd0P2D1 = Pe0R2

(010) d20e0w = d2

0gv = d20rl = d0e

20v = d0e0gu = d0e0rk = d0grj =

d0mz = e30u = e2

0rj = e0gri = e0lz = g2Pv = gkz = gPe0w =rmPe0 = ilm = jkm = jl2 = k2l

(001) h0d0x16,32 = h2Px16,35 = Ph2x16,35

(101) d0ix′ = jPQ1 = B4P

2d0 = Q1 Pj

22 (10) h0d0ix′ = h0jPQ1 = h0B4P

2d0 = h0Q1 Pj = h2iPQ1 =h2x

′Pj = f0P2Q1 = Ph2iQ1 = Ph2jx

′ = B2P2j = P 2h2x13,35

(01) h20d0x16,32 = h0h2Px16,35 = h0Ph2x16,35 = h2Ph2x16,32 =

P 2h2x13,34

(11) h0e0PR2 = h0gR1 = h0Pd0P2D1 = h0Pe0R2 = h2d0PR2 =

h2e0R1 = h2Pd0R2 = d0Ph2R2 = d0Pd0R1

continued



0d0ix′ = h2

0e0PR2 = h20gR1 = h2

0jPQ1 = h20Pd0P

2D1 =h2

0Pe0R2 = h20B4P

2d0 = h20Q1 Pj = h0h2d0PR2 = h0h2e0R1 =

h0h2iPQ1 = h0h2Pd0R2 = h0h2x′Pj = h0d0Ph2R2 =

h0d0Pd0R1 = h0f0P2Q1 = h0Ph2iQ1 = h0Ph2jx

′ = h0B2P2j =

h0P2h2x13,35 = h1d0Pd0x

′ = h1e0P2Q1 = h1gx18,20 =

h1Pe0PQ1 = h1Q1 P 2e0 = h1B21P2d0 = h2

2d0R1 = h2f0x18,20 =h2Ph2ix

′ = h2B2P2i = h2P

2h2P2D1 = h2B4P

3h2 = h2R1P2e0 =

d20Ph1x

′ = d0B1P2d0 = d0P

2h1B21 = e0Ph1PQ1 = e0P2h1Q1 =

e0P2h2R1 = f0P

2h2x′ = gP 2h1x

′ = Ph1Pd0B21 = Ph1Pe0Q1 =Ph2

2P2D1 = Ph2Pe0R1 = Ph2P

2h2B4 = iB2P2h2 = B1Pd2

0 =B23P

3h1

24 (1) d50g = d4

0e20 = d2

0e0gPe0 = d20g

2Pd0 = d20iu = d0e

30Pe0 =

d0e20gPd0 = d0ri

2 = d0jPv = d0kPu = d0vPj = e40Pd0 =

e0g2P 2e0 = e0iPv = e0jPu = e0uPj = g3P 2d0 = g2Pe2

0 =giPu = r2P 2d0 = rjPj = ijz = iPd0w = iPe0v = jPd0v =jPe0u = kPd0u = lP 2v = mP 2u

27 (1) d40Pj = d3

0iPe0 = d30jPd0 = d2

0e0iPd0 = d20gP 2j = d2

0kP 2e0 =d20lP

2d0 = d0e20P

2j = d0e0gP 2i = d0e0jP2e0 = d0e0kP 2d0 =

d0e0Pe0Pj = d0giP 2e0 = d0gjP 2d0 = d0gPd0Pj = d0jPe20 =

d0kPd0Pe0 = d0lPd20 = d0mP 3e0 = e3

0P2i = e2

0iP2e0 =

e20jP

2d0 = e20Pd0Pj = e0giP 2d0 = e0iPe2

0 = e0jPd0Pe0 =e0kPd2

0 = e0lP3e0 = e0mP 3d0 = g2P 3j = giPd0Pe0 = gjPd2

0 =gkP 3e0 = glP 3d0 = lP e0P

2e0 = mPd0P2e0 = mPe0P

2d0

30 (1) d20iP

2i = d0rP4d0 = d0i

2P 2d0 = d0jP3j = d0PjP 2j = e0iP

3j =e0PjP 2i = rPd0P

3d0 = rP 2d20 = i2Pd2

0 = ijP 3e0 = ikP 3d0 =iPe0P

2j = iP jP 2e0 = j2P 3d0 = jPd0P2j = jPe0P

2i =jP jP 2d0 = kPd0P

2i = lP 4j = mP 4i = Pd0Pj2 = zP 4e0

33 (1) P 6v

36 (1) d20P

6d0 = d0Pd0P5d0 = d0P

2d0P4d0 = d0P

3d20 = e0P

7e0 =gP 7d0 = Pd2

0P4d0 = Pd0P

2d0P3d0 = Pe0P

6e0 = P 2d30 =

P 2e0P5e0 = P 3e0P

4e0

continued


Stem 90 continued37 (1) h0d

20P


2d0P4d0 = h0d0P

3d20 =


0P4d0 = h0Pd0P

2d0P3d0 =

h0Pe0P6e0 = h0P

2d30 = h0P

2e0P5e0 = h0P

3e0P4e0 =

h2d0P7e0 = h2e0P


6d0 =h2P

2d0P5e0 = h2P

2e0P5d0 = h2P

3d0P4e0 = h2P

3e0P4d0 =

d0e0P7h2 = d0Ph2P

6e0 = d0Pe0P6h2 = d0P

2h2P5e0 =

d0P2e0P

5h2 = d0P3h2P

4e0 = d0P3e0P

4h2 = e0Ph2P6d0 =

e0Pd0P6h2 = e0P

2h2P5d0 = e0P

2d0P5h2 = e0P

3h2P4d0 =

e0P3d0P

4h2 = Ph2Pd0P5e0 = Ph2Pe0P

5d0 = Ph2P2d0P

4e0 =Ph2P

2e0P4d0 = Ph2P

3d0P3e0 = Pd0Pe0P

5h2 =Pd0P

2h2P4e0 = Pd0P

2e0P4h2 = Pd0P

3h2P3e0 =

Pe0P2h2P

4d0 = Pe0P2d0P

4h2 = Pe0P3h2P

3d0 =P 2h2P

2d0P3e0 = P 2h2P

2e0P3d0 = P 2d0P

2e0P3h2

38 (1) h20d

20P

6d0 = h20d0Pd0P

5d0 = h20d0P

2d0P4d0 = h2

0d0P3d2

0 =h2

0e0P7e0 = h2

0gP 7d0 = h20Pd2

0P4d0 = h2

0Pd0P2d0P

3d0 =h2

0Pe0P6e0 = h2

0P2d3

0 = h20P

2e0P5e0 = h2

0P3e0P

4e0 =h0h2d0P

7e0 = h0h2e0P7d0 = h0h2Pd0P

6e0 = h0h2Pe0P6d0 =

h0h2P2d0P

5e0 = h0h2P2e0P

5d0 = h0h2P3d0P

4e0 =h0h2P

3e0P4d0 = h0d0e0P

7h2 = h0d0Ph2P6e0 =

h0d0Pe0P6h2 = h0d0P

2h2P5e0 = h0d0P

2e0P5h2 =

h0d0P3h2P

4e0 = h0d0P3e0P

4h2 = h0e0Ph2P6d0 =

h0e0Pd0P6h2 = h0e0P

2h2P5d0 = h0e0P

2d0P5h2 =

h0e0P3h2P

4d0 = h0e0P3d0P

4h2 = h0Ph2Pd0P5e0 =

h0Ph2Pe0P5d0 = h0Ph2P

2d0P4e0 = h0Ph2P

2e0P4d0 =

h0Ph2P3d0P

3e0 = h0Pd0Pe0P5h2 = h0Pd0P

2h2P4e0 =

h0Pd0P2e0P

4h2 = h0Pd0P3h2P

3e0 = h0Pe0P2h2P

4d0 =h0Pe0P

2d0P4h2 = h0Pe0P

3h2P3d0 = h0P

2h2P2d0P

3e0 =h0P

2h2P2e0P

3d0 = h0P2d0P

2e0P3h2 = h2

2d0P7d0 =

h22Pd0P

6d0 = h22P

2d0P5d0 = h2

2P3d0P

4d0 = h2d20P

7h2 =h2d0Ph2P


2h2P5d0 =

h2d0P2d0P

5h2 = h2d0P3h2P

4d0 = h2d0P3d0P

4h2 =h2gP 8h2 = h2Ph2Pd0P

5d0 = h2Ph2P2d0P

4d0 = h2Ph2P3d2

0 =h2Pd2

0P5h2 = h2Pd0P

2h2P4d0 = h2Pd0P

2d0P4h2 =

h2Pd0P3h2P

3d0 = h2P2h2P

2d0P3d0 = h2P

2d20P

3h2 = h4P9h2 =

c0P7j = d2

0Ph2P6h2 = d2

0P2h2P

5h2 = d20P

3h2P4h2 =

d0Ph22P

5d0 = d0Ph2Pd0P5h2 = d0Ph2P

2h2P4d0 =

d0Ph2P2d0P

4h2 = d0Ph2P3h2P

3d0 = d0Pd0P2h2P

4h2 =d0Pd0P

3h22 = d0P

2h22P

3d0 = d0P2h2P

2d0P3h2 = gPh2P

7h2 =gP 2h2P

6h2 = gP 3h2P5h2 = gP 4h2

2 = Ph22Pd0P

4d0 =Ph2

2P2d0P

3d0 = Ph2Pd20P

4h2 = Ph2Pd0P2h2P

3d0 =Ph2Pd0P

2d0P3h2 = Ph2P

2h2P2d2

0 = Pc0P6j = jP 7c0 =

Pd20P

2h2P3h2 = Pd0P

2h22P

2d0 = P 2c0P5j = PjP 6c0 =

P 3c0P4j = P 2jP 5c0 = P 4c0P

3j

39 (1) P 8j


Stem 916 (1) h2

4D3

8 (1) x8,75

9 (10) h6d20

(01) h0x8,75

10 (1) h0h6d20 = h2h6Pe0 = h6e0Ph2

11 (10) x11,61

(01) h20h6d

20 = h0h2h6Pe0 = h0h6e0Ph2 = h2

2h6Pd0 = h2h6d0Ph2

12 (01) h0x11,61

(11) rA′ = rA

13 (10) h1x12,55

(01) h20x11,61

14 (1) h30x11,61

15 (1) h40x11,61 = xR1 = rX1 = iG21

16 (1) h50x11,61 = h0xR1 = h0rX1 = h0iG21 = h3x15,42 = yx′

17 (100) g3n = gtm = nr2 = Nw

(001) h60x11,61 = h2

0xR1 = h20rX1 = h2

0iG21 = h0h3x15,42 = h0yx′ =h3rR1 = h3iX1 = h4x16,32 = g2Q

(011) d0e0B4 = gx13,35 = jB23 = kx10,27 = kx10,28 = lB21 = mQ1

18 (1) h70x11,61 = h3

0xR1 = h30rX1 = h3

0iG21 = h20h3x15,42 = h2

0yx′ =h0h3rR1 = h0h3iX1 = h0h4x16,32 = h0d0e0B4 = h0gx13,35 =h0g2Q = h0jB23 = h0kx10,27 = h0kx10,28 = h0lB21 = h0mQ1 =h2d

20B4 = h2e0x13,35 = h2gP 2D1 = h2iB23 = h2jx10,27 =

h2jx10,28 = h2kB21 = h2lQ1 = h2mx′ = h23x16,33 = d0f0B21 =

d0kB2 = e0f0Q1 = e0gR1 = e0jB2 = f0gx′ = gPh2B4 = giB2 =D2P

2e0 = AP 2d0 = Q2Pj = Pd0PA = Pe0B5 = Pe0PD2

continued



0x11,61 = h40xR1 = h4

0rX1 = h40iG21 = h3

0h3x15,42 =h3

0yx′ = h20h3rR1 = h2

0h3iX1 = h20h4x16,32 = h2

0d0e0B4 =h2

0gx13,35 = h20g2Q = h2

0jB23 = h20kx10,27 = h2

0kx10,28 =h2

0lB21 = h20mQ1 = h0h2d

20B4 = h0h2e0x13,35 = h0h2gP 2D1 =

h0h2iB23 = h0h2jx10,27 = h0h2jx10,28 = h0h2kB21 = h0h2lQ1 =h0h2mx′ = h0h

23x16,33 = h0d0f0B21 = h0d0kB2 = h0e0f0Q1 =

h0e0gR1 = h0e0jB2 = h0f0gx′ = h0gPh2B4 = h0giB2 =h0D2P

2e0 = h0AP 2d0 = h0Q2Pj = h0Pd0PA = h0Pe0B5 =h0Pe0PD2 = h1d

20x10,27 = h1d

20x10,28 = h1d0e0B21 = h1d0gQ1 =

h1e20Q1 = h1e0gx′ = h1Pe0B23 = h2

2d0x13,35 = h22e0P

2D1 =h2

2gR2 = h22ix10,27 = h2

2ix10,28 = h22jB21 = h2

2kQ1 = h22lx

′ =h2

2Pe0B4 = h2h4PR2 = h2d0f0Q1 = h2d0gR1 = h2d0jB2 =h2e

20R1 = h2e0f0x

′ = h2e0Ph2B4 = h2e0iB2 = h2D2P2d0 =

h2Pd0B5 = h2Pd0PD2 = h23iR1 = h3xQ = h4Ph2R2 =

h4Pd0R1 = c0rx′ = c0iB4 = d2

0e0B1 = d0Ph2B5 = d0Ph2PD2 =d0D2P

2h2 = e0Ph1B23 = f0Ph2x10,27 = f0Ph2x10,28 =f0B2Pe0 = gPh1x10,27 = gPh1x10,28 = gB1Pe0 = Ph2D2Pd0 =Ph2iQ2 = Ph2lB2 = ryi = A′′P 3h2

20 (10) d0x16,33 = iP 2D1 = jR2

(01) d0e0g3 = d0e0r

2 = d0lw = d0mv = e30g

2 = e0kw = e0lv = e0mu =grz = gjw = gkv = glu = rjm = rkl

21 (1) h0d0x16,33 = h0iP2D1 = h0jR2 = h1d0x16,32 = h2iR2 = d0iR1 =

f0PR2 = Ph1x16,38 = Ph2x16,37 = Pd0W1

23 (1) d40m = d3

0e0l = d30gk = d2

0e20k = d2

0e0gj = d20g

2i = d0e30j =

d0e20gi = d0e0mPe0 = d0glPe0 = d0gmPd0 = d0rPu = e4

0i =e20lP e0 = e2

0mPd0 = e0g2Pj = e0gkPe0 = e0glPd0 = g2jPe0 =

g2kPd0 = rPd0u = i2w = ijv = iku = j2u = zPv

26 (10) Pd0x18,20

(01) d30ij = d2

0e0i2 = d2

0rP2e0 = d2

0kPj = d20Pd0z = d0e0rP

2d0 =d0e0jP j = d0giP j = d0rPd0Pe0 = d0ikPe0 = d0ilPd0 =d0j

2Pe0 = d0jkPd0 = d0mP 2j = e20iP j = e0rPd2

0 = e0ijPe0 =e0ikPd0 = e0j

2Pd0 = e0lP2j = e0mP 2i = e0zP 2e0 = grP 3e0 =

gi2Pe0 = gijPd0 = gkP 2j = glP 2i = gzP 2d0 = imP 2e0 =jlP 2e0 = jmP 2d0 = k2P 2e0 = klP 2d0 = lP e0Pj = mPd0Pj =Pe2

0z

(11) x′P 3d0

27 (1) h0Pd0x18,20 = h0x′P 3d0 = h2P

4Q1 = Ph2P3Q1 = P 2h2P

2Q1 =Q1 P 4h2 = P 3h2PQ1

continued



0Pd0x18,20 = h20x

′P 3d0 = h0h2P4Q1 = h0Ph2P

3Q1 =h0P

2h2P2Q1 = h0Q1 P 4h2 = h0P

3h2PQ1 = h22P

4x′ =h2P

2h2x18,20 = h2x′P 4h2 = Ph2

2x18,20 = Ph2x′P 3h2 = B2P

5h2 =P 2h2

2x′

29 (1) d20P

3u = d0Pd0P2u = d0uP 3d0 = d0P

2d0Pu = e0P4v = gP 4u =

riP 3d0 = rPd0P2i = i3Pd0 = ijP 2j = ikP 2i = iP j2 = j2P 2i =

Pd20Pu = Pd0uP 2d0 = Pe0P

3v = vP 4e0 = wP 4d0 = zP 3j =P 2e0P

2v = PvP 3e0

32 (1) d30P

4e0 = d20e0P

4d0 = d20Pd0P

3e0 = d20Pe0P

3d0 = d20P

2d0P2e0 =

d0e0Pd0P3d0 = d0e0P

2d20 = d0gP 5e0 = d0Pd2

0P2e0 =

d0Pd0Pe0P2d0 = e2

0P5e0 = e0gP 5d0 = e0Pd2

0P2d0 =

e0Pe0P4e0 = e0P

2e0P3e0 = gPd0P

4e0 = gPe0P4d0 =

gP 2d0P3e0 = gP 2e0P

3d0 = Pd30Pe0 = Pe2

0P3e0 = Pe0P

2e20

35 (1) d0iP5d0 = d0Pd0P

4i = d0P2iP 3d0 = e0P

6j = gP 6i =iPd0P

4d0 = iP 2d0P3d0 = jP 6e0 = kP 6d0 = Pd0P

2d0P2i =

Pe0P5j = PjP 5e0 = P 2e0P

4j = P 2jP 4e0 = P 3e0P3j

36 (1) h0d0iP5d0 = h0d0Pd0P

4i = h0d0P2iP 3d0 = h0e0P

6j =h0gP 6i = h0iPd0P

4d0 = h0iP2d0P

3d0 = h0jP6e0 = h0kP 6d0 =

h0Pd0P2d0P

2i = h0Pe0P5j = h0PjP 5e0 = h0P

2e0P4j =

h0P2jP 4e0 = h0P

3e0P3j = h2d0P

6j = h2e0P6i = h2iP

6e0 =h2jP

6d0 = h2Pd0P5j = h2PjP 5d0 = h2P

2d0P4j = h2P

2e0P4i =

h2P2iP 4e0 = h2P

2jP 4d0 = h2P3d0P

3j = d0Ph2P5j =

d0jP6h2 = d0P

2h2P4j = d0PjP 5h2 = d0P

3h2P3j =

d0P2jP 4h2 = e0iP

6h2 = e0P2h2P

4i = e0P2iP 4h2 = f0P

7e0 =Ph2iP

5e0 = Ph2jP5d0 = Ph2Pd0P

4j = Ph2Pe0P4i =

Ph2PjP 4d0 = Ph2P2d0P

3j = Ph2P2iP 3e0 = Ph2P

2jP 3d0 =iPe0P

5h2 = iP 2h2P4e0 = iP 2e0P

4h2 = iP 3h2P3e0 =

jPd0P5h2 = jP 2h2P

4d0 = jP 2d0P4h2 = jP 3h2P

3d0 = lP 7h2 =Pd0P

2h2P3j = Pd0PjP 4h2 = Pd0P

3h2P2j = Pe0P

3h2P2i =

P 2h2PjP 3d0 = P 2h2P2d0P

2j = P 2h2P2e0P

2i = PjP 2d0P3h2

continued



0d0iP5d0 = h2

0d0Pd0P4i = h2

0d0P2iP 3d0 = h2

0e0P6j =

h20gP 6i = h2

0iPd0P4d0 = h2

0iP2d0P

3d0 = h20jP

6e0 =h2

0kP 6d0 = h20Pd0P

2d0P2i = h2

0Pe0P5j = h2

0PjP 5e0 =h2

0P2e0P

4j = h20P

2jP 4e0 = h20P

3e0P3j = h0h2d0P

6j =h0h2e0P

6i = h0h2iP6e0 = h0h2jP

6d0 = h0h2Pd0P5j =

h0h2PjP 5d0 = h0h2P2d0P

4j = h0h2P2e0P

4i = h0h2P2iP 4e0 =

h0h2P2jP 4d0 = h0h2P

3d0P3j = h0d0Ph2P

5j = h0d0jP6h2 =

h0d0P2h2P

4j = h0d0PjP 5h2 = h0d0P3h2P

3j = h0d0P2jP 4h2 =

h0e0iP6h2 = h0e0P

2h2P4i = h0e0P

2iP 4h2 = h0f0P7e0 =



4i =h0Ph2PjP 4d0 = h0Ph2P

2d0P3j = h0Ph2P

2iP 3e0 =h0Ph2P

2jP 3d0 = h0iPe0P5h2 = h0iP

2h2P4e0 = h0iP

2e0P4h2 =

h0iP3h2P

3e0 = h0jPd0P5h2 = h0jP

2h2P4d0 = h0jP

2d0P4h2 =

h0jP3h2P



h0Pd0P3h2P

2j = h0Pe0P3h2P

2i = h0P2h2PjP 3d0 =

h0P2h2P

2d0P2j = h0P

2h2P2e0P

2i = h0PjP 2d0P3h2 =

h1d20P


2d0P4d0 = h1d0P

3d20 =


0P4d0 = h1Pd0P

2d0P3d0 =

h1Pe0P6e0 = h1P

2d30 = h1P

2e0P5e0 = h1P

3e0P4e0 =

h22d0P

6i = h22iP

6d0 = h22P

2d0P4i = h2

2P2iP 4d0 =

h2d0iP6h2 = h2d0P

2h2P4i = h2d0P

2iP 4h2 = h2f0P7d0 =

h2Ph2iP5d0 = h2Ph2Pd0P

4i = h2Ph2P2iP 3d0 = h2iPd0P

5h2 =h2iP

2h2P4d0 = h2iP

2d0P4h2 = h2iP

3h2P3d0 = h2kP 7h2 =

h2Pd0P3h2P

2i = h2P2h2P

2d0P2i = d3

0P6h1 = d2

0Ph1P5d0 =

d20Pd0P

5h1 = d20P

2h1P4d0 = d2

0P2d0P

4h1 = d20P

3h1P3d0 =

d0f0P7h2 = d0gP 7h1 = d0Ph1Pd0P

4d0 = d0Ph1P2d0P

3d0 =d0Ph2

2P4i = d0Ph2iP

5h2 = d0Ph2P3h2P

2i = d0iP2h2P

4h2 =d0iP

3h22 = d0Pd2

0P4h1 = d0Pd0P

2h1P3d0 = d0Pd0P

2d0P3h1 =

d0P2h1P

2d20 = d0P

2h22P

2i = e20P

7h1 = e0Ph1P6e0 =

e0Pe0P6h1 = e0P

2h1P5e0 = e0P

2e0P5h1 = e0P

3h1P4e0 =

e0P3e0P

4h1 = f0Ph2P6d0 = f0Pd0P

6h2 = f0P2h2P

5d0 =f0P

2d0P5h2 = f0P

3h2P4d0 = f0P

3d0P4h2 = gPh1P

6d0 =gPd0P

6h1 = gP 2h1P5d0 = gP 2d0P

5h1 = gP 3h1P4d0 =

gP 3d0P4h1 = Ph1Pd2

0P3d0 = Ph1Pd0P

2d20 = Ph1Pe0P

5e0 =Ph1P

2e0P4e0 = Ph1P

3e20 = Ph2

2iP4d0 = Ph2

2P2d0P

2i =Ph2iPd0P

4h2 = Ph2iP2h2P

3d0 = Ph2iP2d0P

3h2 =Ph2kP 6h2 = Ph2Pd0P

2h2P2i = iPd0P

2h2P3h2 = iP 2h2

2P2d0 =

kP 2h2P5h2 = kP 3h2P

4h2 = Pd30P

3h1 = Pd20P

2h1P2d0 =

Pe20P

5h1 = Pe0P2h1P

4e0 = Pe0P2e0P

4h1 = Pe0P3h1P

3e0 =P 2h1P

2e0P3e0 = P 2e2

0P3h1


Stem 924 (1) g3

5 (1) h0g3

6 (1) h20g3

7 (10) h1h24D3 = h3x6,68 = h5A

′ = c0f2

(01) h30g3

8 (10) h6k

(01) h40g3 = h4x7,57

9 (100) h1x8,75

(010) h0h6k = h2h6j

(001) h50g3 = h0h4x7,57

10 (10) x10,65

(01) h20h6k = h0h2h6j = h1h6d

20 = h2

2h6i = h6f0Ph2 = h6gPh1

11 (10) nA′ = nA = H1r

(01) h0x10,65

12 (10) x12,58

(01) h20x10,65 = h1x11,61

13 (1) h0x12,58

14 (100) rx8,33 = mQ2

(010) h21x12,55 = B2

1

(001) h20x12,58 = h3x13,46

16 (1) rx10,27 = rx10,28 = lB4

18 (1) x18,55

19 (10) e0g2m = e0rw = g3l = grv = r2l

(01) ux′

22 (01) d30gr = d2

0e20r = d2

0km = d20l

2 = d0e0gz = d0e0jm = d0e0kl =d0gim = d0gjl = d0gk2 = d0u

2 = e30z = e2

0im = e20jl = e2

0k2 =

e0grPe0 = e0gil = e0gjk = g2rPd0 = g2ik = g2j2 = riu =lmPe0 = m2Pd0 = vPv = wPu

(11) d20PQ1 = d0Pd0Q1 = d0Pe0x

′ = e0Pd0x′ = gP 2Q1 =

B21P2e0 = x10,27P

2d0 = x10,28P2d0

23 (1) h0d20PQ1 = h0d0Pd0Q1 = h0d0Pe0x

′ = h0e0Pd0x′ =

h0gP 2Q1 = h0B21P2e0 = h0x10,27P

2d0 = h0x10,28P2d0 =

h2d0Pd0x′ = h2e0P

2Q1 = h2gx18,20 = h2Pe0PQ1 =h2Q1 P 2e0 = h2B21P

2d0 = d20Ph2x

′ = d0B2P2d0 = d0P

2h2B21 =e0Ph2PQ1 = e0P

2h2Q1 = gP 2h2x′ = Ph2Pd0B21 =

Ph2Pe0Q1 = Pc0x16,32 = B2Pd20 = B23P

3h2

24 (1) P 2x16,32

continued


Stem 92 continued25 (100) x′P 2i

(001) h0P2x16,32

(101) Pd0R1

(011) d30Pv = d2

0e0Pu = d20rPj = d2

0iz = d20Pd0v = d2

0Pe0u =d0e0Pd0u = d0gP 2v = d0riPe0 = d0rjPd0 = d0i

2l = d0ijk =d0j

3 = d0wP 2e0 = e20P

2v = e0gP 2u = e0riPd0 = e0i2k = e0ij

2 =e0Pe0Pv = e0vP 2e0 = e0wP 2d0 = e0zPj = grP 2j = gi2j =gPd0Pv = gPe0Pu = guP 2e0 = gvP 2d0 = rkP 2e0 = rlP 2d0 =imPj = jlP j = jPe0z = k2Pj = kPd0z = Pd0Pe0w = Pe2

0v

(111) ix18,20

26 (10) h0ix18,20 = h0x′P 2i

(01) h20P

2x16,32

(11) h0Pd0R1 = h2P3R2 = Ph2P

2R2 = P 2h2PR2 = R1P3d0 =

P 3h2R2

27 (10) h20Pd0R1 = h0h2P

3R2 = h0Ph2P2R2 = h0P

2h2PR2 =h0R1P

3d0 = h0P3h2R2 = h1Pd0x18,20 = h1x

′P 3d0 = h22x25,24 =

h2P2h2R1 = d0Ph1x18,20 = d0x

′P 3h1 = Ph1x′P 2d0 = Ph2

2R1 =B1P

4d0 = Pd0P2h1x

′ = B21P4h1

(01) h30P

2x16,32 = h3P4x′

(11) h20ix18,20 = h2

0x′P 2i

28 (10) d50Pd0 = d3

0e0P2e0 = d3

0gP 2d0 = d30Pe2

0 = d20e

20P

2d0 =d20e0Pd0Pe0 = d2

0gPd20 = d0e

20Pd2

0 = d0e0gP 3e0 = d0g2P 3d0 =

d0gPe0P2e0 = d0iP

2u = d0uP 2i = e30P

3e0 = e20gP 3d0 =

e20Pe0P

2e0 = e0gPd0P2e0 = e0gPe0P

2d0 = e0Pe30 =

g2Pd0P2d0 = gPd0Pe2

0 = iPd0Pu = iuP 2d0 = jP 3v = kP 3u =vP 3j = PjP 2v = PvP 2j

(01) h40P

2x16,32 = h30ix18,20 = h3

0x′P 2i = h0h3P

4x′ = xP 4i

(11) riP 2i = i4

29 (1) h50P

2x16,32 = h40ix18,20 = h4

0x′P 2i = h2

0h3P4x′ = h0xP 4i =

h0riP2i = h0i

4

30 (1) h60P

2x16,32 = h50ix18,20 = h5

0x′P 2i = h3

0h3P4x′ = h2

0xP 4i =h2

0riP2i = h2

0i4 = h3rP

4i = h3i2P 2i

31 (1) d30P

3j = d20iP

3e0 = d20jP

3d0 = d20Pd0P

2j = d20Pe0P

2i =d20PjP 2d0 = d0e0iP

3d0 = d0e0Pd0P2i = d0gP 4j = d0iPd0P

2e0 =d0iPe0P

2d0 = d0jPd0P2d0 = d0kP 4e0 = d0lP

4d0 = d0Pd20Pj =

e20P

4j = e0gP 4i = e0iPd0P2d0 = e0jP

4e0 = e0kP 4d0 =e0Pe0P

3j = e0PjP 3e0 = e0P2e0P

2j = giP 4e0 = gjP 4d0 =gPd0P

3j = gPjP 3d0 = gP 2d0P2j = gP 2e0P

2i = iPd20Pe0 =

jPd30 = jPe0P

3e0 = jP 2e20 = kPd0P

3e0 = kPe0P3d0 =

kP 2d0P2e0 = lPd0P

3d0 = lP 2d20 = mP 5e0 = Pe2

0P2j =

Pe0PjP 2e0

34 (1) d0iP4i = d0P

2i2 = rP 6d0 = i2P 4d0 = iP 2d0P2i = jP 5j =

PjP 4j = P 2jP 3j


Stem 933 (1) h2

4h6 = h35

4 (1) h0h24h6 = h0h

35

5 (01) h20h

24h6 = h2

0h35

(11) h1g3

6 (1) h30h

24h6 = h3

0h35

7 (1) h6r

8 (10) x8,78

(01) h0h6r

9 (1) h20h6r = h0x8,78 = h3h6i

10 (100) x10,67

(010) h21x8,75 = h4x9,55 = d1A

′ = d1A = D3q = nH1

(001) h30h6r = h2

0x8,78 = h0h3h6i

11 (10) h1x10,65

(01) h40h6r = h3

0x8,78 = h20h3h6i = h0x10,67 = h4P

2h25

12 (10) x12,60

(01) h50h6r = h4

0x8,78 = h30h3h6i = h2

0x10,67 = h0h4P2h2

5 = h6c0Pd0 =h6d0Pc0

13 (0010) h1x12,58 = h3x12,48

(0110) e0x9,51 = nx8,33 = rx7,34 = tQ2 = D2m = A′l = Al

(0001) h0x12,60 = h2x12,55

(1001) h6P2d0

14 (01) h20x12,60 = h0h2x12,55

(11) h0h6P2d0

15 (10) h3P3h2

5

(01) h30x12,60 = h2

0h2x12,55 = h31x12,55 = h1B

21 = Ph1Px6,53 = xQ1 =

qX1 = Gu = x6,53P2h1

(11) h20h6P

2d0 = h2h6P3h2 = h6Ph2P

2h2

17 (1) x17,57

18 (1) d20B23 = d0e0x10,27 = d0e0x10,28 = d0gB21 = e2

0B21 = e0gQ1 =g2x′

20 (10) d0x16,35

(01) h1ux′ = Ph1x15,42 = Ph1x15,43 = B1Q = B1Pu

(11) e0x16,32

21 (10) d20R2 = d0iQ1 = d0jx

′ = e0ix′ = gPR2 = kPQ1 = Pd0x13,35 =

Pe0P2D1 = B4P

2e0 = B21Pj

(01) d20gw = d2

0rm = d0e20w = d0e0gv = d0e0rl = d0g

2u = d0grk =e30v = e2

0gu = e20rk = e0grj = e0mz = g2ri = glz = im2 = jlm =

k2m = kl2

continued



20R2 = h0d0iQ1 = h0d0jx

′ = h0e0ix′ = h0gPR2 =

h0kPQ1 = h0Pd0x13,35 = h0Pe0P2D1 = h0B4P

2e0 =h0B21Pj = h2d0ix

′ = h2e0PR2 = h2gR1 = h2jPQ1 =h2Pd0P

2D1 = h2Pe0R2 = h2B4P2d0 = h2Q1 Pj =

d0Ph2P2D1 = d0Pe0R1 = d0P

2h2B4 = e0Ph2R2 = e0Pd0R1 =f0Pd0x

′ = Ph2iB21 = Ph2jQ1 = Ph2kx′ = Ph2Pd0B4 =iB2Pd0

23 (1) h20d

20R2 = h2

0d0iQ1 = h20d0jx

′ = h20e0ix

′ = h20gPR2 =

h20kPQ1 = h2

0Pd0x13,35 = h20Pe0P

2D1 = h20B4P

2e0 =h2

0B21Pj = h0h2d0ix′ = h0h2e0PR2 = h0h2gR1 = h0h2jPQ1 =

h0h2Pd0P2D1 = h0h2Pe0R2 = h0h2B4P

2d0 = h0h2Q1 Pj =h0d0Ph2P

2D1 = h0d0Pe0R1 = h0d0P2h2B4 = h0e0Ph2R2 =

h0e0Pd0R1 = h0f0Pd0x′ = h0Ph2iB21 = h0Ph2jQ1 =

h0Ph2kx′ = h0Ph2Pd0B4 = h0iB2Pd0 = h1d20PQ1 =

h1d0Pd0Q1 = h1d0Pe0x′ = h1e0Pd0x

′ = h1gP 2Q1 =h1B21P

2e0 = h1x10,27P2d0 = h1x10,28P

2d0 = h22d0PR2 =

h22e0R1 = h2

2iPQ1 = h22Pd0R2 = h2

2x′Pj = h2d0Ph2R2 =

h2d0Pd0R1 = h2f0P2Q1 = h2Ph2iQ1 = h2Ph2jx

′ =h2B2P

2j = h2P2h2x13,35 = d2

0Ph1Q1 = d20Ph2R1 = d0e0Ph1x

′ =d0B1P

2e0 = d0P2h1x10,27 = d0P

2h1x10,28 = e0B1P2d0 =

e0P2h1B21 = f0Ph2PQ1 = f0P

2h2Q1 = gPh1PQ1 =gP 2h1Q1 = gP 2h2R1 = Ph1Pd0x10,27 = Ph1Pd0x10,28 =Ph1Pe0B21 = Ph2

2x13,35 = Ph2B2Pj = D2P4h2 = Pc0x16,33 =

jB2P2h2 = B1Pd0Pe0 = B5 P 3h2 = PD2P

3h2

24 (10) iR1

(01) d40e0g = d3

0e30 = d2

0g2Pe0 = d2

0iv = d20ju = d0e

20gPe0 =

d0e0g2Pd0 = d0e0iu = d0rij = d0kPv = d0lPu = d0wPj =

e40Pe0 = e3

0gPd0 = e0ri2 = e0jPv = e0kPu = e0vPj = g3P 2e0 =

giPv = gjPu = guPj = r2P 2e0 = rkPj = rPd0z = ikz =iPe0w = j2z = jPd0w = jPe0v = kPd0v = kPe0u = lPd0u =mP 2v

25 (01) h0iR1 = R1P2i

(11) h1P2x16,32 = P 2h1x16,32

26 (1) h20iR1 = h0R1P

2i = h3x25,24

continued



0i = d30e0Pj = d3

0jPe0 = d30kPd0 = d2

0e0iPe0 = d20e0jPd0 =

d20giPd0 = d2

0lP2e0 = d2

0mP 2d0 = d0e20iPd0 = d0e0gP 2j =

d0e0kP 2e0 = d0e0lP2d0 = d0g

2P 2i = d0gjP 2e0 = d0gkP 2d0 =d0gPe0Pj = d0kPe2

0 = d0lPd0Pe0 = d0mPd20 = e3

0P2j =

e20gP 2i = e2

0jP2e0 = e2

0kP 2d0 = e20Pe0Pj = e0giP 2e0 =

e0gjP 2d0 = e0gPd0Pj = e0jPe20 = e0kPd0Pe0 = e0lPd2

0 =e0mP 3e0 = g2iP 2d0 = giPe2

0 = gjPd0Pe0 = gkPd20 = glP 3e0 =

gmP 3d0 = rP 3u = i2Pu = mPe0P2e0

(01) h30iR1 = h2

0R1P2i = h0h3x25,24 = i2Q

28 (1) h40iR1 = h3

0R1P2i = h2

0h3x25,24 = h0i2Q

29 (1) h50iR1 = h4

0R1P2i = h3

0h3x25,24 = h20i

2Q = h3QP 2i = c0P4x′ =

yP 4i = x′P 4c0 = P 2c0x18,20

30 (1) d20iP

2j = d20jP

2i = d0e0iP2i = d0rP

4e0 = d0i2P 2e0 =

d0ijP2d0 = d0iPd0Pj = d0kP 3j = d0zP 3d0 = e0rP

4d0 =e0i

2P 2d0 = e0jP3j = e0PjP 2j = giP 3j = gPjP 2i = rPd0P

3e0 =rPe0P

3d0 = rP 2d0P2e0 = i2Pd0Pe0 = ijPd2

0 = ikP 3e0 =ilP 3d0 = j2P 3e0 = jkP 3d0 = jPe0P

2j = jP jP 2e0 = kPd0P2j =

kPe0P2i = kPjP 2d0 = lPd0P

2i = mP 4j = Pd0zP 2d0 = Pe0Pj2

33 (1) d0P5u = Pd0P

4u = uP 5d0 = P 2d0P3u = PuP 4d0 = P 3d0P

2u

36 (1) d20P

6e0 = d0e0P6d0 = d0Pd0P

5e0 = d0Pe0P5d0 = d0P

2d0P4e0 =

d0P2e0P

4d0 = d0P3d0P

3e0 = e0Pd0P5d0 = e0P

2d0P4d0 =

e0P3d2

0 = gP 7e0 = Pd20P

4e0 = Pd0Pe0P4d0 = Pd0P

2d0P3e0 =

Pd0P2e0P

3d0 = Pe0P2d0P

3d0 = P 2d20P

2e0

39 (1) iP 7d0 = Pd0P6i = P 2iP 5d0 = P 3d0P

4i


Stem 944 (1) h1h

24h6 = h1h

35

6 (10) h6n

(01) h21g3 = h4x1

8 (1) x8,80

9 (001) h0x8,80

(101) h6d0e0

(011) h1x8,78 = h2x8,75 = d1H1

10 (100) x10,70

(001) h20x8,80 = pA′

(011) h0h6d0e0 = h2h6d20 = h6gPh2

11 (10) h1x10,67 = h3x10,60 = H1q

(01) h20h6d0e0 = h0h2h6d

20 = h0h6gPh2 = h2

2h6Pe0 = h2h6e0Ph2 =h6c0i

12 (01) h21x10,65 = d1x8,32 = xQ2

(11) h2x11,61

13 (1) h0h2x11,61 = h1x12,60

14 (1) h1h6P2d0 = h6d0P

2h1 = h6Ph1Pd0

15 (1) x15,56

16 (1) x16,54

17 (1) d0gB4 = e20B4 = kB23 = lx10,27 = lx10,28 = mB21

19 (1) x19,49

20 (10) d0g4 = d0gr2 = d0mw = e2

0g3 = e2

0r2 = e0lw = e0mv = gkw =

glv = gmu = rkm = rl2

(01) d0x16,37 = e0x16,33 = rPQ1 = ix13,35 = jP 2D1 = kR2 = B4Pj =zx′

21 (1) h0d0x16,37 = h0e0x16,33 = h0rPQ1 = h0ix13,35 = h0jP2D1 =

h0kR2 = h0B4Pj = h0zx′ = h21ux′ = h1d0x16,35 = h1Ph1x15,42 =

h1Ph1x15,43 = h1B1Q = h1B1Pu = h2d0x16,33 = h2iP2D1 =

h2jR2 = h3Px16,35 = d0jR1 = e0iR1 = f0ix′ = D3P

4h1 =Ph1qx

′ = Ph1B1u = Ph1x16,42 = Ph2rx′ = Ph2iB4 = i2B2 =

PD3P3h1 = P 2h1P

2D3 = X1P2e0

22 (1) x22,39

23 (10) d30e0m = d3

0gl = d20e

20l = d2

0e0gk = d20g

2j = d0e30k = d0e

20gj =

d0e0g2i = d0gmPe0 = d0rPv = d0uz = e4

0j = e30gi = e2

0mPe0 =e0glPe0 = e0gmPd0 = e0rPu = g3Pj = g2kPe0 = g2lPd0 =r2Pj = riz = rPd0v = rPe0u = ijw = ikv = ilu = j2v = jku

(01) h0x22,39

24 (1) h20x22,39

25 (1) h30x22,39

continued


Stem 94 continued26 (0011) Q2

(1011) d0P3Q1 = Pd0P

2Q1 = Q1 P 3d0 = P 2d0PQ1

(0100) uP 2u = Pu2

(0010) h21P

2x16,32 = h1P2h1x16,32 = Ph2

1x16,32 = X1P4h1 = P 3h1W1 =

QPu

(1111) Pe0x18,20

(0110) d30rPd0 = d3

0ik = d30j

2 = d20e0ij = d2

0gi2 = d20lP j = d2

0Pe0z =d0e

20i

2 = d0e0rP2e0 = d0e0kPj = d0e0Pd0z = d0grP 2d0 =

d0gjPj = d0rPe20 = d0ilPe0 = d0imPd0 = d0jkPe0 = d0jlPd0 =

d0k2Pd0 = e2

0rP2d0 = e2

0jP j = e0giP j = e0rPd0Pe0 =e0ikPe0 = e0ilPd0 = e0j

2Pe0 = e0jkPd0 = e0mP 2j = grPd20 =

gijPe0 = gikPd0 = gj2Pd0 = glP 2j = gmP 2i = gzP 2e0 =jmP 2e0 = klP 2e0 = kmP 2d0 = l2P 2d0 = mPe0Pj

(0001) h40x22,39

(1001) x′P 3e0

27 (01) h50x22,39 = h0Q

2

(11) h0d0P3Q1 = h0Pd0P

2Q1 = h0Pe0x18,20 = h0x′P 3e0 =

h0Q1 P 3d0 = h0P2d0PQ1 = h2Pd0x18,20 = h2x

′P 3d0 =d0Ph2x18,20 = d0x

′P 3h2 = Ph2x′P 2d0 = B2P

4d0 = Pd0P2h2x

′ =B21P

4h2

28 (10) h20d0P

3Q1 = h20Pd0P

2Q1 = h20Pe0x18,20 = h2

0x′P 3e0 =

h20Q1 P 3d0 = h2

0P2d0PQ1 = h0h2Pd0x18,20 = h0h2x

′P 3d0 =h0d0Ph2x18,20 = h0d0x

′P 3h2 = h0Ph2x′P 2d0 = h0B2P

4d0 =h0Pd0P

2h2x′ = h0B21P

4h2 = h22P

4Q1 = h2Ph2P3Q1 =

h2P2h2P

2Q1 = h2Q1 P 4h2 = h2P3h2PQ1 = c0x25,24 =

Ph22P

2Q1 = Ph2P2h2PQ1 = Ph2Q1 P 3h2 = P 2h2

2Q1 =P 2c0R1

(01) h60x22,39 = h2

0Q2

29 (10) d20P

3v = d0e0P3u = d0rP

3j = d0i2Pj = d0Pd0P

2v =d0Pe0P

2u = d0uP 3e0 = d0vP 3d0 = d0zP 2i = d0P2d0Pv =

d0P2e0Pu = e0Pd0P

2u = e0uP 3d0 = e0P2d0Pu = gP 4v =

riP 3e0 = rjP 3d0 = rPd0P2j = rPe0P

2i = rPjP 2d0 = i3Pe0 =i2jPd0 = ikP 2j = ilP 2i = izP 2d0 = j2P 2j = jkP 2i = jP j2 =Pd2

0Pv = Pd0Pe0Pu = Pd0uP 2e0 = Pd0vP 2d0 = Pe0uP 2d0 =wP 4e0

(01) h70x22,39 = h3

0Q2

30 (1) h80x22,39 = h4

0Q2 = h4P

4Q

31 (10) Ph1P4x′ = x′P 5h1 = P 3h1x18,20

(01) h90x22,39 = h5

0Q2 = h0h4P

4Q

continued



0P3d0 = d3

0Pd0P2d0 = d2

0e0P4e0 = d2

0gP 4d0 = d20Pd3

0 =d20Pe0P

3e0 = d20P

2e20 = d0e

20P

4d0 = d0e0Pd0P3e0 =

d0e0Pe0P3d0 = d0e0P

2d0P2e0 = d0gPd0P

3d0 = d0gP 2d20 =

d0Pd0Pe0P2e0 = d0Pe2

0P2d0 = e2

0Pd0P3d0 = e2

0P2d2

0 =e0gP 5e0 = e0Pd2

0P2e0 = e0Pd0Pe0P

2d0 = g2P 5d0 =gPd2

0P2d0 = gPe0P

4e0 = gP 2e0P3e0 = iP 4u = Pd2

0Pe20 =

uP 4i = P 2iP 2u

(01) h100 x22,39 = h6

0Q2 = h2

0h4P4Q

33 (1) h110 x22,39 = h7

0Q2 = h3

0h4P4Q

34 (1) h120 x22,39 = h8

0Q2 = h4

0h4P4Q

35 (01) h130 x22,39 = h9

0Q2 = h5

0h4P4Q

(11) d20P

5j = d0iP5e0 = d0jP

5d0 = d0Pd0P4j = d0Pe0P

4i =d0PjP 4d0 = d0P

2d0P3j = d0P

2iP 3e0 = d0P2jP 3d0 = e0iP

5d0 =e0Pd0P

4i = e0P2iP 3d0 = gP 6j = iPd0P

4e0 = iPe0P4d0 =

iP 2d0P3e0 = iP 2e0P

3d0 = jPd0P4d0 = jP 2d0P

3d0 = kP 6e0 =lP 6d0 = Pd2

0P3j = Pd0PjP 3d0 = Pd0P

2d0P2j = Pd0P

2e0P2i =

Pe0P2d0P

2i = PjP 2d20

36 (1) h140 x22,39 = h10

0 Q2 = h60h4P

4Q = h0d20P

5j = h0d0iP5e0 =

h0d0jP5d0 = h0d0Pd0P

4j = h0d0Pe0P4i = h0d0PjP 4d0 =

h0d0P2d0P

3j = h0d0P2iP 3e0 = h0d0P

2jP 3d0 = h0e0iP5d0 =

h0e0Pd0P4i = h0e0P

2iP 3d0 = h0gP 6j = h0iPd0P4e0 =

h0iPe0P4d0 = h0iP

2d0P3e0 = h0iP

2e0P3d0 = h0jPd0P

4d0 =h0jP

2d0P3d0 = h0kP 6e0 = h0lP

6d0 = h0Pd20P

3j =h0Pd0PjP 3d0 = h0Pd0P

2d0P2j = h0Pd0P

2e0P2i =

h0Pe0P2d0P

2i = h0PjP 2d20 = h2d0iP

5d0 = h2d0Pd0P4i =

h2d0P2iP 3d0 = h2e0P

6j = h2gP 6i = h2iPd0P4d0 =

h2iP2d0P

3d0 = h2jP6e0 = h2kP 6d0 = h2Pd0P

2d0P2i =

h2Pe0P5j = h2PjP 5e0 = h2P

2e0P4j = h2P

2jP 4e0 =h2P

3e0P3j = d2

0Ph2P4i = d2

0iP5h2 = d2

0P3h2P

2i = d0f0P6d0 =

d0Ph2iP4d0 = d0Ph2P

2d0P2i = d0iPd0P

4h2 = d0iP2h2P

3d0 =d0iP

2d0P3h2 = d0kP 6h2 = d0Pd0P

2h2P2i = e0Ph2P

5j =e0jP

6h2 = e0P2h2P

4j = e0PjP 5h2 = e0P3h2P

3j =e0P

2jP 4h2 = f0Pd0P5d0 = f0P

2d0P4d0 = f0P

3d20 = giP 6h2 =

gP 2h2P4i = gP 2iP 4h2 = Ph2iPd0P

3d0 = Ph2iP2d2

0 =Ph2jP

5e0 = Ph2kP 5d0 = Ph2Pd20P

2i = Ph2Pe0P4j =

Ph2PjP 4e0 = Ph2P2e0P

3j = Ph2P2jP 3e0 = iPd2

0P3h2 =

iPd0P2h2P

2d0 = jPe0P5h2 = jP 2h2P

4e0 = jP 2e0P4h2 =

jP 3h2P3e0 = kPd0P

5h2 = kP 2h2P4d0 = kP 2d0P

4h2 =kP 3h2P

3d0 = mP 7h2 = Pe0P2h2P

3j = Pe0PjP 4h2 =Pe0P

3h2P2j = P 2h2PjP 3e0 = P 2h2P

2e0P2j = PjP 2e0P

3h2

continued



0 x22,39 = h110 Q2 = h7

0h4P4Q = h2

0d20P

5j = h20d0iP

5e0 =h2

0d0jP5d0 = h2

0d0Pd0P4j = h2

0d0Pe0P4i = h2

0d0PjP 4d0 =h2

0d0P2d0P

3j = h20d0P

2iP 3e0 = h20d0P

2jP 3d0 = h20e0iP

5d0 =h2

0e0Pd0P4i = h2

0e0P2iP 3d0 = h2

0gP 6j = h20iPd0P

4e0 =h2

0iPe0P4d0 = h2

0iP2d0P

3e0 = h20iP

2e0P3d0 = h2

0jPd0P4d0 =

h20jP

2d0P3d0 = h2

0kP 6e0 = h20lP

6d0 = h20Pd2

0P3j =

h20Pd0PjP 3d0 = h2

0Pd0P2d0P

2j = h20Pd0P

2e0P2i =

h20Pe0P

2d0P2i = h2

0PjP 2d20 = h0h2d0iP

5d0 = h0h2d0Pd0P4i =

h0h2d0P2iP 3d0 = h0h2e0P

6j = h0h2gP 6i = h0h2iPd0P4d0 =

h0h2iP2d0P

3d0 = h0h2jP6e0 = h0h2kP 6d0 = h0h2Pd0P

2d0P2i =

h0h2Pe0P5j = h0h2PjP 5e0 = h0h2P

2e0P4j = h0h2P

2jP 4e0 =h0h2P

3e0P3j = h0d

20Ph2P

4i = h0d20iP

5h2 = h0d20P

3h2P2i =

h0d0f0P6d0 = h0d0Ph2iP

4d0 = h0d0Ph2P2d0P

2i =h0d0iPd0P

4h2 = h0d0iP2h2P

3d0 = h0d0iP2d0P

3h2 =h0d0kP 6h2 = h0d0Pd0P

2h2P2i = h0e0Ph2P

5j = h0e0jP6h2 =

h0e0P2h2P

4j = h0e0PjP 5h2 = h0e0P3h2P

3j = h0e0P2jP 4h2 =

h0f0Pd0P5d0 = h0f0P

2d0P4d0 = h0f0P

3d20 = h0giP 6h2 =

h0gP 2h2P4i = h0gP 2iP 4h2 = h0Ph2iPd0P

3d0 = h0Ph2iP2d2

0 =h0Ph2jP

5e0 = h0Ph2kP 5d0 = h0Ph2Pd20P

2i = h0Ph2Pe0P4j =

h0Ph2PjP 4e0 = h0Ph2P2e0P

3j = h0Ph2P2jP 3e0 =

h0iPd20P

3h2 = h0iPd0P2h2P

2d0 = h0jPe0P5h2 =

h0jP2h2P

4e0 = h0jP2e0P

4h2 = h0jP3h2P

3e0 = h0kPd0P5h2 =

h0kP 2h2P4d0 = h0kP 2d0P

4h2 = h0kP 3h2P3d0 = h0mP 7h2 =

h0Pe0P2h2P

3j = h0Pe0PjP 4h2 = h0Pe0P3h2P

2j =h0P

2h2PjP 3e0 = h0P2h2P

2e0P2j = h0PjP 2e0P

3h2 =h1d

20P


5e0 = h1d0Pe0P5d0 =

h1d0P2d0P

4e0 = h1d0P2e0P

4d0 = h1d0P3d0P

3e0 =h1e0Pd0P

5d0 = h1e0P2d0P

4d0 = h1e0P3d2

0 = h1gP 7e0 =h1Pd2

0P4e0 = h1Pd0Pe0P

4d0 = h1Pd0P2d0P

3e0 =h1Pd0P

2e0P3d0 = h1Pe0P

2d0P3d0 = h1P

2d20P

2e0 =h2

2d0P6j = h2

2e0P6i = h2

2iP6e0 = h2

2jP6d0 = h2

2Pd0P5j =

h22PjP 5d0 = h2

2P2d0P

4j = h22P

2e0P4i = h2

2P2iP 4e0 =

h22P

2jP 4d0 = h22P

3d0P3j = h2d0Ph2P

5j = h2d0jP6h2 =

h2d0P2h2P

4j = h2d0PjP 5h2 = h2d0P3h2P

3j = h2d0P2jP 4h2 =

h2e0iP6h2 = h2e0P

2h2P4i = h2e0P

2iP 4h2 = h2f0P7e0 =



4i =h2Ph2PjP 4d0 = h2Ph2P

2d0P3j = h2Ph2P

2iP 3e0 =h2Ph2P

2jP 3d0 = h2iPe0P5h2 = h2iP

2h2P4e0 = h2iP

2e0P4h2 =

h2iP3h2P

3e0 = h2jPd0P5h2 = h2jP

2h2P4d0 = h2jP

2d0P4h2 =

h2jP3h2P



h2Pd0P3h2P

2j = h2Pe0P3h2P

2i = (continued)


Stem 86 continued37 (1) (continued) = h2P

2h2PjP 3d0 = h2P2h2P

2d0P2j =

h2P2h2P

2e0P2i = h2PjP 2d0P

3h2 = d20e0P

6h1 = d20Ph1P

5e0 =d20Pe0P

5h1 = d20P

2h1P4e0 = d2

0P2e0P

4h1 = d20P

3h1P3e0 =

d0e0Ph1P5d0 = d0e0Pd0P

5h1 = d0e0P2h1P

4d0 =d0e0P

2d0P4h1 = d0e0P

3h1P3d0 = d0Ph1Pd0P

4e0 =d0Ph1Pe0P

4d0 = d0Ph1P2d0P

3e0 = d0Ph1P2e0P

3d0 =d0Ph2

2P4j = d0Ph2jP

5h2 = d0Ph2P2h2P

3j = d0Ph2PjP 4h2 =d0Ph2P

3h2P2j = d0jP

2h2P4h2 = d0jP

3h22 = d0Pd0Pe0P

4h1 =d0Pd0P

2h1P3e0 = d0Pd0P

2e0P3h1 = d0Pe0P

2h1P3d0 =

d0Pe0P2d0P

3h1 = d0P2h1P

2d0P2e0 = d0P

2h22P

2j =d0P

2h2PjP 3h2 = e0f0P7h2 = e0gP 7h1 = e0Ph1Pd0P

4d0 =e0Ph1P

2d0P3d0 = e0Ph2

2P4i = e0Ph2iP

5h2 = e0Ph2P3h2P

2i =e0iP

2h2P4h2 = e0iP

3h22 = e0Pd2

0P4h1 = e0Pd0P

2h1P3d0 =

e0Pd0P2d0P

3h1 = e0P2h1P

2d20 = e0P

2h22P

2i = f0Ph2P6e0 =

f0Pe0P6h2 = f0P

2h2P5e0 = f0P

2e0P5h2 = f0P

3h2P4e0 =

f0P3e0P

4h2 = gPh1P6e0 = gPe0P

6h1 = gP 2h1P5e0 =

gP 2e0P5h1 = gP 3h1P

4e0 = gP 3e0P4h1 = Ph1Pd2

0P3e0 =

Ph1Pd0Pe0P3d0 = Ph1Pd0P

2d0P2e0 = Ph1Pe0P

2d20 =

Ph22iP

4e0 = Ph22jP

4d0 = Ph22Pd0P

3j = Ph22PjP 3d0 =

Ph22P

2d0P2j = Ph2

2P2e0P

2i = Ph2iPe0P4h2 =

Ph2iP2h2P

3e0 = Ph2iP2e0P

3h2 = Ph2jPd0P4h2 =

Ph2jP2h2P

3d0 = Ph2jP2d0P

3h2 = Ph2lP6h2 =

Ph2Pd0P2h2P

2j = Ph2Pd0PjP 3h2 = Ph2Pe0P2h2P

2i =Ph2P

2h2PjP 2d0 = rP 7c0 = Pc0iP4i = Pc0P

2i2 = i2P 5c0 =iPe0P

2h2P3h2 = iP 2h2

2P2e0 = iP 3c0P

2i = jPd0P2h2P

3h2 =jP 2h2

2P2d0 = lP 2h2P

5h2 = lP 3h2P4h2 = Pd2

0Pe0P3h1 =

Pd20P

2h1P2e0 = Pd0Pe0P

2h1P2d0 = Pd0P

2h22Pj

38 (1) iP 6i = P 2iP 4i

39 (1) h0iP6i = h0P

2iP 4i


Stem 955 (10) h6d1

(01) h2g3 = h4e2

6 (1) h0h2g3 = h0h4e2

7 (10) x7,79

(01) h6q

8 (10) h6l

(01) h0x7,79

9 (10) h1x8,80

(01) h0h6l = h2h6k = h6d0f0

10 (10) x10,73

(01) h20h6l = h0h2h6k = h0h6d0f0 = h1h6d0e0 = h2

2h6j

11 (10) h2x10,65

(01) h0x10,73 = e1Q2 = xD2

13 (1) h2x12,58 = h3x12,51 = yQ2

14 (1) h0h2x12,58 = h0h3x12,51 = h0yQ2 = h23x12,45 = px10,27

15 (1) h21h6P

2d0 = h1h6d0P2h1 = h1h6Ph1Pd0 = h3h6P

3h1 =h4x14,42 = h6c0P

2c0 = h6d0Ph21 = h6Pc2

0

16 (100) rB23 = mB4

(010) h6P3c0

(001) h1x15,56

18 (1) x18,57

19 (10) g3m = grw = r2m

(01) rR2 = uQ1 = vx′

21 (10) x21,43

(01) Px17,50

22 (010) d20e0gr = d2

0lm = d0e30r = d0e0km = d0e0l

2 = d0g2z = d0gjm =

d0gkl = d0uv = e20gz = e2

0jm = e20kl = e0gim = e0gjl = e0gk2 =

e0u2 = g2rPe0 = g2il = g2jk = riv = rju = m2Pe0 = wPv

(110) d30x

′ = d0e0PQ1 = d0Pd0B21 = d0Pe0Q1 = e0Pd0Q1 =e0Pe0x

′ = gPd0x′ = x10,27P

2e0 = x10,28P2e0 = B23P

2d0

(001) h0x21,43

continued



30x

′ = h0d0e0PQ1 = h0d0Pd0B21 = h0d0Pe0Q1 =h0e0Pd0Q1 = h0e0Pe0x

′ = h0gPd0x′ = h0x10,27P

2e0 =h0x10,28P

2e0 = h0B23P2d0 = h1x22,39 = h2d

20PQ1 =

h2d0Pd0Q1 = h2d0Pe0x′ = h2e0Pd0x

′ = h2gP 2Q1 =h2B21P

2e0 = h2x10,27P2d0 = h2x10,28P

2d0 = h4P3Q1 =

c0Px16,35 = d20Ph2Q1 = d0e0Ph2x

′ = d0B2P2e0 =

d0P2h2x10,27 = d0P

2h2x10,28 = e0B2P2d0 = e0P

2h2B21 =gPh2PQ1 = gP 2h2Q1 = Ph2Pd0x10,27 = Ph2Pd0x10,28 =Ph2Pe0B21 = Pc0x16,35 = B2Pd0Pe0 = Q2P

3d0

(01) h20x21,43

24 (01) h30x21,43

(11) P 2x16,35

25 (0011) h0P2x16,35 = h2P

2x16,32 = P 2h2x16,32

(1000) iP 2Q1 = x′P 2j = Q1 P 2i

(1011) d0P2R2 = Pd0PR2 = Pe0R1 = P 2d0R2

(0100) d40u = d3

0ri = d20e0Pv = d2

0gPu = d20jz = d2

0Pd0w = d20Pe0v =

d0e20Pu = d0e0rPj = d0e0iz = d0e0Pd0v = d0e0Pe0u =

d0gPd0u = d0rjPe0 = d0rkPd0 = d0i2m = d0ijl = d0ik

2 =d0j

2k = e20Pd0u = e0gP 2v = e0riPe0 = e0rjPd0 = e0i

2l =e0ijk = e0j

3 = e0wP 2e0 = g2P 2u = griPd0 = gi2k = gij2 =gPe0Pv = gvP 2e0 = gwP 2d0 = gzPj = rlP 2e0 = rmP 2d0 =jmPj = klP j = kPe0z = lPd0z = Pe2

0w

(1100) jx18,20

(0001) h40x21,43

26 (100) h0iP2Q1 = h0jx18,20 = h0x

′P 2j = h0Q1 P 2i = h2ix18,20 =h2x

′P 2i = iP 2h2x′ = B4P

4h2

(001) h50x21,43

(011) h20P

2x16,35 = h0h2P2x16,32 = h0P

2h2x16,32

(111) h0d0P2R2 = h0Pd0PR2 = h0Pe0R1 = h0P

2d0R2 =h2Pd0R1 = d0Ph2R1 = R1P

3e0 = P 3h2P2D1

continued



0iP2Q1 = h2

0jx18,20 = h20x

′P 2j = h20Q1 P 2i = h0h2ix18,20 =

h0h2x′P 2i = h0iP

2h2x′ = h0B4P

4h2 = h1Pe0x18,20 =h1x

′P 3e0 = e0Ph1x18,20 = e0x′P 3h1 = Ph1x

′P 2e0 = B1P4e0 =

Pe0P2h1x

′ = x10,28P4h1

(001) h60x21,43

(011) h30P

2x16,35 = h20h2P

2x16,32 = h20P

2h2x16,32 = h31P

2x16,32 =h2

1P2h1x16,32 = h1Ph2

1x16,32 = h1uP 2u = h1X1P4h1 =

h1P3h1W1 = h1Q

2 = h1QPu = h1Pu2 = h3P4Q1 =

Ph1P2h1W1 = Ph1uQ = Ph1uPu = Ph1X1P

3h1 = qP 3u =GP 5h1 = P 2h2

1X1 = P 2h1u2

(111) h20d0P

2R2 = h20Pd0PR2 = h2

0Pe0R1 = h20P

2d0R2 =h0h2Pd0R1 = h0d0Ph2R1 = h0R1P

3e0 = h0P3h2P

2D1 =h1d0P

3Q1 = h1Pd0P2Q1 = h1Q1 P 3d0 = h1P

2d0PQ1 =h2

2P3R2 = h2Ph2P

2R2 = h2P2h2PR2 = h2R1P

3d0 =h2P

3h2R2 = d0Ph1P2Q1 = d0P

2h1PQ1 = d0R1P3h2 =

d0Q1 P 3h1 = Ph1Pd0PQ1 = Ph1Q1 P 2d0 = Ph22PR2 =

Ph2P2h2R2 = Ph2R1P

2d0 = Pd0P2h1Q1 = Pd0P

2h2R1 =x10,27P

4h1

28 (10) d50Pe0 = d4

0e0Pd0 = d30gP 2e0 = d2

0e20P

2e0 = d20e0gP 2d0 =

d20e0Pe2

0 = d20gPd0Pe0 = d0e

30P

2d0 = d0e20Pd0Pe0 = d0e0gPd2

0 =d0g

2P 3e0 = d0iP2v = d0jP

2u = d0uP 2j = d0vP 2i = d0PjPu =e30Pd2

0 = e20gP 3e0 = e0g

2P 3d0 = e0gPe0P2e0 = e0iP

2u =e0uP 2i = g2Pd0P

2e0 = g2Pe0P2d0 = gPe3

0 = riP 2j = rjP 2i =i3j = iPd0Pv = iPe0Pu = iuP 2e0 = ivP 2d0 = jPd0Pu =juP 2d0 = kP 3v = lP 3u = Pd0uPj = wP 3j

(01) h70x21,43

29 (1) h80x21,43

30 (1) h90x21,43

31 (10) d40P

2i = d30iP

2d0 = d20e0P

3j = d20iPd2

0 = d20jP

3e0 =d20kP 3d0 = d2

0Pe0P2j = d2

0PjP 2e0 = d0e0iP3e0 = d0e0jP

3d0 =d0e0Pd0P

2j = d0e0Pe0P2i = d0e0PjP 2d0 = d0giP 3d0 =

d0gPd0P2i = d0iPe0P

2e0 = d0jPd0P2e0 = d0jPe0P

2d0 =d0kPd0P

2d0 = d0lP4e0 = d0mP 4d0 = d0Pd0Pe0Pj =

e20iP

3d0 = e20Pd0P

2i = e0gP 4j = e0iPd0P2e0 = e0iPe0P

2d0 =e0jPd0P

2d0 = e0kP 4e0 = e0lP4d0 = e0Pd2

0Pj = g2P 4i =giPd0P

2d0 = gjP 4e0 = gkP 4d0 = gPe0P3j = gPjP 3e0 =

gP 2e0P2j = iPd0Pe2

0 = jPd20Pe0 = kPd3

0 = kPe0P3e0 =

kP 2e20 = lPd0P

3e0 = lP e0P3d0 = lP 2d0P

2e0 = mPd0P3d0 =

mP 2d20

(01) h100 x21,43

continued


Stem 95 continued32 (10) h1Ph1P

4x′ = h1x′P 5h1 = h1P

3h1x18,20 = Ph1P2h1x18,20 =

Ph1x′P 4h1 = B1P

6h1 = P 2h1x′P 3h1

(01) h110 x21,43

33 (1) h120 x21,43

34 (10) d0iP4j = d0jP

4i = d0P2iP 2j = e0iP

4i = e0P2i2 = rP 6e0 =

i2P 4e0 = ijP 4d0 = iPd0P3j = iP jP 3d0 = iP 2d0P

2j =iP 2e0P

2i = jP 2d0P2i = kP 5j = Pd0PjP 2i = zP 5d0

(01) h130 x21,43

35 (1) h140 x21,43

36 (1) h150 x21,43

37 (10) P 7u

(01) h160 x21,43

38 (1) h170 x21,43

39 (1) h180 x21,43


Stem 965 (1) h6p

6 (1) h0h6p = h1h6d1

8 (10) x8,83

(01) h1h6q = h2h6r

9 (10) h2x8,78

(01) h0x8,83

10 (1) h20x8,83 = h2

1x8,80

12 (10) x12,64

(01) h3x11,59 = yD2

13 (100) gx9,51 = rx7,40 = A′m = Am

(010) h6P2e0

(001) h0x12,64 = h2x12,60

14 (10) h0h6P2e0 = h2h6P

2d0 = h6d0P2h2 = h6Ph2Pd0

(01) h20x12,64 = h0h2x12,60 = h2

2x12,55 = h5R2 = B22

15 (10) x15,58

(01) h20h6P

2e0 = h0h2h6P2d0 = h0h6d0P

2h2 = h0h6Ph2Pd0

16 (1) h0x15,58

17 (10) h1h6P3c0 = h6c0P

3h1 = h6Ph1P2c0 = h6Pc0P

2h1

(01) h20x15,58 = h2

1x15,56

18 (10) g3t = gnw = grN = nrm = r2t

(01) d0e0B23 = d0gx10,27 = d0gx10,28 = e20x10,27 = e2

0x10,28 = e0gB21 =g2Q1

20 (1) d0x16,38 = e0x16,35 = gx16,32

21 (01) d20P

2D1 = d0e0R2 = d0iB21 = d0jQ1 = d0kx′ = d0Pd0B4 =e0iQ1 = e0jx

′ = gix′ = lPQ1 = Pe0x13,35 = x10,27Pj = x10,28Pj

(11) d0e0gw = d0e0rm = d0g2v = d0grl = e3

0w = e20gv = e2

0rl =e0g

2u = e0grk = g2rj = gmz = jm2 = klm = l3

22 (10) h1x21,43 = h1Px17,50 = Ph1x17,50

(01) h0d20P

2D1 = h0d0e0R2 = h0d0iB21 = h0d0jQ1 = h0d0kx′ =h0d0Pd0B4 = h0e0iQ1 = h0e0jx

′ = h0gix′ = h0lPQ1 =h0Pe0x13,35 = h0x10,27Pj = h0x10,28Pj = h2d

20R2 = h2d0iQ1 =

h2d0jx′ = h2e0ix

′ = h2gPR2 = h2kPQ1 = h2Pd0x13,35 =h2Pe0P

2D1 = h2B4P2e0 = h2B21Pj = h4P

2R2 = d30R1 =

d0f0PQ1 = d0Ph2x13,35 = d0B2Pj = e0Ph2P2D1 = e0Pe0R1 =

e0P2h2B4 = f0Pd0Q1 = f0Pe0x

′ = gPh2R2 = gPd0R1 =Ph2ix10,27 = Ph2ix10,28 = Ph2jB21 = Ph2kQ1 = Ph2lx

′ =Ph2Pe0B4 = D2P

3d0 = iB2Pe0 = jB2Pd0 = Q2P2i =

B5 P 2d0 = PD2P2d0

continued



0d20P

2D1 = h20d0e0R2 = h2

0d0iB21 = h20d0jQ1 = h2

0d0kx′ =h2

0d0Pd0B4 = h20e0iQ1 = h2

0e0jx′ = h2

0gix′ = h20lPQ1 =

h20Pe0x13,35 = h2

0x10,27Pj = h20x10,28Pj = h0h2d

20R2 =

h0h2d0iQ1 = h0h2d0jx′ = h0h2e0ix

′ = h0h2gPR2 =h0h2kPQ1 = h0h2Pd0x13,35 = h0h2Pe0P

2D1 = h0h2B4P2e0 =

h0h2B21Pj = h0h4P2R2 = h0d

30R1 = h0d0f0PQ1 =

h0d0Ph2x13,35 = h0d0B2Pj = h0e0Ph2P2D1 = h0e0Pe0R1 =

h0e0P2h2B4 = h0f0Pd0Q1 = h0f0Pe0x

′ = h0gPh2R2 =h0gPd0R1 = h0Ph2ix10,27 = h0Ph2ix10,28 = h0Ph2jB21 =h0Ph2kQ1 = h0Ph2lx

′ = h0Ph2Pe0B4 = h0D2P3d0 =

h0iB2Pe0 = h0jB2Pd0 = h0Q2P2i = h0B5 P 2d0 = h0PD2P

2d0 =h1d

30x

′ = h1d0e0PQ1 = h1d0Pd0B21 = h1d0Pe0Q1 =h1e0Pd0Q1 = h1e0Pe0x

′ = h1gPd0x′ = h1x10,27P

2e0 =h1x10,28P

2e0 = h1B23P2d0 = h2

2d0ix′ = h2

2e0PR2 = h22gR1 =

h22jPQ1 = h2

2Pd0P2D1 = h2

2Pe0R2 = h22B4P

2d0 =h2

2Q1 Pj = h2d0Ph2P2D1 = h2d0Pe0R1 = h2d0P

2h2B4 =h2e0Ph2R2 = h2e0Pd0R1 = h2f0Pd0x

′ = h2Ph2iB21 =h2Ph2jQ1 = h2Ph2kx′ = h2Ph2Pd0B4 = h2iB2Pd0 =h4Ph2R1 = c0iR2 = d2

0Ph1B21 = d20B1Pd0 = d0e0Ph1Q1 =

d0e0Ph2R1 = d0f0Ph2x′ = d0gPh1x

′ = d0Ph22B4 = d0Ph2iB2 =

d0P2h1B23 = e2

0Ph1x′ = e0B1P

2e0 = e0P2h1x10,27 =

e0P2h1x10,28 = f0B2P

2d0 = f0P2h2B21 = gB1P

2d0 =gP 2h1B21 = Ph1Pd0B23 = Ph1Pe0x10,27 = Ph1Pe0x10,28 =AP 4h2 = Pc0x16,37 = kB2P

2h2 = B1Pe20 = PAP 3h2

24 (10) iPR2 = jR1

(01) d40g

2 = d30e

20g = d2

0e40 = d2

0iw = d20jv = d2

0ku = d0e0g2Pe0 =

d0e0iv = d0e0ju = d0g3Pd0 = d0giu = d0r

2Pd0 = d0rik =d0rj

2 = d0lPv = d0mPu = d0z2 = e3

0gPe0 = e20g

2Pd0 = e20iu =

e0rij = e0kPv = e0lPu = e0wPj = gri2 = gjPv = gkPu =gvPj = rlP j = rPe0z = ilz = jkz = jPe0w = kPd0w = kPe0v =lPd0v = lP e0u = mPd0u

25 (1) h0iPR2 = h0jR1 = h1P2x16,35 = h2iR1 = Ph1Px16,35 =

P 2h1x16,35 = P 2h2x16,33 = R1P2j

continued



0j = d40e0i = d3

0gPj = d30kPe0 = d3

0lPd0 = d20e

20Pj =

d20e0jPe0 = d2

0e0kPd0 = d20giPe0 = d2

0gjPd0 = d20mP 2e0 =

d0e20iPe0 = d0e

20jPd0 = d0e0giPd0 = d0e0lP

2e0 = d0e0mP 2d0 =d0g

2P 2j = d0gkP 2e0 = d0glP 2d0 = d0lP e20 = d0mPd0Pe0 =

e30iPd0 = e2

0gP 2j = e20kP 2e0 = e2

0lP2d0 = e0g

2P 2i = e0gjP 2e0 =e0gkP 2d0 = e0gPe0Pj = e0kPe2

0 = e0lPd0Pe0 = e0mPd20 =

g2iP 2e0 = g2jP 2d0 = g2Pd0Pj = gjPe20 = gkPd0Pe0 = glPd2

0 =gmP 3e0 = rP 3v = i2Pv = ijPu = iuPj = zP 2u

30 (01) d20rP

3d0 = d20i

2Pd0 = d20jP

2j = d20kP 2i = d2

0Pj2 = d0e0iP2j =

d0e0jP2i = d0giP 2i = d0rPd0P

2d0 = d0ijP2e0 = d0ikP 2d0 =

d0iPe0Pj = d0j2P 2d0 = d0jPd0Pj = d0lP

3j = d0zP 3e0 =e20iP

2i = e0rP4e0 = e0i

2P 2e0 = e0ijP2d0 = e0iPd0Pj =

e0kP 3j = e0zP 3d0 = grP 4d0 = gi2P 2d0 = gjP 3j = gPjP 2j =rPd3

0 = rPe0P3e0 = rP 2e2

0 = i2Pe20 = ijPd0Pe0 = ikPd2

0 =ilP 3e0 = imP 3d0 = j2Pd2

0 = jkP 3e0 = jlP 3d0 = k2P 3d0 =kPe0P

2j = kPjP 2e0 = lPd0P2j = lP e0P

2i = lP jP 2d0 =mPd0P

2i = Pd0zP 2e0 = Pe0zP 2d0

(11) P 5Q1

31 (1) h0P5Q1 = Ph2P

4x′ = x′P 5h2 = P 3h2x18,20

32 (1) h20P

5Q1 = h0Ph2P4x′ = h0x

′P 5h2 = h0P3h2x18,20

33 (10) d0P5v = Pd0P

4v = vP 5d0 = P 2d0P3v = PvP 4d0 = P 3d0P

2v

(01) h30P

5Q1 = h20Ph2P

4x′ = h20x

′P 5h2 = h20P

3h2x18,20 =h2

1Ph1P4x′ = h2

1x′P 5h1 = h2

1P3h1x18,20 = h1Ph1P

2h1x18,20 =h1Ph1x

′P 4h1 = h1B1P6h1 = h1P

2h1x′P 3h1 = e0P

4Q =Ph3

1x18,20 = Ph21x

′P 3h1 = Ph1B1P5h1 = Ph1P

2h21x

′ =B1P

2h1P4h1 = B1P

3h21 = QP 4e0

(11) e0P5u = rP 5j = i2P 3j = iP jP 2i = Pe0P

4u = uP 5e0 = zP 4i =P 2e0P

3u = PuP 4e0 = P 3e0P2u

36 (1) d30P

5d0 = d20Pd0P

4d0 = d20P

2d0P3d0 = d0e0P

6e0 = d0gP 6d0 =d0Pd2

0P3d0 = d0Pd0P

2d20 = d0Pe0P

5e0 = d0P2e0P

4e0 =d0P

3e20 = e2

0P6d0 = e0Pd0P

5e0 = e0Pe0P5d0 = e0P

2d0P4e0 =

e0P2e0P

4d0 = e0P3d0P

3e0 = gPd0P5d0 = gP 2d0P

4d0 =gP 3d2

0 = Pd30P

2d0 = Pd0Pe0P4e0 = Pd0P

2e0P3e0 = Pe2

0P4d0 =

Pe0P2d0P

3e0 = Pe0P2e0P

3d0 = P 2d0P2e2

0

38 (1) h1P7u = Ph1P

6u = P 2h1P4Q = P 2h1P

5u = uP 7h1 =P 3h1P

4u = QP 6h1 = PuP 6h1 = P 4h1P3u = P 2uP 5h1

39 (1) d0P7j = iP 7e0 = jP 7d0 = Pd0P

6j = Pe0P6i = PjP 6d0 =

P 2d0P5j = P 2iP 5e0 = P 2jP 5d0 = P 3d0P

4j = P 3e0P4i =

P 3jP 4d0


Stem 977 (10) x7,81

(01) h2h6n

8 (1) h0x7,81

9 (10) h6d0g = h6e20

(01) h20x7,81 = h1x8,83 = h2x8,80

10 (10) x10,76

(01) h0h6d0g = h0h6e20 = h2h6d0e0

11 (10) h0x10,76

(01) h20h6d0g = h2

0h6e20 = h0h2h6d0e0 = h2

2h6d20 = h2h6gPh2 =

h3x10,63 = h4h6P2h2 = h5PD2 = h6c0j = f1Q2

12 (100) gx8,57 = nx7,40 = H1m = tA′ = tA

(010) h6Pj

(001) h20x10,76

13 (010) h0h6Pj = h6Ph2i

(001) h30x10,76 = h3x12,55

(101) h1x12,64 = h22x11,61

14 (01) h40x10,76 = h0h3x12,55 = g2x

′ = xB4

(11) h20h6Pj = h0h6Ph2i = h1h6P

2e0 = h6e0P2h1 = h6Ph1Pe0

15 (10) g2Q2 = rx9,39 = mx8,33

(01) h50x10,76 = h2

0h3x12,55 = h0g2x′ = h0xB4 = rx9,40 = ix8,51

16 (1) h60x10,76 = h3

0h3x12,55 = h20g2x

′ = h20xB4 = h0rx9,40 = h0ix8,51 =

h3xx′ = h3rB4

17 (1) e0gB4 = lB23 = mx10,27 = mx10,28

19 (1) d0x15,41

20 (10) e0g4 = e0gr2 = e0mw = glw = gmv = rlm

(01) d0rx′ = d0iB4 = e0x16,37 = gx16,33 = jx13,35 = kP 2D1 = lR2 =

zQ1

22 (1) Px18,50

23 (10) d30gm = d2

0e20m = d2

0e0gl = d20g

2k = d20ru = d0e

30l = d0e

20gk =

d0e0g2j = d0g

3i = d0r2i = d0vz = e4

0k = e30gj = e2

0g2i =

e0gmPe0 = e0rPv = e0uz = g2lP e0 = g2mPd0 = grPu = rjz =rPd0w = rPe0v = ikw = ilv = imu = j2w = jkv = jlu = k2u

(01) h0Px18,50 = h21x21,43 = h2

1Px17,50 = h1Ph1x17,50 = h2x22,39 =P 2h1x14,42

continued


Stem 97 continued26 (10) d0x

′P 2d0 = e0P3Q1 = Pd2

0x′ = Pe0P

2Q1 = Q1 P 3e0 =B21P

3d0 = P 2e0PQ1

(01) d40z = d3

0rPe0 = d30il = d3

0jk = d20e0rPd0 = d2

0e0ik = d20e0j

2 =d20gij = d2

0mPj = d0e20ij = d0e0gi2 = d0e0lP j = d0e0Pe0z =

d0grP 2e0 = d0gkPj = d0gPd0z = d0imPe0 = d0jlPe0 =d0jmPd0 = d0k

2Pe0 = d0klPd0 = e30i

2 = e20rP

2e0 = e20kPj =

e20Pd0z = e0grP 2d0 = e0gjPj = e0rPe2

0 = e0ilPe0 = e0imPd0 =e0jkPe0 = e0jlPd0 = e0k

2Pd0 = g2iP j = grPd0Pe0 = gikPe0 =gilPd0 = gj2Pe0 = gjkPd0 = gmP 2j = kmP 2e0 = l2P 2e0 =lmP 2d0 = uP 2v = vP 2u = PuPv

(11) d20x18,20

27 (1) h0d20x18,20 = h0d0x

′P 2d0 = h0e0P3Q1 = h0Pd2

0x′ =

h0Pe0P2Q1 = h0Q1 P 3e0 = h0B21P

3d0 = h0P2e0PQ1 =

h2d0P3Q1 = h2Pd0P

2Q1 = h2Pe0x18,20 = h2x′P 3e0 =

h2Q1 P 3d0 = h2P2d0PQ1 = d0Ph2P

2Q1 = d0P2h2PQ1 =

d0Q1 P 3h2 = e0Ph2x18,20 = e0x′P 3h2 = Ph2Pd0PQ1 =

Ph2x′P 2e0 = Ph2Q1 P 2d0 = B2P

4e0 = Pd0P2h2Q1 =

Pe0P2h2x

′ = x10,27P4h2 = x10,28P

4h2

28 (1) h20d

20x18,20 = h2

0d0x′P 2d0 = h2

0e0P3Q1 = h2

0Pd20x

′ =h2

0Pe0P2Q1 = h2

0Q1 P 3e0 = h20B21P

3d0 = h20P

2e0PQ1 =h0h2d0P

3Q1 = h0h2Pd0P2Q1 = h0h2Pe0x18,20 = h0h2x

′P 3e0 =h0h2Q1 P 3d0 = h0h2P

2d0PQ1 = h0d0Ph2P2Q1 =

h0d0P2h2PQ1 = h0d0Q1 P 3h2 = h0e0Ph2x18,20 = h0e0x

′P 3h2 =h0Ph2Pd0PQ1 = h0Ph2x

′P 2e0 = h0Ph2Q1 P 2d0 = h0B2P4e0 =

h0Pd0P2h2Q1 = h0Pe0P

2h2x′ = h0x10,27P

4h2 = h0x10,28P4h2 =

h22Pd0x18,20 = h2

2x′P 3d0 = h2d0Ph2x18,20 = h2d0x

′P 3h2 =h2Ph2x

′P 2d0 = h2B2P4d0 = h2Pd0P

2h2x′ = h2B21P

4h2 =c0P

3R2 = d0Ph2P2h2x

′ = d0B2P4h2 = Ph2

2Pd0x′ =

Ph2B2P3d0 = Ph2B21P

3h2 = Pc0P2R2 = B2Pd0P

3h2 =B2P

2h2P2d0 = P 2h2

2B21 = P 2c0PR2 = R2 P 3c0

continued


Stem 97 continued29 (10) P 4R2

(01) d30P

2u = d20rP

2i = d20i

3 = d20Pd0Pu = d2

0uP 2d0 = d0e0P3v =

d0gP 3u = d0riP2d0 = d0ijP j = d0Pd2

0u = d0Pe0P2v =

d0vP 3e0 = d0wP 3d0 = d0zP 2j = d0P2e0Pv = e2

0P3u = e0rP

3j =e0i

2Pj = e0Pd0P2v = e0Pe0P

2u = e0uP 3e0 = e0vP 3d0 =e0zP 2i = e0P

2d0Pv = e0P2e0Pu = gPd0P

2u = guP 3d0 =gP 2d0Pu = riPd2

0 = rjP 3e0 = rkP 3d0 = rPe0P2j = rPjP 2e0 =

i2jPe0 = i2kPd0 = ij2Pd0 = ilP 2j = imP 2i = izP 2e0 =jkP 2j = jlP 2i = jzP 2d0 = k2P 2i = kPj2 = Pd0Pe0Pv =Pd0vP 2e0 = Pd0wP 2d0 = Pd0zPj = Pe2

0Pu = Pe0uP 2e0 =Pe0vP 2d0

30 (1) h0P4R2 = Ph2x25,24 = P 3h2R1

31 (1) h20P

4R2 = h0Ph2x25,24 = h0P3h2R1 = h1P

5Q1 = Ph1P4Q1 =

P 2h1P3Q1 = R1P

5h2 = Q1 P 5h1 = P 3h1P2Q1 = PQ1 P 4h1

32 (1) d40P

3e0 = d30e0P

3d0 = d30Pd0P

2e0 = d30Pe0P

2d0 =d20e0Pd0P

2d0 = d20gP 4e0 = d2

0Pd20Pe0 = d0e

20P

4e0 = d0e0gP 4d0 =d0e0Pd3

0 = d0e0Pe0P3e0 = d0e0P

2e20 = d0gPd0P

3e0 =d0gPe0P

3d0 = d0gP 2d0P2e0 = d0Pe2

0P2e0 = e3

0P4d0 =

e20Pd0P

3e0 = e20Pe0P

3d0 = e20P

2d0P2e0 = e0gPd0P

3d0 =e0gP 2d2

0 = e0Pd0Pe0P2e0 = e0Pe2

0P2d0 = g2P 5e0 = gPd2

0P2e0 =

gPd0Pe0P2d0 = iP 4v = jP 4u = Pd0Pe3

0 = uP 4j = vP 4i =PjP 3u = PuP 3j = P 2iP 2v = P 2jP 2u

35 (1) d30P

4i = d20iP

4d0 = d20P

2d0P2i = d0e0P

5j = d0iPd0P3d0 =

d0iP2d2

0 = d0jP5e0 = d0kP 5d0 = d0Pd2

0P2i = d0Pe0P

4j =d0PjP 4e0 = d0P

2e0P3j = d0P

2jP 3e0 = e0iP5e0 = e0jP

5d0 =e0Pd0P

4j = e0Pe0P4i = e0PjP 4d0 = e0P

2d0P3j = e0P

2iP 3e0 =e0P

2jP 3d0 = giP 5d0 = gPd0P4i = gP 2iP 3d0 = iPd2

0P2d0 =

iPe0P4e0 = iP 2e0P

3e0 = jPd0P4e0 = jPe0P

4d0 = jP 2d0P3e0 =

jP 2e0P3d0 = kPd0P

4d0 = kP 2d0P3d0 = lP 6e0 = mP 6d0 =

Pd0Pe0P3j = Pd0PjP 3e0 = Pd0P

2e0P2j = Pe0PjP 3d0 =

Pe0P2d0P

2j = Pe0P2e0P

2i = PjP 2d0P2e0

38 (1) iP 6j = jP 6i = P 2iP 4j = P 2jP 4i

39 (1) h0iP6j = h0jP

6i = h0P2iP 4j = h0P

2jP 4i = h21P

7u =h1Ph1P

6u = h1P2h1P

4Q = h1P2h1P

5u = h1uP 7h1 =h1P

3h1P4u = h1QP 6h1 = h1PuP 6h1 = h1P

4h1P3u =

h1P2uP 5h1 = h2iP

6i = h2P2iP 4i = Ph2

1P4Q = Ph2

1P5u =

Ph1P2h1P

4u = Ph1uP 6h1 = Ph1P3h1P

3u = Ph1QP 5h1 =Ph1PuP 5h1 = Ph1P

4h1P2u = rP 8h2 = qP 8h1 = i2P 6h2 =

iP 2h2P4i = iP 2iP 4h2 = P 2h2

1P3u = P 2h1uP 5h1 =

P 2h1P3h1P

2u = P 2h1QP 4h1 = P 2h1PuP 4h1 = P 2h2P2i2 =

uP 3h1P4h1 = P 3h2

1Q = P 3h21Pu


Stem 986 (1) h2h6d1 = h4h6g = h5Q3

8 (10) h6m

(01) h2x7,79

9 (10) h3x8,75

(01) h0h6m = h2h6l = h6e0f0

10 (01) h20h6m = h0h2h6l = h0h6e0f0 = h1h6d0g = h1h6e

20 = h2

2h6k =h2h6d0f0

(11) h0h3x8,75 = c2Q2 = f1D2

11 (10) h2x10,73 = d1x7,40 = H1t

(01) h1x10,76

12 (10) h3x11,61

(11) h22x10,65 = h5x11,35

13 (1) h0h3x11,61

14 (100) x14,67

(010) e0gA′ = e0gA = g2D2 = nx9,39 = tx8,33 = lx7,40 = mx7,34

(001) h20h3x11,61 = g2R1 = xX1

(011) rG21

15 (1) h30h3x11,61 = h0g2R1 = h0xX1 = h0rG21 = c0x12,55 = yB4

18 (1) x18,60

19 (1) d0x15,43 = rP 2D1 = uB21 = vQ1 = wx′

21 (1) Px17,52

22 (10) d20g

2r = d20m

2 = d0e20gr = d0e0lm = d0gkm = d0gl2 = d0uw =

d0v2 = e4

0r = e20km = e2

0l2 = e0g

2z = e0gjm = e0gkl = e0uv =g2im = g2jl = g2k2 = gu2 = riw = rjv = rku

(01) d30Q1 = d2

0e0x′ = d0gPQ1 = d0Pd0x10,27 = d0Pd0x10,28 =

d0Pe0B21 = e20PQ1 = e0Pd0B21 = e0Pe0Q1 = gPd0Q1 =

gPe0x′ = B23P

2e0

24 (1) Pd0x16,32

25 (100) iPd0x′ = jP 2Q1 = B4P

3d0 = Q1 P 2j = B21P2i = PjPQ1

(010) d40v = d3

0e0u = d30rj = d2

0e0ri = d20gPv = d2

0kz = d20Pe0w =

d0e20Pv = d0e0gPu = d0e0jz = d0e0Pd0w = d0e0Pe0v =

d0grPj = d0giz = d0gPd0v = d0gPe0u = d0rkPe0 = d0rlPd0 =d0ijm = d0ikl = d0j

2l = d0jk2 = e3

0Pu = e20rPj = e2

0iz =e20Pd0v = e2

0Pe0u = e0gPd0u = e0rjPe0 = e0rkPd0 = e0i2m =

e0ijl = e0ik2 = e0j

2k = g2P 2v = griPe0 = grjPd0 = gi2l =gijk = gj3 = gwP 2e0 = rmP 2e0 = kmPj = l2Pj = lP e0z =mPd0z

(110) kx18,20

(001) h0Pd0x16,32 = h2P2x16,35 = Ph2Px16,35 = P 2h2x16,35

(101) d20R1 = e0P

2R2 = Pe0PR2 = P 2d0P2D1 = P 2e0R2

continued


Stem 98 continued26 (10) h0iPd0x

′ = h0jP2Q1 = h0kx18,20 = h0B4P

3d0 = h0Q1 P 2j =h0B21P

2i = h0PjPQ1 = h2iP2Q1 = h2jx18,20 = h2x

′P 2j =h2Q1 P 2i = f0P

3Q1 = Ph2iPQ1 = Ph2x′Pj = iP 2h2Q1 =

jP 2h2x′ = B2P

3j = P 3h2x13,35

(01) h20Pd0x16,32 = h0h2P

2x16,35 = h0Ph2Px16,35 = h0P2h2x16,35 =

h22P

2x16,32 = h2P2h2x16,32 = Ph2

2x16,32 = P 3h2x13,34

(11) h0d20R1 = h0e0P

2R2 = h0Pe0PR2 = h0P2d0P

2D1 =h0P

2e0R2 = h2d0P2R2 = h2Pd0PR2 = h2Pe0R1 =

h2P2d0R2 = d0Ph2PR2 = d0P

2h2R2 = d0R1P2d0 =

e0Ph2R1 = Ph2Pd0R2 = Pd20R1

27 (1) h20d

20R1 = h2

0e0P2R2 = h2

0iPd0x′ = h2

0jP2Q1 = h2

0kx18,20 =h2

0Pe0PR2 = h20B4P

3d0 = h20Q1 P 2j = h2

0B21P2i = h2

0PjPQ1 =h2

0P2d0P

2D1 = h20P

2e0R2 = h0h2d0P2R2 = h0h2iP

2Q1 =h0h2jx18,20 = h0h2Pd0PR2 = h0h2Pe0R1 = h0h2x

′P 2j =h0h2Q1 P 2i = h0h2P

2d0R2 = h0d0Ph2PR2 = h0d0P2h2R2 =

h0d0R1P2d0 = h0e0Ph2R1 = h0f0P

3Q1 = h0Ph2iPQ1 =h0Ph2Pd0R2 = h0Ph2x

′Pj = h0iP2h2Q1 = h0jP

2h2x′ =

h0B2P3j = h0Pd2

0R1 = h0P3h2x13,35 = h1d

20x18,20 =

h1d0x′P 2d0 = h1e0P

3Q1 = h1Pd20x

′ = h1Pe0P2Q1 =

h1Q1 P 3e0 = h1B21P3d0 = h1P

2e0PQ1 = h22ix18,20 =

h22Pd0R1 = h2

2x′P 2i = h2d0Ph2R1 = h2iP

2h2x′ = h2B4P

4h2 =h2R1P

3e0 = h2P3h2P

2D1 = d20P

2h1x′ = d0Ph1Pd0x

′ =d0B1P

3d0 = d0B21P3h1 = e0Ph1P

2Q1 = e0P2h1PQ1 =

e0R1P3h2 = e0Q1 P 3h1 = f0Ph2x18,20 = f0x

′P 3h2 =gPh1x18,20 = gx′P 3h1 = Ph1Pe0PQ1 = Ph1Q1 P 2e0 =Ph1B21P

2d0 = Ph22ix

′ = Ph2B2P2i = Ph2P

2h2P2D1 =

Ph2B4P3h2 = Ph2R1P

2e0 = iB2P3h2 = B1Pd0P

2d0 =Pd0P

2h1B21 = Pe0P2h1Q1 = Pe0P

2h2R1 = P 2h22B4 = B23P

4h1

28 (1) d70 = d4

0e0Pe0 = d40gPd0 = d3

0e20Pd0 = d2

0e0gP 2e0 = d20g

2P 2d0 =d20gPe2

0 = d20iPu = d0e

30P

2e0 = d0e20gP 2d0 = d0e

20Pe2

0 =d0e0gPd0Pe0 = d0g

2Pd20 = d0iPd0u = d0jP

2v = d0kP 2u =d0vP 2j = d0wP 2i = d0PjPv = e4

0P2d0 = e3

0Pd0Pe0 = e20gPd2

0 =e0g

2P 3e0 = e0iP2v = e0jP

2u = e0uP 2j = e0vP 2i = e0PjPu =g3P 3d0 = g2Pe0P

2e0 = giP 2u = guP 2i = r2P 3d0 = ri2Pd0 =rjP 2j = rkP 2i = rPj2 = i3k = i2j2 = iPe0Pv = ivP 2e0 =iwP 2d0 = izP j = jPd0Pv = jPe0Pu = juP 2e0 = jvP 2d0 =kPd0Pu = kuP 2d0 = lP 3v = mP 3u = Pd0vPj = Pe0uPj

continued



0P2j = d3

0e0P2i = d3

0iP2e0 = d3

0jP2d0 = d3

0Pd0Pj =d20e0iP

2d0 = d20gP 3j = d2

0iPd0Pe0 = d20jPd2

0 = d20kP 3e0 =

d20lP

3d0 = d0e20P

3j = d0e0iPd20 = d0e0jP

3e0 = d0e0kP 3d0 =d0e0Pe0P

2j = d0e0PjP 2e0 = d0giP 3e0 = d0gjP 3d0 =d0gPd0P

2j = d0gPe0P2i = d0gPjP 2d0 = d0jPe0P

2e0 =d0kPd0P

2e0 = d0kPe0P2d0 = d0lPd0P

2d0 = d0mP 4e0 =d0Pe2

0Pj = e20iP

3e0 = e20jP

3d0 = e20Pd0P

2j = e20Pe0P

2i =e20PjP 2d0 = e0giP 3d0 = e0gPd0P

2i = e0iPe0P2e0 =

e0jPd0P2e0 = e0jPe0P

2d0 = e0kPd0P2d0 = e0lP

4e0 =e0mP 4d0 = e0Pd0Pe0Pj = g2P 4j = giPd0P

2e0 = giPe0P2d0 =

gjPd0P2d0 = gkP 4e0 = glP 4d0 = gPd2

0Pj = iPe30 = jPd0Pe2

0 =kPd2

0Pe0 = lPd30 = lP e0P

3e0 = lP 2e20 = mPd0P

3e0 =mPe0P

3d0 = mP 2d0P2e0

34 (1) d0rP5d0 = d0i

2P 3d0 = d0iPd0P2i = d0jP

4j = d0kP 4i =d0PjP 3j = d0P

2j2 = e0iP4j = e0jP

4i = e0P2iP 2j = giP 4i =

gP 2i2 = rPd0P4d0 = rP 2d0P

3d0 = i2Pd0P2d0 = ijP 4e0 =

ikP 4d0 = iPe0P3j = iP jP 3e0 = iP 2e0P

2j = j2P 4d0 =jPd0P

3j = jP jP 3d0 = jP 2d0P2j = jP 2e0P

2i = kP 2d0P2i =

lP 5j = Pd0PjP 2j = Pe0PjP 2i = zP 5e0 = Pj2P 2d0

37 (1) P 7v


Stem 995 (1) h3g3 = h4f2

6 (1) h0h3g3 = h0h4f2 = h24p

′

7 (100) x7,83

(010) x7,84

(101) h6t

8 (1) h0x7,84

9 (10) x9,86

(01) h20x7,84 = h2x8,83 = h5G21 = c2D2

10 (10) h22x8,78 = e1A

′

(01) h30x7,84 = h0h2x8,83 = h0h5G21 = h0c2D2 = h1h3x8,75 = pr1 =

D3y = xH1

(11) e1A

11 (1) h3x10,65

12 (10) h21x10,76

(01) h0h3x10,65 = yA′

13 (100) h2x12,64

(001) h20h3x10,65 = h0yA′ = h1h3x11,61 = e1X1 = nG21 = xx8,32

(011) h6d0Pd0

(111) h3x12,58

14 (10) h0h2x12,64 = h22x12,60 = h5P

2D1 = c0x11,61

(01) h0h6d0Pd0 = h2h6P2e0 = h6e0P

2h2 = h6Ph2Pe0

(11) h0h3x12,58

15 (1) h20h3x12,58 = h2

0h6d0Pd0 = h0h2h6P2e0 = h0h6e0P

2h2 =h0h6Ph2Pe0 = h2

2h6P2d0 = h2h6d0P

2h2 = h2h6Ph2Pd0 =h2

3x13,46 = h6d0Ph22 = xx10,27 = yX1

16 (1) h2x15,58

17 (10) gx13,42

(01) Ph1x12,55 = B1x′

18 (1) d0gB23 = e20B23 = e0gx10,27 = e0gx10,28 = g2B21 = uB4

20 (1) d0x16,42 = e0x16,38 = gx16,35

21 (10) d0g2w = d0grm = e2

0gw = e20rm = e0g

2v = e0grl = g3u = g2rk =r2u = km2 = l2m

(01) d20x13,35 = d0e0P

2D1 = d0gR2 = d0ix10,27 = d0ix10,28 =d0jB21 = d0kQ1 = d0lx

′ = d0Pe0B4 = e20R2 = e0iB21 =

e0jQ1 = e0kx′ = e0Pd0B4 = giQ1 = gjx′ = mPQ1 = B23Pj

23 (1) ix16,32

continued


Stem 99 continued24 (100) i2x′ = B4P

2i

(010) d30e0g

2 = d20e

30g = d2

0rz = d20jw = d2

0kv = d20lu = d0e

50 = d0e0iw =

d0e0jv = d0e0ku = d0g3Pe0 = d0giv = d0gju = d0r

2Pe0 =d0ril = d0rjk = d0mPv = e2

0g2Pe0 = e2

0iv = e20ju = e0g

3Pd0 =e0giu = e0r

2Pd0 = e0rik = e0rj2 = e0lPv = e0mPu = e0z

2 =grij = gkPv = glPu = gwPj = rmPj = imz = jlz = k2z =kPe0w = lPd0w = lP e0v = mPd0v = mPe0u

(110) rx18,20

(001) h0ix16,32

(101) jPR2 = kR1 = Pd0x16,33 = PjR2

25 (10) h0rx18,20 = h0i2x′ = h0B4P

2i = h3P2x16,32

(01) h20ix16,32

(11) h0jPR2 = h0kR1 = h0Pd0x16,33 = h0PjR2 = h1Pd0x16,32 =h2iPR2 = h2jR1 = d0Ph1x16,32 = f0P

2R2 = Ph2iR2 =iPd0R1 = P 2h1x16,38 = P 2h2x16,37 = P 2d0W1

26 (1) h30ix16,32 = h2

0rx18,20 = h20i

2x′ = h20B4P

2i = h0h3P2x16,32 =

h3ix18,20 = h3x′P 2i

27 (10) d50k = d4

0e0j = d40gi = d3

0e20i = d3

0lP e0 = d30mPd0 = d2

0e0gPj =d20e0kPe0 = d2

0e0lPd0 = d20gjPe0 = d2

0gkPd0 = d0e30Pj =

d0e20jPe0 = d0e

20kPd0 = d0e0giPe0 = d0e0gjPd0 = d0e0mP 2e0 =

d0g2iPd0 = d0glP 2e0 = d0gmP 2d0 = d0rP

2u = d0i2u =

d0mPe20 = e3

0iPe0 = e30jPd0 = e2

0giPd0 = e20lP

2e0 = e20mP 2d0 =

e0g2P 2j = e0gkP 2e0 = e0glP 2d0 = e0lP e2

0 = e0mPd0Pe0 =g3P 2i = g2jP 2e0 = g2kP 2d0 = g2Pe0Pj = gkPe2

0 = glPd0Pe0 =gmPd2

0 = rPd0Pu = ruP 2d0 = ijPv = ikPu = ivPj = j2Pu =juPj = zP 2v

(01) h40ix16,32 = h3

0rx18,20 = h30i

2x′ = h30B4P

2i = h20h3P

2x16,32 =h0h3ix18,20 = h0h3x

′P 2i = g2P4i = xiP 2i

(11) r2P 2i = ri3

28 (1) h50ix16,32 = h4

0rx18,20 = h40i

2x′ = h40B4P

2i = h30h3P

2x16,32 =h2

0h3ix18,20 = h20h3x

′P 2i = h0g2P4i = h0xiP 2i = h0r

2P 2i =h0ri

3 = h23P

4x′

continued



4x′ = x′P 4d0

(01) d30iP j = d2

0rP3e0 = d2

0i2Pe0 = d2

0ijPd0 = d20kP 2j = d2

0lP2i =

d20zP 2d0 = d0e0rP

3d0 = d0e0i2Pd0 = d0e0jP

2j = d0e0kP 2i =d0e0Pj2 = d0giP 2j = d0gjP 2i = d0rPd0P

2e0 = d0rPe0P2d0 =

d0ikP 2e0 = d0ilP2d0 = d0j

2P 2e0 = d0jkP 2d0 = d0jPe0Pj =d0kPd0Pj = d0mP 3j = d0Pd2

0z = e20iP

2j = e20jP

2i = e0giP 2i =e0rPd0P

2d0 = e0ijP2e0 = e0ikP 2d0 = e0iPe0Pj = e0j

2P 2d0 =e0jPd0Pj = e0lP

3j = e0zP 3e0 = grP 4e0 = gi2P 2e0 = gijP 2d0 =giPd0Pj = gkP 3j = gzP 3d0 = rPd2

0Pe0 = ijPe20 = ikPd0Pe0 =

ilPd20 = imP 3e0 = j2Pd0Pe0 = jkPd2

0 = jlP 3e0 = jmP 3d0 =k2P 3e0 = klP 3d0 = lP e0P

2j = lP jP 2e0 = mPd0P2j =

mPe0P2i = mPjP 2d0 = Pe0zP 2e0

(11) P 2d0x18,20

31 (1) h0d0P4x′ = h0x

′P 4d0 = h0P2d0x18,20 = h2P

5Q1 = Ph2P4Q1 =

P 2h2P3Q1 = Q1 P 5h2 = P 3h2P

2Q1 = PQ1 P 4h2

32 (1) h20d0P

4x′ = h20x

′P 4d0 = h20P

2d0x18,20 = h0h2P5Q1 =

h0Ph2P4Q1 = h0P

2h2P3Q1 = h0Q1 P 5h2 = h0P

3h2P2Q1 =

h0PQ1 P 4h2 = h2Ph2P4x′ = h2x

′P 5h2 = h2P3h2x18,20 =

Ph2P2h2x18,20 = Ph2x

′P 4h2 = B2P6h2 = P 2h2x

′P 3h2

33 (1) d20P

4u = d0rP4i = d0i

2P 2i = d0Pd0P3u = d0uP 4d0 =

d0P2d0P

2u = d0PuP 3d0 = e0P5v = gP 5u = riP 4d0 =

rP 2d0P2i = i3P 2d0 = ijP 3j = iP jP 2j = jP jP 2i = Pd2

0P2u =

Pd0uP 3d0 = Pd0P2d0Pu = Pe0P

4v = uP 2d20 = vP 5e0 =

wP 5d0 = zP 4j = P 2e0P3v = PvP 4e0 = P 3e0P

2v

36 (1) d30P

5e0 = d20e0P

5d0 = d20Pd0P

4e0 = d20Pe0P

4d0 = d20P

2d0P3e0 =

d20P

2e0P3d0 = d0e0Pd0P

4d0 = d0e0P2d0P

3d0 = d0gP 6e0 =d0Pd2

0P3e0 = d0Pd0Pe0P

3d0 = d0Pd0P2d0P

2e0 = d0Pe0P2d2

0 =e20P

6e0 = e0gP 6d0 = e0Pd20P

3d0 = e0Pd0P2d2

0 = e0Pe0P5e0 =

e0P2e0P

4e0 = e0P3e2

0 = gPd0P5e0 = gPe0P

5d0 = gP 2d0P4e0 =

gP 2e0P4d0 = gP 3d0P

3e0 = Pd30P

2e0 = Pd20Pe0P

2d0 =Pe2

0P4e0 = Pe0P

2e0P3e0 = P 2e3

0

39 (1) d20P

6i = d0iP6d0 = d0P

2d0P4i = d0P

2iP 4d0 = e0P7j =

iPd0P5d0 = iP 2d0P

4d0 = iP 3d20 = jP 7e0 = kP 7d0 = Pd2

0P4i =

Pd0P2iP 3d0 = Pe0P

6j = PjP 6e0 = P 2d20P

2i = P 2e0P5j =

P 2jP 5e0 = P 3e0P4j = P 3jP 4e0


Stem 1004 (1) h4c3

5 (1) h0h4c3 = h5p′

6 (10) h6x

(01) h20h4c3 = h0h5p

′ = h1h3g3 = h1h4f2 = h24p1

7 (1) h0h6x

8 (1000) h2x7,81

(0100) h3h6r

(0010) h1x7,84

(0001) h20h6x

(0101) h1h6t = h1x7,83 = h22h6n = h6c1f0

9 (100) h6e0g

(010) e1H1

(001) h30h6x = h0h3h6r

(011) h3x8,78

10 (100) x10,82

(010) h1x9,86

(001) h40h6x = h2

0h3h6r = h0h3x8,78 = h0h6e0g = h2h6d0g = h2h6e20 =

h23h6i = h4h6Pd0

11 (100) h3x10,67

(010) h0x10,82

(110) h2x10,76

(001) h50h6x = h3

0h3h6r = h20h3x8,78 = h2

0h6e0g = h0h2h6d0g =h0h2h6e

20 = h0h

23h6i = h0h4h6Pd0 = h2

2h6d0e0 = h5PA = h6c0k

(101) H1y

12 (100) h6d0i

(010) h1h3x10,65 = d1G21 = e1x8,32

(001) h20x10,82 = h0h2x10,76

13 (100) x13,73

(010) h0h6d0i = h2h6Pj = h6Ph2j

(001) h30x10,82 = h2

0h2x10,76 = h31x10,76 = h3x12,60 = D3u = Ph1x8,75 =

GB1

14 (1) h20h6d0i = h0h2h6Pj = h0h6Ph2j = h1h3x12,58 = h1h6d0Pd0 =

h2h6Ph2i = h23x12,48 = h6d

20Ph1 = h6f0P

2h2 = h6gP 2h1 =e1x10,27 = g2Q1 = qG21 = yx8,32

16 (1) gx12,44

17 (1) g2B4 = mB23

18 (1) h1Ph1x12,55 = h1B1x′ = uX1

19 (1) e0x15,41

continued


Stem 100 continued20 (10) g5 = g2r2 = gmw = rm2

(01) d0rQ1 = d0jB4 = e0rx′ = e0iB4 = gx16,37 = kx13,35 = lP 2D1 =

mR2 = zB21

22 (1) Px18,55

23 (100) d20e0gm = d2

0g2l = d2

0rv = d0e30m = d0e

20gl = d0e0g

2k = d0e0ru =d0g

3j = d0r2j = d0wz = e4

0l = e30gk = e2

0g2j = e0g

3i = e0r2i =

e0vz = g2mPe0 = grPv = guz = rkz = rPe0w = ilw = imv =jkw = jlv = jmu = k2v = klu

(010) x′Q

(001) x′Pu

(011) rR1 = ix16,33

24 (1) h0rR1 = h0ix16,33 = h0x′Q = i2R1 = X1P

2i

25 (1) h20rR1 = h2

0ix16,33 = h20x

′Q = h0i2R1 = h0X1P

2i = h3iR1

26 (100) d20P

2Q1 = d0Pd0PQ1 = d0x′P 2e0 = d0Q1 P 2d0 = e0x

′P 2d0 =gP 3Q1 = Pd2

0Q1 = Pd0Pe0x′ = B21P

3e0 = x10,27P3d0 =

x10,28P3d0

(010) d50r = d3

0e0z = d30im = d3

0jl = d30k

2 = d20e0rPe0 = d2

0e0il =d20e0jk = d2

0grPd0 = d20gik = d2

0gj2 = d0e20rPd0 = d0e

20ik =

d0e20j

2 = d0e0gij = d0e0mPj = d0g2i2 = d0glP j = d0gPe0z =

d0jmPe0 = d0klPe0 = d0kmPd0 = d0l2Pd0 = d0uPu = e3

0ij =e20gi2 = e2

0lP j = e20Pe0z = e0grP 2e0 = e0gkPj = e0gPd0z =

e0imPe0 = e0jlPe0 = e0jmPd0 = e0k2Pe0 = e0klPd0 =

g2rP 2d0 = g2jP j = grPe20 = gilPe0 = gimPd0 = gjkPe0 =

gjlPd0 = gk2Pd0 = riPu = lmP 2e0 = m2P 2d0 = Pd0u2 =

vP 2v = wP 2u = Pv2

(110) d0e0x18,20

(001) h30rR1 = h3

0ix16,33 = h30x

′Q = h20i

2R1 = h20X1P

2i = h0h3iR1 =h3R1P

2i = riQ

continued


Stem 100 continued27 (10) h4P

4x′ = c0P2x16,32 = P 2c0x16,32

(01) h40rR1 = h4

0ix16,33 = h40x

′Q = h30i

2R1 = h30X1P

2i = h20h3iR1 =

h0h3R1P2i = h0riQ = h2

3x25,24

(11) h0d20P

2Q1 = h0d0e0x18,20 = h0d0Pd0PQ1 = h0d0x′P 2e0 =

h0d0Q1 P 2d0 = h0e0x′P 2d0 = h0gP 3Q1 = h0Pd2

0Q1 =h0Pd0Pe0x

′ = h0B21P3e0 = h0x10,27P

3d0 = h0x10,28P3d0 =

h2d20x18,20 = h2d0x

′P 2d0 = h2e0P3Q1 = h2Pd2

0x′ =

h2Pe0P2Q1 = h2Q1 P 3e0 = h2B21P

3d0 = h2P2e0PQ1 =

d20P

2h2x′ = d0Ph2Pd0x

′ = d0B2P3d0 = d0B21P

3h2 =e0Ph2P

2Q1 = e0P2h2PQ1 = e0Q1 P 3h2 = gPh2x18,20 =

gx′P 3h2 = Ph2Pe0PQ1 = Ph2Q1 P 2e0 = Ph2B21P2d0 =

B2Pd0P2d0 = Pd0P

2h2B21 = Pe0P2h2Q1 = B23P

4h2

28 (1) h50rR1 = h5

0ix16,33 = h50x

′Q = h40i

2R1 = h40X1P

2i =h3

0h3iR1 = h20h3R1P

2i = h20d

20P

2Q1 = h20d0e0x18,20 =

h20d0Pd0PQ1 = h2

0d0x′P 2e0 = h2

0d0Q1 P 2d0 = h20e0x

′P 2d0 =h2

0gP 3Q1 = h20riQ = h2

0Pd20Q1 = h2

0Pd0Pe0x′ =

h20B21P

3e0 = h20x10,27P

3d0 = h20x10,28P

3d0 = h0h2d20x18,20 =

h0h2d0x′P 2d0 = h0h2e0P

3Q1 = h0h2Pd20x

′ = h0h2Pe0P2Q1 =

h0h2Q1 P 3e0 = h0h2B21P3d0 = h0h2P

2e0PQ1 =h0h

23x25,24 = h0d

20P

2h2x′ = h0d0Ph2Pd0x

′ = h0d0B2P3d0 =

h0d0B21P3h2 = h0e0Ph2P

2Q1 = h0e0P2h2PQ1 =

h0e0Q1 P 3h2 = h0gPh2x18,20 = h0gx′P 3h2 = h0Ph2Pe0PQ1 =h0Ph2Q1 P 2e0 = h0Ph2B21P

2d0 = h0B2Pd0P2d0 =

h0Pd0P2h2B21 = h0Pe0P

2h2Q1 = h0B23P4h2 = h2

2d0P3Q1 =

h22Pd0P

2Q1 = h22Pe0x18,20 = h2

2x′P 3e0 = h2

2Q1 P 3d0 =h2

2P2d0PQ1 = h2d0Ph2P

2Q1 = h2d0P2h2PQ1 =

h2d0Q1 P 3h2 = h2e0Ph2x18,20 = h2e0x′P 3h2 = h2Ph2Pd0PQ1 =

h2Ph2x′P 2e0 = h2Ph2Q1 P 2d0 = h2B2P

4e0 = h2Pd0P2h2Q1 =

h2Pe0P2h2x

′ = h2x10,27P4h2 = h2x10,28P

4h2 = h3i2Q =

c0ix18,20 = c0Pd0R1 = c0x′P 2i = d0Ph2

2PQ1 =d0Ph2P

2h2Q1 = d0Pc0R1 = e0Ph2P2h2x

′ = e0B2P4h2 =

Ph22Pd0Q1 = Ph2

2Pe0x′ = Ph2B2P

3e0 = Ph2x10,27P3h2 =

Ph2x10,28P3h2 = yiP 2i = ix′P 2c0 = B2Pe0P

3h2 =B2P

2h2P2e0 = Q2P

5h2 = P 2h22x10,27 = P 2h2

2x10,28 = B4P4c0 =

P 2D1P3c0

continued


Stem 100 continued29 (10) P 2d0R1

(01) d30P

2v = d20e0P

2u = d20rP

2j = d20i

2j = d20Pd0Pv = d2

0Pe0Pu =d20uP 2e0 = d2

0vP 2d0 = d0e0rP2i = d0e0i

3 = d0e0Pd0Pu =d0e0uP 2d0 = d0gP 3v = d0riP

2e0 = d0rjP2d0 = d0rPd0Pj =

d0ikPj = d0iPd0z = d0j2Pj = d0Pd2

0v = d0Pd0Pe0u =d0wP 3e0 = e2

0P3v = e0gP 3u = e0riP

2d0 = e0ijP j = e0Pd20u =

e0Pe0P2v = e0vP 3e0 = e0wP 3d0 = e0zP 2j = e0P

2e0Pv =grP 3j = gi2Pj = gPd0P

2v = gPe0P2u = guP 3e0 = gvP 3d0 =

gzP 2i = gP 2d0Pv = gP 2e0Pu = riPd0Pe0 = rjPd20 = rkP 3e0 =

rlP 3d0 = i2kPe0 = i2lPd0 = ij2Pe0 = ijkPd0 = imP 2j =j3Pd0 = jlP 2j = jmP 2i = jzP 2e0 = k2P 2j = klP 2i = kzP 2d0 =lP j2 = Pd0wP 2e0 = Pe2

0Pv = Pe0vP 2e0 = Pe0wP 2d0 = Pe0zPj

(11) d0x25,24

30 (1) h0d0x25,24 = h0P2d0R1 = h2P

4R2 = Ph2P3R2 = P 2h2P

2R2 =R1P

4d0 = P 3h2PR2 = R2 P 4h2

31 (1) h20d0x25,24 = h2

0P2d0R1 = h0h2P

4R2 = h0Ph2P3R2 =

h0P2h2P

2R2 = h0R1P4d0 = h0P

3h2PR2 = h0R2 P 4h2 =h1d0P

4x′ = h1x′P 4d0 = h1P

2d0x18,20 = h2Ph2x25,24 =h2P

3h2R1 = d0P2h1x18,20 = d0x

′P 4h1 = Ph1Pd0x18,20 =Ph1x

′P 3d0 = Ph2P2h2R1 = B1P

5d0 = Pd0x′P 3h1 =

P 2h1x′P 2d0 = B21P

5h1

32 (1) d50P

2d0 = d40Pd2

0 = d30e0P

3e0 = d30gP 3d0 = d3

0Pe0P2e0 =

d20e

20P

3d0 = d20e0Pd0P

2e0 = d20e0Pe0P

2d0 = d20gPd0P

2d0 =d20Pd0Pe2

0 = d0e20Pd0P

2d0 = d0e0gP 4e0 = d0e0Pd20Pe0 =

d0g2P 4d0 = d0gPd3

0 = d0gPe0P3e0 = d0gP 2e2

0 = d0iP3u =

d0PuP 2i = e30P

4e0 = e20gP 4d0 = e2

0Pd30 = e2

0Pe0P3e0 = e2

0P2e2

0 =e0gPd0P

3e0 = e0gPe0P3d0 = e0gP 2d0P

2e0 = e0Pe20P

2e0 =g2Pd0P

3d0 = g2P 2d20 = gPd0Pe0P

2e0 = gPe20P

2d0 = iPd0P2u =

iuP 3d0 = iP 2d0Pu = jP 4v = kP 4u = Pd0uP 2i = Pe40 = vP 4j =

wP 4i = PjP 3v = PvP 3j = P 2jP 2v

35 (1) d30P

4j = d20e0P

4i = d20iP

4e0 = d20jP

4d0 = d20Pd0P

3j =d20PjP 3d0 = d2

0P2d0P

2j = d20P

2e0P2i = d0e0iP

4d0 =d0e0P

2d0P2i = d0gP 5j = d0iPd0P

3e0 = d0iPe0P3d0 =

d0iP2d0P

2e0 = d0jPd0P3d0 = d0jP

2d20 = d0kP 5e0 = d0lP

5d0 =d0Pd2

0P2j = d0Pd0Pe0P

2i = d0Pd0PjP 2d0 = e20P

5j =e0iPd0P

3d0 = e0iP2d2

0 = e0jP5e0 = e0kP 5d0 = e0Pd2

0P2i =

e0Pe0P4j = e0PjP 4e0 = e0P

2e0P3j = e0P

2jP 3e0 = giP 5e0 =gjP 5d0 = gPd0P

4j = gPe0P4i = gPjP 4d0 = gP 2d0P

3j =gP 2iP 3e0 = gP 2jP 3d0 = iPd2

0P2e0 = iPd0Pe0P

2d0 =jPd2

0P2d0 = jPe0P

4e0 = jP 2e0P3e0 = kPd0P

4e0 = kPe0P4d0 =

kP 2d0P3e0 = kP 2e0P

3d0 = lPd0P4d0 = lP 2d0P

3d0 = mP 6e0 =Pd3

0Pj = Pe20P

3j = Pe0PjP 3e0 = Pe0P2e0P

2j = PjP 2e20

38 (1) rP 7d0 = i2P 5d0 = iPd0P4i = iP 2iP 3d0 = jP 6j = kP 6i =

Pd0P2i2 = PjP 5j = P 2jP 4j = P 3j2


Stem 1015 (1) h6e1

7 (010) x7,88

(001) h1h6x = h22h6d1 = h2h4h6g = h2h5Q3 = h3h6n = h6c

21

(101) h6y

8 (10) x8,93

(01) h0h6y

9 (0100) h21x7,84 = h2

2x7,79 = g3Ph1

(1011) h3x8,80

(0010) h0x8,93

(0001) h20h6y = h2h6m = h6f0g

10 (10) h20x8,93

(01) h30h6y = h0h2h6m = h0h6f0g = h1h6e0g = h2

2h6l = h2h6e0f0 =h6c0r

(11) h0h3x8,80 = f1A′

11 (100) g2Q2

(010) x11,80

(001) h30x8,93 = h2

0h3x8,80 = h0f1A′ = h2

1x9,86 = h3pA′ = h3x10,70 =e1x7,33 = xA′′

12 (1) h0g2Q2 = h0x11,80 = pG21

13 (1) h20g2Q2 = h2

0x11,80 = h0pG21 = h21h3x10,65 = h1d1G21 =

h1e1x8,32 = h32x10,65 = h2h5x11,35 = h3d1x8,32 = h3xQ2 =

h4x12,48 = f1X1 = yx7,33

14 (1) g2A′ = g2A = mx7,40

15 (1) h2x14,67

16 (1) Px12,60

17 (01) h0Px12,60 = Ph2x12,55 = B2x′

(11) h6P3d0

18 (10) x18,63

(01) h20Px12,60 = h0h6P

3d0 = h0Ph2x12,55 = h0B2x′ = h5R1

19 (100) g2nr = gtw = gmN = nm2 = rtm

(010) d0x15,47 = e0x15,43 = rx13,35 = ux10,27 = ux10,28 = vB21 =wQ1 = B4z

(001) h0x18,63

20 (1) h20x18,63

21 (10) d0x17,50

(01) h30x18,63

continued



0B21 = d20e0Q1 = d2

0gx′ = d0e20x

′ = d0Pd0B23 = d0Pe0x10,27 =d0Pe0x10,28 = e0gPQ1 = e0Pd0x10,27 = e0Pd0x10,28 =e0Pe0B21 = gPd0B21 = gPe0Q1

(001) h40x18,63

(101) d0e0g2r = d0e0m

2 = d0glm = d0vw = e30gr = e2

0lm = e0gkm =e0gl2 = e0uw = e0v

2 = g3z = g2jm = g2kl = guv = r2z = rjw =rkv = rlu

23 (1) h50x18,63 = h3x22,39 = R1Q

24 (110) d0Px16,35 = Pd0x16,35

(001) h60x18,63 = h0h3x22,39 = h0R1Q

(101) Pe0x16,32

(011) h1x′Q = h1x

′Pu = Ph1ux′ = qx18,20 = B1P2u = P 2h1x15,42 =

P 2h1x15,43

25 (100) d0iPQ1 = d0x′Pj = iPd0Q1 = iPe0x

′ = jPd0x′ = kP 2Q1 =

B4P3e0 = B21P

2j = x10,28P2i = P 2d0x13,35

(010) d40w = d3

0e0v = d30gu = d3

0rk = d20e

20u = d2

0e0rj = d20gri = d2

0lz =d0e

20ri = d0e0gPv = d0e0kz = d0e0Pe0w = d0g

2Pu = d0gjz =d0gPd0w = d0gPe0v = d0rlPe0 = d0rmPd0 = d0ikm = d0il

2 =d0j

2m = d0jkl = d0k3 = e3

0Pv = e20gPu = e2

0jz = e20Pd0w =

e20Pe0v = e0grPj = e0giz = e0gPd0v = e0gPe0u = e0rkPe0 =

e0rlPd0 = e0ijm = e0ikl = e0j2l = e0jk

2 = g2Pd0u = grjPe0 =grkPd0 = gi2m = gijl = gik2 = gj2k = iu2 = lmPj = mPe0z

(110) lx18,20

(001) h70x18,63 = h2

0h3x22,39 = h20R1Q = h0d0Px16,35 = h0Pd0x16,35 =

h0Pe0x16,32 = h2Pd0x16,32 = d0Ph2x16,32 = P 2h2x16,38 =P 2d0x13,34

(101) d20PR2 = d0e0R1 = d0Pd0R2 = gP 2R2 = x10,27P

2i =P 2e0P

2D1

continued


Stem 101 continued26 (10) h0d0iPQ1 = h0d0x

′Pj = h0iPd0Q1 = h0iPe0x′ = h0jPd0x

′ =h0kP 2Q1 = h0lx18,20 = h0B4P

3e0 = h0B21P2j = h0x10,28P

2i =h0P

2d0x13,35 = h2iPd0x′ = h2jP

2Q1 = h2kx18,20 = h2B4P3d0 =

h2Q1 P 2j = h2B21P2i = h2PjPQ1 = h4x25,24 = d0f0x18,20 =

d0Ph2ix′ = d0B2P

2i = d0B4P3h2 = f0x

′P 2d0 = Ph2jPQ1 =Ph2B4P

2d0 = Ph2Q1 Pj = iB2P2d0 = iP 2h2B21 = jP 2h2Q1 =

kP 2h2x′ = Pd0P

2h2B4

(01) h80x18,63 = h3

0h3x22,39 = h30R1Q = h2

0d0Px16,35 = h20Pd0x16,35 =

h20Pe0x16,32 = h0h2Pd0x16,32 = h0d0Ph2x16,32 = h0P

2h2x16,38 =h0P

2d0x13,34 = h22P

2x16,35 = h2Ph2Px16,35 = h2P2h2x16,35 =

Ph22x16,35

(11) h0d20PR2 = h0d0e0R1 = h0d0Pd0R2 = h0gP 2R2 =

h0x10,27P2i = h0P

2e0P2D1 = h2d

20R1 = h2e0P

2R2 =h2Pe0PR2 = h2P

2d0P2D1 = h2P

2e0R2 = d0P2h2P

2D1 =d0R1P

2e0 = e0Ph2PR2 = e0P2h2R2 = e0R1P

2d0 = gPh2R1 =Ph2Pd0P

2D1 = Ph2Pe0R2 = Pd0Pe0R1

27 (1) h20d

20PR2 = h2

0d0e0R1 = h20d0iPQ1 = h2

0d0Pd0R2 =h2

0d0x′Pj = h2

0gP 2R2 = h20iPd0Q1 = h2

0iPe0x′ =

h20jPd0x

′ = h20kP 2Q1 = h2

0lx18,20 = h20B4P

3e0 =h2

0B21P2j = h2

0x10,27P2i = h2

0x10,28P2i = h2

0P2d0x13,35 =

h20P

2e0P2D1 = h0h2d

20R1 = h0h2e0P

2R2 = h0h2iPd0x′ =

h0h2jP2Q1 = h0h2kx18,20 = h0h2Pe0PR2 = h0h2B4P

3d0 =h0h2Q1 P 2j = h0h2B21P

2i = h0h2PjPQ1 = h0h2P2d0P

2D1 =h0h2P

2e0R2 = h0h4x25,24 = h0d0f0x18,20 = h0d0Ph2ix′ =

h0d0B2P2i = h0d0P

2h2P2D1 = h0d0B4P

3h2 = h0d0R1P2e0 =

h0e0Ph2PR2 = h0e0P2h2R2 = h0e0R1P

2d0 = h0f0x′P 2d0 =

h0gPh2R1 = h0Ph2jPQ1 = h0Ph2Pd0P2D1 = h0Ph2Pe0R2 =

h0Ph2B4P2d0 = h0Ph2Q1 Pj = h0iB2P

2d0 = h0iP2h2B21 =

h0jP2h2Q1 = h0kP 2h2x

′ = h0Pd0Pe0R1 = h0Pd0P2h2B4 =

h1d20P

2Q1 = h1d0e0x18,20 = h1d0Pd0PQ1 = h1d0x′P 2e0 =

h1d0Q1 P 2d0 = h1e0x′P 2d0 = h1gP 3Q1 = h1Pd2

0Q1 =h1Pd0Pe0x

′ = h1B21P3e0 = h1x10,27P

3d0 = h1x10,28P3d0 =

h22d0P

2R2 = h22iP

2Q1 = h22jx18,20 = h2

2Pd0PR2 = h22Pe0R1 =

h22x

′P 2j = h22Q1 P 2i = h2

2P2d0R2 = h2d0Ph2PR2 =

h2d0P2h2R2 = h2d0R1P

2d0 = h2e0Ph2R1 = h2f0P3Q1 =

h2Ph2iPQ1 = h2Ph2Pd0R2 = h2Ph2x′Pj = h2iP

2h2Q1 =h2jP

2h2x′ = h2B2P

3j = h2Pd20R1 = h2P

3h2x13,35 = c0iR1 =d20Ph1PQ1 = d2

0P2h1Q1 = d2

0P2h2R1 = d0e0P

2h1x′ =

d0Ph1Pd0Q1 = d0Ph1Pe0x′ = d0Ph2

2R2 = d0Ph2Pd0R1 =d0B1P

3e0 = d0x10,27P3h1 = d0x10,28P

3h1 = e0Ph1Pd0x′ =

(continued)


Stem 101 continued27 (1) (continued) = e0B1P

3d0 = e0B21P3h1 = f0Ph2P

2Q1 =f0P

2h2PQ1 = f0Q1 P 3h2 = gPh1P2Q1 = gP 2h1PQ1 =

gR1P3h2 = gQ1 P 3h1 = Ph1B21P

2e0 = Ph1x10,27P2d0 =

Ph1x10,28P2d0 = Ph2

2iQ1 = Ph22jx

′ = Ph2B2P2j =

Ph2P2h2x13,35 = D2P

5h2 = jB2P3h2 = B1Pd0P

2e0 =B1Pe0P

2d0 = B2P2h2Pj = Pd0P

2h1x10,27 = Pd0P2h1x10,28 =

Pe0P2h1B21 = B5 P 4h2 = PD2P

4h2 = P 2c0x16,33

28 (1) d60e0 = d4

0gPe0 = d30e

20Pe0 = d3

0e0gPd0 = d20e

30Pd0 = d2

0g2P 2e0 =

d20iPv = d2

0jPu = d20uPj = d0e

20gP 2e0 = d0e0g

2P 2d0 =d0e0gPe2

0 = d0e0iPu = d0g2Pd0Pe0 = d0riP j = d0i

2z =d0iPd0v = d0iPe0u = d0jPd0u = d0kP 2v = d0lP

2u = d0wP 2j =e40P

2e0 = e30gP 2d0 = e3

0Pe20 = e2

0gPd0Pe0 = e0g2Pd2

0 =e0iPd0u = e0jP

2v = e0kP 2u = e0vP 2j = e0wP 2i = e0PjPv =g3P 3e0 = giP 2v = gjP 2u = guP 2j = gvP 2i = gPjPu =r2P 3e0 = ri2Pe0 = rijPd0 = rkP 2j = rlP 2i = rzP 2d0 = i3l =i2jk = ij3 = iwP 2e0 = jPe0Pv = jvP 2e0 = jwP 2d0 = jzPj =kPd0Pv = kPe0Pu = kuP 2e0 = kvP 2d0 = lPd0Pu = luP 2d0 =mP 3v = Pd0wPj = Pe0vPj

29 (1) Ph1P2x16,32 = P 3h1x16,32

31 (1) d40iPd0 = d3

0e0P2j = d3

0gP 2i = d30jP

2e0 = d30kP 2d0 =

d30Pe0Pj = d2

0e20P

2i = d20e0iP

2e0 = d20e0jP

2d0 = d20e0Pd0Pj =

d20giP 2d0 = d2

0iPe20 = d2

0jPd0Pe0 = d20kPd2

0 = d20lP

3e0 =d20mP 3d0 = d0e

20iP

2d0 = d0e0gP 3j = d0e0iPd0Pe0 = d0e0jPd20 =

d0e0kP 3e0 = d0e0lP3d0 = d0giPd2

0 = d0gjP 3e0 = d0gkP 3d0 =d0gPe0P

2j = d0gPjP 2e0 = d0kPe0P2e0 = d0lPd0P

2e0 =d0lP e0P

2d0 = d0mPd0P2d0 = e3

0P3j = e2

0iPd20 = e2

0jP3e0 =

e20kP 3d0 = e2

0Pe0P2j = e2

0PjP 2e0 = e0giP 3e0 = e0gjP 3d0 =e0gPd0P

2j = e0gPe0P2i = e0gPjP 2d0 = e0jPe0P

2e0 =e0kPd0P

2e0 = e0kPe0P2d0 = e0lPd0P

2d0 = e0mP 4e0 =e0Pe2

0Pj = g2iP 3d0 = g2Pd0P2i = giPe0P

2e0 = gjPd0P2e0 =

gjPe0P2d0 = gkPd0P

2d0 = glP 4e0 = gmP 4d0 = gPd0Pe0Pj =rP 4u = i2P 2u = iuP 2i = jPe3

0 = kPd0Pe20 = lPd2

0Pe0 =mPd3

0 = mPe0P3e0 = mP 2e2

0

continued



0iP3j = d2

0PjP 2i = d0rP5e0 = d0i

2P 3e0 = d0ijP3d0 =

d0iPd0P2j = d0iPe0P

2i = d0iP jP 2d0 = d0jPd0P2i = d0kP 4j =

d0lP4i = d0zP 4d0 = e0rP

5d0 = e0i2P 3d0 = e0iPd0P

2i =e0jP

4j = e0kP 4i = e0PjP 3j = e0P2j2 = giP 4j = gjP 4i =

gP 2iP 2j = rPd0P4e0 = rPe0P

4d0 = rP 2d0P3e0 = rP 2e0P

3d0 =i2Pd0P

2e0 = i2Pe0P2d0 = ijPd0P

2d0 = ikP 4e0 = ilP 4d0 =iPd2

0Pj = j2P 4e0 = jkP 4d0 = jPe0P3j = jP jP 3e0 =

jP 2e0P2j = kPd0P

3j = kPjP 3d0 = kP 2d0P2j = kP 2e0P

2i =lP 2d0P

2i = mP 5j = Pd0zP 3d0 = Pe0PjP 2j = zP 2d20 =

Pj2P 2e0

(11) P 4x18,20

35 (1) h0P4x18,20

36 (1) h20P

4x18,20

37 (10) d0P6u = Pd0P

5u = uP 6d0 = P 2d0P4u = PuP 5d0 = P 3d0P

3u =P 2uP 4d0

(01) h30P

4x18,20

(11) rP 6i = i2P 4i = iP 2i2

38 (1) h40P

4x18,20 = h0rP6i = h0i

2P 4i = h0iP2i2

39 (1) h50P

4x18,20 = h20rP

6i = h20i

2P 4i = h20iP

2i2 = h3iP6i = h3P

2iP 4i


Stem 1026 (1) h1h6e1 = h3h6d1

8 (100) h3x7,79

(010) h1h6y = h2h6t = h3h6q = h6c1g

(001) h1x7,88 = h2x7,84

(011) h2x7,83 = h4x7,74

9 (1) h0h3x7,79 = h1x8,93 = c2A′ = f1H1

10 (100) h6u

(010) g2D2

(001) h1h3x8,80 = h2x9,86

11 (1) h0g2D2 = h3x10,73

12 (1) h20g2D2 = h0h3x10,73 = h1g2Q2 = h3e1Q2 = h3xD2 = c2X1 =

f1x8,32 = yA′′

13 (01) h6d0Pe0 = h6e0Pd0

(11) g2H1 = tx7,40

14 (10) x14,74

(01) h0h6d0Pe0 = h0h6e0Pd0 = h22x12,64 = h2h6d0Pd0 = h5x13,34 =

h6d20Ph2 = h6gP 2h2

15 (1) x15,65

16 (100) g2x8,33 = mx9,39 = Q2w

(010) h6P2i

(001) h0x15,65 = Ph2x11,61

17 (10) h0h6P2i

(01) h20x15,65 = h0Ph2x11,61 = h1Px12,60 = Ph1x12,60 = B1Q1 =

B2R1

18 (10) e0gB23 = g2x10,27 = g2x10,28 = vB4

(01) h20h6P

2i = h1h6P3d0 = h4x17,50 = h6d0P

3h1 = h6Ph1P2d0 =

h6Pd0P2h1 = c0x15,56

19 (10) x19,58

(01) h1x18,63

20 (10) d0x16,48 = e0x16,42 = gx16,38

(01) h0x19,58

21 (100) e0g2w = e0grm = g3v = g2rl = r2v = lm2

(010) d30B4 = d0e0x13,35 = d0gP 2D1 = d0iB23 = d0jx10,27 =

d0jx10,28 = d0kB21 = d0lQ1 = d0mx′ = e20P

2D1 = e0gR2 =e0ix10,27 = e0ix10,28 = e0jB21 = e0kQ1 = e0lx

′ = e0Pe0B4 =giB21 = gjQ1 = gkx′ = gPd0B4

(001) h20x19,58

22 (1) h30x19,58 = h3x21,43

23 (01) h40x19,58 = h0h3x21,43

(11) ix16,35 = jx16,32

continued



0g3 = d3

0r2 = d2

0e20g

2 = d20kw = d2

0lv = d20mu = d0e

40g = d0e0rz =

d0e0jw = d0e0kv = d0e0lu = d0giw = d0gjv = d0gku = d0rim =d0rjl = d0rk

2 = e60 = e2

0iw = e20jv = e2

0ku = e0g3Pe0 = e0giv =

e0gju = e0r2Pe0 = e0ril = e0rjk = e0mPv = g4Pd0 = g2iu =

gr2Pd0 = grik = grj2 = glPv = gmPu = gz2 = jmz = klz =lP e0w = mPd0w = mPe0v

(010) rP 2Q1 = i2Q1 = ijx′ = B4P2j

(001) h50x19,58 = h2

0h3x21,43 = h0ix16,35 = h0jx16,32 = h2ix16,32 =P 2h2x15,41

(011) d0iR2 = kPR2 = lR1 = Pd0x16,37 = Pe0x16,33 = PjP 2D1

25 (10) h0rP2Q1 = h0i

2Q1 = h0ijx′ = h0B4P

2j = h21x

′Q =h2

1x′Pu = h1Ph1ux′ = h1qx18,20 = h1B1P

2u = h1P2h1x15,42 =

h1P2h1x15,43 = h2rx18,20 = h2i

2x′ = h2B4P2i = h3P

2x16,35 =D3P

5h1 = Ph21x15,42 = Ph2

1x15,43 = Ph1B1Q = Ph1B1Pu =rP 2h2x

′ = qP 2h1x′ = iP 2h2B4 = B1P

2h1u = PD3P4h1 =

X1P3e0 = P 2D3P

3h1

(01) h60x19,58 = h3

0h3x21,43 = h20ix16,35 = h2

0jx16,32 = h0h2ix16,32 =h0P

2h2x15,41 = h1Pe0x16,32 = e0Ph1x16,32 = P 2e0W1

(11) h0d0iR2 = h0kPR2 = h0lR1 = h0Pd0x16,37 = h0Pe0x16,33 =h0PjP 2D1 = h1d0Px16,35 = h1Pd0x16,35 = h2jPR2 = h2kR1 =h2Pd0x16,33 = h2PjR2 = c0x22,39 = d0f0R1 = d0Ph1x16,35 =d0Ph2x16,33 = d0R1Pj = Ph2iP

2D1 = Ph2jR2 = iPe0R1 =jPd0R1 = P 2h1x16,42

27 (1) d50l = d4

0e0k = d40gj = d3

0e20j = d3

0e0gi = d30mPe0 = d2

0e30i =

d20e0lP e0 = d2

0e0mPd0 = d20g

2Pj = d20gkPe0 = d2

0glPd0 =d0e

20gPj = d0e

20kPe0 = d0e

20lPd0 = d0e0gjPe0 = d0e0gkPd0 =

d0g2iPe0 = d0g

2jPd0 = d0gmP 2e0 = d0rP2v = d0i

2v = d0iju =d0zPu = e4

0Pj = e30jPe0 = e3

0kPd0 = e20giPe0 = e2

0gjPd0 =e20mP 2e0 = e0g

2iPd0 = e0glP 2e0 = e0gmP 2d0 = e0rP2u =

e0i2u = e0mPe2

0 = g3P 2j = g2kP 2e0 = g2lP 2d0 = glPe20 =

gmPd0Pe0 = r2P 2j = ri2j = rPd0Pv = rPe0Pu = ruP 2e0 =rvP 2d0 = ikPv = ilPu = iwPj = j2Pv = jkPu = jvPj =kuPj = Pd0uz

continued



4Q1 = Pd0P3Q1 = Q1 P 4d0 = P 2d0P

2Q1 = PQ1 P 3d0

(010) uP 3u = PuP 2u

(110) P 2e0x18,20

(001) h1Ph1P2x16,32 = h1P

3h1x16,32 = Ph1P2h1x16,32 = X1P

5h1 =QP 2u = W1P

4h1

(101) e0P4x′ = x′P 4e0

(011) d40i

2 = d30rP

2d0 = d30jP j = d2

0e0iP j = d20rPd2

0 = d20ijPe0 =

d20ikPd0 = d2

0j2Pd0 = d2

0lP2j = d2

0mP 2i = d20zP 2e0 =

d0e0rP3e0 = d0e0i

2Pe0 = d0e0ijPd0 = d0e0kP 2j = d0e0lP2i =

d0e0zP 2d0 = d0grP 3d0 = d0gi2Pd0 = d0gjP 2j = d0gkP 2i =d0gPj2 = d0rPe0P

2e0 = d0ilP2e0 = d0imP 2d0 = d0jkP 2e0 =

d0jlP2d0 = d0k

2P 2d0 = d0kPe0Pj = d0lPd0Pj = d0Pd0Pe0z =e20rP

3d0 = e20i

2Pd0 = e20jP

2j = e20kP 2i = e2

0Pj2 = e0giP 2j =e0gjP 2i = e0rPd0P

2e0 = e0rPe0P2d0 = e0ikP 2e0 = e0ilP

2d0 =e0j

2P 2e0 = e0jkP 2d0 = e0jPe0Pj = e0kPd0Pj = e0mP 3j =e0Pd2

0z = g2iP 2i = grPd0P2d0 = gijP 2e0 = gikP 2d0 =

giPe0Pj = gj2P 2d0 = gjPd0Pj = glP 3j = gzP 3e0 = rPd0Pe20 =

ikPe20 = ilPd0Pe0 = imPd2

0 = j2Pe20 = jkPd0Pe0 = jlPd2

0 =jmP 3e0 = k2Pd2

0 = klP 3e0 = kmP 3d0 = l2P 3d0 = mPe0P2j =

mPjP 2e0

31 (1) h0d0P4Q1 = h0e0P

4x′ = h0Pd0P3Q1 = h0x

′P 4e0 =h0Q1 P 4d0 = h0P

2d0P2Q1 = h0P

2e0x18,20 = h0PQ1 P 3d0 =h2d0P

4x′ = h2x′P 4d0 = h2P

2d0x18,20 = d0P2h2x18,20 =

d0x′P 4h2 = Ph2Pd0x18,20 = Ph2x

′P 3d0 = B2P5d0 =

Pd0x′P 3h2 = P 2h2x

′P 2d0 = B21P5h2

32 (1) h20d0P

4Q1 = h20e0P

4x′ = h20Pd0P

3Q1 = h20x

′P 4e0 =h2

0Q1 P 4d0 = h20P

2d0P2Q1 = h2

0P2e0x18,20 = h2

0PQ1 P 3d0 =h0h2d0P

4x′ = h0h2x′P 4d0 = h0h2P

2d0x18,20 = h0d0P2h2x18,20 =

h0d0x′P 4h2 = h0Ph2Pd0x18,20 = h0Ph2x

′P 3d0 = h0B2P5d0 =

h0Pd0x′P 3h2 = h0P

2h2x′P 2d0 = h0B21P

5h2 = h22P

5Q1 =h2Ph2P

4Q1 = h2P2h2P

3Q1 = h2Q1 P 5h2 = h2P3h2P

2Q1 =h2PQ1 P 4h2 = Ph2

2P3Q1 = Ph2P

2h2P2Q1 = Ph2Q1 P 4h2 =

Ph2P3h2PQ1 = Pc0x25,24 = P 2h2

2PQ1 = P 2h2Q1 P 3h2 =P 3c0R1

continued



0P4v = d0e0P

4u = d0rP4j = d0i

2P 2j = d0ijP2i = d0Pd0P

3v =d0Pe0P

3u = d0uP 4e0 = d0vP 4d0 = d0P2d0P

2v = d0P2e0P

2u =d0PuP 3e0 = d0PvP 3d0 = e0rP

4i = e0i2P 2i = e0Pd0P

3u =e0uP 4d0 = e0P

2d0P2u = e0PuP 3d0 = gP 5v = riP 4e0 =

rjP 4d0 = rPd0P3j = rPjP 3d0 = rP 2d0P

2j = rP 2e0P2i =

i3P 2e0 = i2jP 2d0 = i2Pd0Pj = ikP 3j = izP 3d0 = j2P 3j =jP jP 2j = kPjP 2i = Pd2

0P2v = Pd0Pe0P

2u = Pd0uP 3e0 =Pd0vP 3d0 = Pd0zP 2i = Pd0P

2d0Pv = Pd0P2e0Pu =

Pe0uP 3d0 = Pe0P2d0Pu = uP 2d0P

2e0 = vP 2d20 = wP 5e0 = Pj3

(11) P 4R1

34 (1) h0P4R1

35 (10) h1P4x18,20 = P 2h1P

4x′ = x′P 6h1 = P 4h1x18,20

(01) h20P

4R1

36 (10) d40P

4d0 = d30Pd0P

3d0 = d30P

2d20 = d2

0e0P5e0 = d2

0gP 5d0 =d20Pd2

0P2d0 = d2

0Pe0P4e0 = d2

0P2e0P

3e0 = d0e20P

5d0 =d0e0Pd0P

4e0 = d0e0Pe0P4d0 = d0e0P

2d0P3e0 =

d0e0P2e0P

3d0 = d0gPd0P4d0 = d0gP 2d0P

3d0 = d0Pd40 =

d0Pd0Pe0P3e0 = d0Pd0P

2e20 = d0Pe2

0P3d0 = d0Pe0P

2d0P2e0 =

e20Pd0P

4d0 = e20P

2d0P3d0 = e0gP 6e0 = e0Pd2

0P3e0 =

e0Pd0Pe0P3d0 = e0Pd0P

2d0P2e0 = e0Pe0P

2d20 = g2P 6d0 =

gPd20P

3d0 = gPd0P2d2

0 = gPe0P5e0 = gP 2e0P

4e0 = gP 3e20 =

iP 5u = Pd20Pe0P

2e0 = Pd0Pe20P

2d0 = PuP 4i = P 2iP 3u

(01) h30P

4R1 = iP 4Q = QP 4i

37 (1) h40P

4R1 = h0iP4Q = h0QP 4i

38 (1) h50P

4R1 = h20iP

4Q = h20QP 4i


Stem 1035 (1) h6f1

6 (1) h0h6f1 = h3h6p

7 (10) x7,90

(01) h20h6f1 = h0h3h6p = h2

1h6e1 = h1h3h6d1

9 (1) h3x8,83

10 (1) h0h3x8,83

11 (1) h1h6u

12 (10) x12,78

(01) h6d0j = h6e0i

13 (1) h0h6d0j = h0h6e0i = h0x12,78 = h2h6d0i = h6f0Pd0 = h6Ph2k

14 (1) h20h6d0j = h2

0h6e0i = h20x12,78 = h0h2h6d0i = h0h6f0Pd0 =

h0h6Ph2k = h1h6d0Pe0 = h1h6e0Pd0 = h22h6Pj = h2h6Ph2j =

h6d0e0Ph1 = B1Q2

15 (10) e0gx7,40 = g2x7,34 = tx9,39 = D2w = A′v = Av = mG21 = Q2N

(01) h1x14,74

19 (1) gx15,41

20 (10) d0rB21 = d0kB4 = e0rQ1 = e0jB4 = grx′ = giB4 = lx13,35 =mP 2D1 = zx10,27 = zx10,28

(01) h21x18,63 = Ph1x15,56

22 (1) d0x18,50

23 (10) d20g

2m = d20rw = d0e

20gm = d0e0g

2l = d0e0rv = d0g3k = d0gru =

d0r2k = e4

0m = e30gl = e2

0g2k = e2

0ru = e0g3j = e0r

2j = e0wz =g4i = gr2i = gvz = rlz = imw = jlw = jmv = k2w = klv =kmu = l2u

(01) rPR2 = ix16,37 = jx16,33 = uPQ1 = x′Pv = Q1 Pu

25 (1) P 2x17,50

26 (10) d20Pd0x

′ = d0e0P2Q1 = d0Pe0PQ1 = d0Q1 P 2e0 = d0B21P

2d0 =e0Pd0PQ1 = e0x

′P 2e0 = e0Q1 P 2d0 = gx′P 2d0 = Pd20B21 =

Pd0Pe0Q1 = Pe20x

′ = x10,27P3e0 = x10,28P

3e0 = B23P3d0

(01) d40e0r = d3

0gz = d30jm = d3

0kl = d20e

20z = d2

0e0im = d20e0jl =

d20e0k

2 = d20grPe0 = d2

0gil = d20gjk = d0e

20rPe0 = d0e

20il =

d0e20jk = d0e0grPd0 = d0e0gik = d0e0gj2 = d0g

2ij = d0gmPj =d0kmPe0 = d0l

2Pe0 = d0lmPd0 = d0uPv = d0vPu = e30rPd0 =

e30ik = e3

0j2 = e2

0gij = e20mPj = e0g

2i2 = e0glP j = e0gPe0z =e0jmPe0 = e0klPe0 = e0kmPd0 = e0l

2Pd0 = e0uPu =g2rP 2e0 = g2kPj = g2Pd0z = gimPe0 = gjlPe0 = gjmPd0 =gk2Pe0 = gklPd0 = riPv = rjPu = ruPj = iuz = m2P 2e0 =Pd0uv = Pe0u

2 = wP 2v

(11) d0gx18,20 = e20x18,20

continued



20Pd0x

′ = h0d0e0P2Q1 = h0d0gx18,20 = h0d0Pe0PQ1 =

h0d0Q1 P 2e0 = h0d0B21P2d0 = h0e

20x18,20 = h0e0Pd0PQ1 =

h0e0x′P 2e0 = h0e0Q1 P 2d0 = h0gx′P 2d0 = h0Pd2

0B21 =h0Pd0Pe0Q1 = h0Pe2

0x′ = h0x10,27P

3e0 = h0x10,28P3e0 =

h0B23P3d0 = h2d

20P

2Q1 = h2d0e0x18,20 = h2d0Pd0PQ1 =h2d0x

′P 2e0 = h2d0Q1 P 2d0 = h2e0x′P 2d0 = h2gP 3Q1 =

h2Pd20Q1 = h2Pd0Pe0x

′ = h2B21P3e0 = h2x10,27P

3d0 =h2x10,28P

3d0 = h4P4Q1 = c0P

2x16,35 = d20Ph2PQ1 =

d20P

2h2Q1 = d0e0P2h2x

′ = d0Ph2Pd0Q1 = d0Ph2Pe0x′ =

d0B2P3e0 = d0x10,27P

3h2 = d0x10,28P3h2 = e0Ph2Pd0x

′ =e0B2P

3d0 = e0B21P3h2 = gPh2P

2Q1 = gP 2h2PQ1 =gQ1 P 3h2 = Ph1x22,39 = Ph2B21P

2e0 = Ph2x10,27P2d0 =

Ph2x10,28P2d0 = Pc0Px16,35 = B2Pd0P

2e0 = B2Pe0P2d0 =

Q2P4d0 = Pd0P

2h2x10,27 = Pd0P2h2x10,28 = Pe0P

2h2B21 =P 2c0x16,35

28 (1) P 3x16,35

29 (100) Pjx18,20

(010) d40Pu = d3

0Pd0u = d20e0P

2v = d20gP 2u = d2

0riPd0 = d20i

2k =d20ij

2 = d20Pe0Pv = d2

0vP 2e0 = d20wP 2d0 = d2

0zPj = d0e20P

2u =d0e0rP

2j = d0e0i2j = d0e0Pd0Pv = d0e0Pe0Pu = d0e0uP 2e0 =

d0e0vP 2d0 = d0grP 2i = d0gi3 = d0gPd0Pu = d0guP 2d0 =d0rjP

2e0 = d0rkP 2d0 = d0rPe0Pj = d0ilP j = d0iPe0z =d0jkPj = d0jPd0z = d0Pd2

0w = d0Pd0Pe0v = d0Pe20u =

e20rP

2i = e20i

3 = e20Pd0Pu = e2

0uP 2d0 = e0gP 3v = e0riP2e0 =

e0rjP2d0 = e0rPd0Pj = e0ikPj = e0iPd0z = e0j

2Pj =e0Pd2

0v = e0Pd0Pe0u = e0wP 3e0 = g2P 3u = griP 2d0 = gijP j =gPd2

0u = gPe0P2v = gvP 3e0 = gwP 3d0 = gzP 2j = gP 2e0Pv =

riPe20 = rjPd0Pe0 = rkPd2

0 = rlP 3e0 = rmP 3d0 = i2lP e0 =i2mPd0 = ijkPe0 = ijlPd0 = ik2Pd0 = j3Pe0 = j2kPd0 =jmP 2j = klP 2j = kmP 2i = kzP 2e0 = l2P 2i = lzP 2d0 = mPj2 =Pe0wP 2e0

(110) iP 3Q1 = x′P 3j = PQ1 P 2i

(001) h0P3x16,35 = Ph2P

2x16,32 = P 3h2x16,32

(101) e0x25,24

(111) d0P3R2 = Pd0P

2R2 = P 2d0PR2 = P 2e0R1 = R2 P 3d0

continued


Stem 103 continued30 (10) h0iP

3Q1 = h0x′P 3j = h0Pjx18,20 = h0PQ1 P 2i = f0P

4x′ =Ph2ix18,20 = Ph2x

′P 2i = ix′P 3h2 = B2P4i = B4P

5h2

(01) h20P

3x16,35 = h0Ph2P2x16,32 = h0P

3h2x16,32

(11) h0d0P3R2 = h0e0x25,24 = h0Pd0P

2R2 = h0P2d0PR2 =

h0P2e0R1 = h0R2 P 3d0 = h2d0x25,24 = h2P

2d0R1 =d0P

2h2R1 = Ph2Pd0R1 = R1P4e0 = P 2D1P

4h2

31 (10) h20iP

3Q1 = h20x

′P 3j = h20Pjx18,20 = h2

0PQ1 P 2i =h0f0P

4x′ = h0Ph2ix18,20 = h0Ph2x′P 2i = h0ix

′P 3h2 =h0B2P

4i = h0B4P5h2 = h1e0P

4x′ = h1x′P 4e0 = h1P

2e0x18,20 =e0P

2h1x18,20 = e0x′P 4h1 = Ph1Pe0x18,20 = Ph1x

′P 3e0 =B1P

5e0 = Pe0x′P 3h1 = P 2h1x

′P 2e0 = x10,28P5h1

(01) h30P

3x16,35 = h20Ph2P

2x16,32 = h20P

3h2x16,32 = h21Ph1P

2x16,32 =h2

1P3h1x16,32 = h1Ph1P

2h1x16,32 = h1uP 3u = h1X1P5h1 =

h1QP 2u = h1PuP 2u = h1W1P4h1 = h3P

5Q1 = Ph31x16,32 =

Ph1uP 2u = Ph1X1P4h1 = Ph1P

3h1W1 = Ph1Q2 = Ph1QPu =

Ph1Pu2 = qP 4u = GP 6h1 = P 2h21W1 = P 2h1uQ = P 2h1uPu =

P 2h1X1P3h1 = u2P 3h1

(11) h20d0P

3R2 = h20e0x25,24 = h2

0Pd0P2R2 = h2

0P2d0PR2 =

h20P

2e0R1 = h20R2 P 3d0 = h0h2d0x25,24 = h0h2P

2d0R1 =h0d0P

2h2R1 = h0Ph2Pd0R1 = h0R1P4e0 = h0P

2D1P4h2 =

h1d0P4Q1 = h1Pd0P

3Q1 = h1Q1 P 4d0 = h1P2d0P

2Q1 =h1PQ1 P 3d0 = h2

2P4R2 = h2Ph2P

3R2 = h2P2h2P

2R2 =h2R1P

4d0 = h2P3h2PR2 = h2R2 P 4h2 = d0Ph1P

3Q1 =d0P

2h1P2Q1 = d0R1P

4h2 = d0Q1 P 4h1 = d0P3h1PQ1 =

Ph1Pd0P2Q1 = Ph1Q1 P 3d0 = Ph1P

2d0PQ1 = Ph22P

2R2 =Ph2P

2h2PR2 = Ph2R1P3d0 = Ph2P

3h2R2 = Pd0P2h1PQ1 =

Pd0R1P3h2 = Pd0Q1 P 3h1 = P 2h1Q1 P 2d0 = P 2h2

2R2 =P 2h2R1P

2d0 = x10,27P5h1

32 (1) d50P

2e0 = d40e0P

2d0 = d40Pd0Pe0 = d3

0e0Pd20 = d3

0gP 3e0 =d20e

20P

3e0 = d20e0gP 3d0 = d2

0e0Pe0P2e0 = d2

0gPd0P2e0 =

d20gPe0P

2d0 = d20Pe3

0 = d0e30P

3d0 = d0e20Pd0P

2e0 =d0e

20Pe0P

2d0 = d0e0gPd0P2d0 = d0e0Pd0Pe2

0 = d0g2P 4e0 =

d0gPd20Pe0 = d0iP

3v = d0jP3u = d0uP 3j = d0PjP 2u =

d0PuP 2j = d0PvP 2i = e30Pd0P

2d0 = e20gP 4e0 = e2

0Pd20Pe0 =

e0g2P 4d0 = e0gPd3

0 = e0gPe0P3e0 = e0gP 2e2

0 = e0iP3u =

e0PuP 2i = g2Pd0P3e0 = g2Pe0P

3d0 = g2P 2d0P2e0 =

gPe20P

2e0 = riP 3j = rPjP 2i = i3Pj = iPd0P2v = iPe0P

2u =iuP 3e0 = ivP 3d0 = izP 2i = iP 2d0Pv = iP 2e0Pu = jPd0P

2u =juP 3d0 = jP 2d0Pu = kP 4v = lP 4u = Pd0uP 2j = Pd0vP 2i =Pd0PjPu = Pe0uP 2i = uPjP 2d0 = wP 4j

continued



0iP3d0 = d3

0Pd0P2i = d2

0e0P4j = d2

0gP 4i = d20iPd0P

2d0 =d20jP

4e0 = d20kP 4d0 = d2

0Pe0P3j = d2

0PjP 3e0 = d20P

2e0P2j =

d0e20P

4i = d0e0iP4e0 = d0e0jP

4d0 = d0e0Pd0P3j =

d0e0PjP 3d0 = d0e0P2d0P

2j = d0e0P2e0P

2i = d0giP 4d0 =d0gP 2d0P

2i = d0iPd30 = d0iPe0P

3e0 = d0iP2e2

0 = d0jPd0P3e0 =

d0jPe0P3d0 = d0jP

2d0P2e0 = d0kPd0P

3d0 = d0kP 2d20 =

d0lP5e0 = d0mP 5d0 = d0Pd0Pe0P

2j = d0Pd0PjP 2e0 =d0Pe2

0P2i = d0Pe0PjP 2d0 = e2

0iP4d0 = e2

0P2d0P

2i = e0gP 5j =e0iPd0P

3e0 = e0iPe0P3d0 = e0iP

2d0P2e0 = e0jPd0P

3d0 =e0jP

2d20 = e0kP 5e0 = e0lP

5d0 = e0Pd20P

2j = e0Pd0Pe0P2i =

e0Pd0PjP 2d0 = giPd0P3d0 = giP 2d2

0 = gjP 5e0 = gkP 5d0 =gPd2

0P2i = gPe0P

4j = gPjP 4e0 = gP 2e0P3j = gP 2jP 3e0 =

iPd0Pe0P2e0 = iPe2

0P2d0 = jPd2

0P2e0 = jPd0Pe0P

2d0 =kPd2

0P2d0 = kPe0P

4e0 = kP 2e0P3e0 = lPd0P

4e0 = lP e0P4d0 =

lP 2d0P3e0 = lP 2e0P

3d0 = mPd0P4d0 = mP 2d0P

3d0 =Pd2

0Pe0Pj

36 (1) h21P

4x18,20 = h1P2h1P

4x′ = h1x′P 6h1 = h1P

4h1x18,20 =Ph2

1P4x′ = Ph1x

′P 5h1 = Ph1P3h1x18,20 = B1P

7h1 =P 2h2

1x18,20 = P 2h1x′P 4h1 = x′P 3h2

1


Stem 1044 (1) h6c2

5 (1) h0h6c2

6 (1) h20h6c2 = h1h6f1 = h2h6e1

8 (1) h3x7,81

9 (10) x9,97

(01) h0h3x7,81 = h2x8,93

10 (1) h0x9,97

11 (10) h6z

(01) h20x9,97

(11) h3x10,76

12 (100) x12,80

(010) h0h6z = h21h6u = h2x11,80 = h6f0i = h6Ph1q = h6Ph2r

(001) h30x9,97

(011) h0h3x10,76

13 (10) h0x12,80 = h1x12,78

(01) h40x9,97 = h2

0h3x10,76 = g2B4

14 (1) h50x9,97 = h3

0h3x10,76 = h0g2B4 = h23x12,55 = xx9,40 = rx8,51

16 (1) d0x12,55

17 (10) h6P3e0

(01) h0d0x12,55 = h2Px12,60 = Ph2x12,60 = B2Q1

18 (100) gx14,46

(010) x18,68

(001) h20d0x12,55 = h0h2Px12,60 = h0h6P

3e0 = h0Ph2x12,60 =h0B2Q1 = h2h6P

3d0 = h2Ph2x12,55 = h2B2x′ = h5PR2 =

h6d0P3h2 = h6Ph2P

2d0 = h6Pd0P2h2

19 (10) d0rB4 = e0x15,47 = gx15,43 = uB23 = vx10,27 = vx10,28 = wB21

(01) h0x18,68 = h2x18,63

20 (1) h20x18,68 = h0h2x18,63

21 (10) e0x17,50

(01) h30x18,68 = h2

0h2x18,63 = h31x18,63 = h1Ph1x15,56

(11) d0x17,52

22 (10) d0g3r = d0gm2 = d0r

3 = d0w2 = e2

0g2r = e2

0m2 = e0glm =

e0vw = g2km = g2l2 = guw = gv2 = rkw = rlv = rmu

(01) d30x10,27 = d3

0x10,28 = d20e0B21 = d2

0gQ1 = d0e20Q1 = d0e0gx′ =

d0Pe0B23 = e30x

′ = e0Pd0B23 = e0Pe0x10,27 = e0Pe0x10,28 =g2PQ1 = gPd0x10,27 = gPd0x10,28 = gPe0B21 = uR2

24 (1) d20x16,32 = e0Px16,35 = Pd0x16,38 = Pe0x16,35

continued



0e0w = d30gv = d3

0rl = d20e

20v = d2

0e0gu = d20e0rk = d2

0grj =d20mz = d0e

30u = d0e

20rj = d0e0gri = d0e0lz = d0g

2Pv = d0gkz =d0gPe0w = d0rmPe0 = d0ilm = d0jkm = d0jl

2 = d0k2l = e3

0ri =e20gPv = e2

0kz = e20Pe0w = e0g

2Pu = e0gjz = e0gPd0w =e0gPe0v = e0rlPe0 = e0rmPd0 = e0ikm = e0il

2 = e0j2m =

e0jkl = e0k3 = g2rPj = g2iz = g2Pd0v = g2Pe0u = grkPe0 =

grlPd0 = gijm = gikl = gj2l = gjk2 = iuv = ju2 = m2Pj

(01) d20ix

′ = d0e0PR2 = d0gR1 = d0jPQ1 = d0Pd0P2D1 =

d0Pe0R2 = d0B4P2d0 = d0Q1 Pj = e2

0R1 = e0iPQ1 =e0Pd0R2 = e0x

′Pj = iPd0B21 = iPe0Q1 = jPd0Q1 = jPe0x′ =

kPd0x′ = lP 2Q1 = Pd2

0B4 = x10,27P2j = x10,28P

2j = B23P2i =

P 2e0x13,35

(11) mx18,20

26 (10) h1P2x17,50 = Ph1x21,43 = Ph1Px17,50 = P 2h1x17,50

(01) h0d20ix

′ = h0d0e0PR2 = h0d0gR1 = h0d0jPQ1 =h0d0Pd0P

2D1 = h0d0Pe0R2 = h0d0B4P2d0 = h0d0Q1 Pj =

h0e20R1 = h0e0iPQ1 = h0e0Pd0R2 = h0e0x

′Pj = h0iPd0B21 =h0iPe0Q1 = h0jPd0Q1 = h0jPe0x

′ = h0kPd0x′ = h0lP

2Q1 =h0mx18,20 = h0Pd2

0B4 = h0x10,27P2j = h0x10,28P

2j =h0B23P

2i = h0P2e0x13,35 = h2d

20PR2 = h2d0e0R1 =

h2d0iPQ1 = h2d0Pd0R2 = h2d0x′Pj = h2gP 2R2 =

h2iPd0Q1 = h2iPe0x′ = h2jPd0x

′ = h2kP 2Q1 = h2lx18,20 =h2B4P

3e0 = h2B21P2j = h2x10,27P

2i = h2x10,28P2i =

h2P2d0x13,35 = h2P

2e0P2D1 = h4P

3R2 = d20Ph2R2 =

d20Pd0R1 = d0f0P

2Q1 = d0Ph2iQ1 = d0Ph2jx′ =

d0B2P2j = d0P

2h2x13,35 = e0f0x18,20 = e0Ph2ix′ = e0B2P

2i =e0P

2h2P2D1 = e0B4P

3h2 = e0R1P2e0 = f0Pd0PQ1 =

f0x′P 2e0 = f0Q1 P 2d0 = gPh2PR2 = gP 2h2R2 = gR1P

2d0 =Ph2kPQ1 = Ph2Pd0x13,35 = Ph2Pe0P

2D1 = Ph2B4P2e0 =

Ph2B21Pj = D2P4d0 = iB2P

2e0 = iP 2h2x10,27 = iP 2h2x10,28 =jB2P

2d0 = jP 2h2B21 = kP 2h2Q1 = lP 2h2x′ = B2Pd0Pj =

Pe20R1 = Pe0P

2h2B4 = B5 P 3d0 = PD2P3d0

continued



0d20ix

′ = h20d0e0PR2 = h2

0d0gR1 = h20d0jPQ1 =

h20d0Pd0P

2D1 = h20d0Pe0R2 = h2

0d0B4P2d0 = h2

0d0Q1 Pj =h2

0e20R1 = h2

0e0iPQ1 = h20e0Pd0R2 = h2

0e0x′Pj = h2

0iPd0B21 =h2

0iPe0Q1 = h20jPd0Q1 = h2

0jPe0x′ = h2

0kPd0x′ = h2

0lP2Q1 =

h20mx18,20 = h2

0Pd20B4 = h2

0x10,27P2j = h2

0x10,28P2j =

h20B23P

2i = h20P

2e0x13,35 = h0h2d20PR2 = h0h2d0e0R1 =

h0h2d0iPQ1 = h0h2d0Pd0R2 = h0h2d0x′Pj = h0h2gP 2R2 =

h0h2iPd0Q1 = h0h2iPe0x′ = h0h2jPd0x

′ = h0h2kP 2Q1 =h0h2lx18,20 = h0h2B4P

3e0 = h0h2B21P2j = h0h2x10,27P

2i =h0h2x10,28P

2i = h0h2P2d0x13,35 = h0h2P

2e0P2D1 =

h0h4P3R2 = h0d

20Ph2R2 = h0d

20Pd0R1 = h0d0f0P

2Q1 =h0d0Ph2iQ1 = h0d0Ph2jx

′ = h0d0B2P2j = h0d0P

2h2x13,35 =h0e0f0x18,20 = h0e0Ph2ix

′ = h0e0B2P2i = h0e0P

2h2P2D1 =

h0e0B4P3h2 = h0e0R1P

2e0 = h0f0Pd0PQ1 = h0f0x′P 2e0 =

h0f0Q1 P 2d0 = h0gPh2PR2 = h0gP 2h2R2 = h0gR1P2d0 =

h0Ph2kPQ1 = h0Ph2Pd0x13,35 = h0Ph2Pe0P2D1 =

h0Ph2B4P2e0 = h0Ph2B21Pj = h0D2P

4d0 = h0iB2P2e0 =

h0iP2h2x10,27 = h0iP

2h2x10,28 = h0jB2P2d0 = h0jP

2h2B21 =h0kP 2h2Q1 = h0lP

2h2x′ = h0B2Pd0Pj = h0Pe2

0R1 =h0Pe0P

2h2B4 = h0B5 P 3d0 = h0PD2P3d0 = h1d

20Pd0x

′ =h1d0e0P

2Q1 = h1d0gx18,20 = h1d0Pe0PQ1 = h1d0Q1 P 2e0 =h1d0B21P

2d0 = h1e20x18,20 = h1e0Pd0PQ1 = h1e0x

′P 2e0 =h1e0Q1 P 2d0 = h1gx′P 2d0 = h1Pd2

0B21 = h1Pd0Pe0Q1 =h1Pe2

0x′ = h1x10,27P

3e0 = h1x10,28P3e0 = h1B23P

3d0 =h2

2d20R1 = h2

2e0P2R2 = h2

2iPd0x′ = h2

2jP2Q1 = h2

2kx18,20 =h2

2Pe0PR2 = h22B4P

3d0 = h22Q1 P 2j = h2

2B21P2i = h2

2PjPQ1 =h2

2P2d0P

2D1 = h22P

2e0R2 = h2h4x25,24 = h2d0f0x18,20 =h2d0Ph2ix

′ = h2d0B2P2i = h2d0P

2h2P2D1 = h2d0B4P

3h2 =h2d0R1P

2e0 = h2e0Ph2PR2 = h2e0P2h2R2 = h2e0R1P

2d0 =h2f0x

′P 2d0 = h2gPh2R1 = h2Ph2jPQ1 = h2Ph2Pd0P2D1 =

h2Ph2Pe0R2 = h2Ph2B4P2d0 = h2Ph2Q1 Pj = h2iB2P

2d0 =h2iP

2h2B21 = h2jP2h2Q1 = h2kP 2h2x

′ = h2Pd0Pe0R1 =h2Pd0P

2h2B4 = h4P2h2R1 = c0iPR2 = c0jR1 =

d30Ph1x

′ = d20B1P

2d0 = d20P

2h1B21 = d0e0Ph1PQ1 =d0e0P

2h1Q1 = d0e0P2h2R1 = d0f0P

2h2x′ = d0gP 2h1x

′ =d0Ph1Pd0B21 = d0Ph1Pe0Q1 = d0Ph2

2P2D1 = d0Ph2Pe0R1 =

d0Ph2P2h2B4 = d0iB2P

2h2 = d0B1Pd20 = d0B23P

3h1 =e20P

2h1x′ = e0Ph1Pd0Q1 = e0Ph1Pe0x

′ = e0Ph22R2 =

e0Ph2Pd0R1 = e0B1P3e0 = e0x10,27P

3h1 = e0x10,28P3h1 =

f0Ph2Pd0x′ = f0B2P

3d0 = f0B21P3h2 = gPh1Pd0x

′ =gB1P

3d0 = gB21P3h1 = Ph1x10,27P

2e0 = Ph1x10,28P2e0 =

Ph1B23P2d0 = Ph2

2iB21 = Ph22jQ1 = Ph2

2kx′ = Ph22Pd0B4 =

Ph2iB2Pd0 = AP 5h2 = Pc0iR2 = kB2P3h2 = B1Pe0P

2e0 =Pd0P

2h1B23 = Pe0P2h1x10,27 = Pe0P

2h1x10,28 = PAP 4h2 =P 2c0x16,37

continued


Stem 104 continued28 (10) iP 2R2 = PjR1 = R2 P 2i

(01) d60g = d5

0e20 = d3

0e0gPe0 = d30g

2Pd0 = d30iu = d2

0e30Pe0 =

d20e

20gPd0 = d2

0ri2 = d2

0jPv = d20kPu = d2

0vPj = d0e40Pd0 =

d0e0g2P 2e0 = d0e0iPv = d0e0jPu = d0e0uPj = d0g

3P 2d0 =d0g

2Pe20 = d0giPu = d0r

2P 2d0 = d0rjPj = d0ijz = d0iPd0w =d0iPe0v = d0jPd0v = d0jPe0u = d0kPd0u = d0lP

2v =d0mP 2u = e3

0gP 2e0 = e20g

2P 2d0 = e20gPe2

0 = e20iPu =

e0g2Pd0Pe0 = e0riP j = e0i

2z = e0iPd0v = e0iPe0u =e0jPd0u = e0kP 2v = e0lP

2u = e0wP 2j = g3Pd20 = giPd0u =

gjP 2v = gkP 2u = gvP 2j = gwP 2i = gPjPv = r2Pd20 =

rijPe0 = rikPd0 = rj2Pd0 = rlP 2j = rmP 2i = rzP 2e0 =i3m = i2jl = i2k2 = ij2k = j4 = jwP 2e0 = kPe0Pv = kvP 2e0 =kwP 2d0 = kzPj = lPd0Pv = lP e0Pu = luP 2e0 = lvP 2d0 =mPd0Pu = muP 2d0 = Pd0z

2 = Pe0wPj

29 (1) h0iP2R2 = h0PjR1 = h0R2 P 2i = h1P

3x16,35 = f0x25,24 =Ph1P

2x16,35 = Ph2iR1 = P 2h1Px16,35 = R1P3j = P 3h1x16,35 =

P 3h2x16,33

31 (1) d50Pj = d4

0iPe0 = d40jPd0 = d3

0e0iPd0 = d30gP 2j = d3

0kP 2e0 =d30lP

2d0 = d20e

20P

2j = d20e0gP 2i = d2

0e0jP2e0 = d2

0e0kP 2d0 =d20e0Pe0Pj = d2

0giP 2e0 = d20gjP 2d0 = d2

0gPd0Pj = d20jPe2

0 =d20kPd0Pe0 = d2

0lPd20 = d2

0mP 3e0 = d0e30P

2i = d0e20iP

2e0 =d0e

20jP

2d0 = d0e20Pd0Pj = d0e0giP 2d0 = d0e0iPe2

0 =d0e0jPd0Pe0 = d0e0kPd2

0 = d0e0lP3e0 = d0e0mP 3d0 =

d0g2P 3j = d0giPd0Pe0 = d0gjPd2

0 = d0gkP 3e0 = d0glP 3d0 =d0lP e0P

2e0 = d0mPd0P2e0 = d0mPe0P

2d0 = e30iP

2d0 =e20gP 3j = e2

0iPd0Pe0 = e20jPd2

0 = e20kP 3e0 = e2

0lP3d0 =

e0giPd20 = e0gjP 3e0 = e0gkP 3d0 = e0gPe0P

2j = e0gPjP 2e0 =e0kPe0P

2e0 = e0lPd0P2e0 = e0lP e0P

2d0 = e0mPd0P2d0 =

g2iP 3e0 = g2jP 3d0 = g2Pd0P2j = g2Pe0P

2i = g2PjP 2d0 =gjPe0P

2e0 = gkPd0P2e0 = gkPe0P

2d0 = glPd0P2d0 =

gmP 4e0 = gPe20Pj = rP 4v = i2P 2v = ijP 2u = iuP 2j = ivP 2i =

iP jPu = juP 2i = kPe30 = lPd0Pe2

0 = mPd20Pe0 = zP 3u



0iP2i = d2

0rP4d0 = d2

0i2P 2d0 = d2

0jP3j = d2

0PjP 2j =d0e0iP

3j = d0e0PjP 2i = d0rPd0P3d0 = d0rP

2d20 = d0i

2Pd20 =

d0ijP3e0 = d0ikP 3d0 = d0iPe0P

2j = d0iP jP 2e0 = d0j2P 3d0 =

d0jPd0P2j = d0jPe0P

2i = d0jP jP 2d0 = d0kPd0P2i =

d0lP4j = d0mP 4i = d0Pd0Pj2 = d0zP 4e0 = e0rP

5e0 =e0i

2P 3e0 = e0ijP3d0 = e0iPd0P

2j = e0iPe0P2i = e0iP jP 2d0 =

e0jPd0P2i = e0kP 4j = e0lP

4i = e0zP 4d0 = grP 5d0 =gi2P 3d0 = giPd0P

2i = gjP 4j = gkP 4i = gPjP 3j =gP 2j2 = rPd2

0P2d0 = rPe0P

4e0 = rP 2e0P3e0 = i2Pe0P

2e0 =ijPd0P

2e0 = ijPe0P2d0 = ikPd0P

2d0 = ilP 4e0 = imP 4d0 =iPd0Pe0Pj = j2Pd0P

2d0 = jkP 4e0 = jlP 4d0 = jPd20Pj =

k2P 4d0 = kPe0P3j = kPjP 3e0 = kP 2e0P

2j = lPd0P3j =

lP jP 3d0 = lP 2d0P2j = lP 2e0P

2i = mP 2d0P2i = Pd0zP 3e0 =

Pe0zP 3d0 = zP 2d0P2e0

(11) P 6Q1

35 (1) h0P6Q1 = h2P

4x18,20 = P 2h2P4x′ = x′P 6h2 = P 4h2x18,20

36 (1) h20P

6Q1 = h0h2P4x18,20 = h0P

2h2P4x′ = h0x

′P 6h2 =h0P

4h2x18,20


Stem 1057 (1) x7,92

8 (1) h0x7,92 = g2D3

9 (1) x9,99

10 (100) h23x8,75 = g2A

(001) h0x9,99 = h1x9,97 = h6v

(111) g2A′

11 (10) h0h23x8,75 = h0g2A = h2g2D2 = h3c2Q2 = h3f1D2 = h4x10,63 =

n1y

(11) h0g2A′

13 (10) h23x11,61 = g2X1 = xG21

(01) h1x12,80 = h4x12,55 = c0x10,76

(11) h6d30 = h6e0Pe0 = h6gPd0

14 (1) h0h23x11,61 = h0h6d

30 = h0h6e0Pe0 = h0h6gPd0 = h0g2X1 =

h0xG21 = h2h6d0Pe0 = h2h6e0Pd0 = h6d0e0Ph2 = B2Q2

15 (10) x15,68

(01) d0x11,61

16 (100) h6P2j

(010) h0x15,68

(001) h0d0x11,61 = h2x15,65

17 (100) h0h6P2j = h2h6P

2i = h6iP2h2

(010) h20x15,68

(001) h20d0x11,61 = h0h2x15,65 = h1d0x12,55 = h2Ph2x11,61 =

Ph1x12,64 = B1B21

18 (10) g2B23 = wB4

(01) h20h6P

2j = h0h2h6P2i = h0h6iP

2h2 = h1h6P3e0 = h4x17,52 =

h6e0P3h1 = h6Ph1P

2e0 = h6Pe0P2h1

19 (1) h1x18,68

20 (1) e0x16,48 = gx16,42

21 (10) g3w = g2rm = r2w = m3

(01) d20e0B4 = d0gx13,35 = d0jB23 = d0kx10,27 = d0kx10,28 = d0lB21 =

d0mQ1 = e20x13,35 = e0gP 2D1 = e0iB23 = e0jx10,27 = e0jx10,28 =

e0kB21 = e0lQ1 = e0mx′ = g2R2 = gix10,27 = gix10,28 =gjB21 = gkQ1 = glx′ = gPe0B4

23 (1) ix16,38 = jx16,35 = kx16,32 = Pd0x15,41

continued



0x16,33 = d0iP2D1 = d0jR2 = e0iR2 = rPd0x

′ = i2B21 =ijQ1 = ikx′ = iPd0B4 = j2x′ = lPR2 = mR1 = Pe0x16,37 =zPQ1 = Pjx13,35

(11) d20e0g

3 = d20e0r

2 = d20lw = d2

0mv = d0e30g

2 = d0e0kw = d0e0lv =d0e0mu = d0grz = d0gjw = d0gkv = d0glu = d0rjm = d0rkl =e50g = e2

0rz = e20jw = e2

0kv = e20lu = e0giw = e0gjv = e0gku =

e0rim = e0rjl = e0rk2 = g4Pe0 = g2iv = g2ju = gr2Pe0 = gril =

grjk = gmPv = kmz = l2z = mPe0w

26 (1) P 2x18,50

27 (10) d50m = d4

0e0l = d40gk = d3

0e20k = d3

0e0gj = d30g

2i = d20e

30j =

d20e

20gi = d2

0e0mPe0 = d20glPe0 = d2

0gmPd0 = d20rPu = d0e

40i =

d0e20lP e0 = d0e

20mPd0 = d0e0g

2Pj = d0e0gkPe0 = d0e0glPd0 =d0g

2jPe0 = d0g2kPd0 = d0rPd0u = d0i

2w = d0ijv = d0iku =d0j

2u = d0zPv = e30gPj = e3

0kPe0 = e30lPd0 = e2

0gjPe0 =e20gkPd0 = e0g

2iPe0 = e0g2jPd0 = e0gmP 2e0 = e0rP

2v =e0i

2v = e0iju = e0zPu = g3iPd0 = g2lP 2e0 = g2mP 2d0 =grP 2u = gi2u = gmPe2

0 = r2iPd0 = ri2k = rij2 = rPe0Pv =rvP 2e0 = rwP 2d0 = rzPj = ilPv = imPu = iz2 = jkPv =jlPu = jwPj = k2Pu = kvPj = luPj = Pd0vz = Pe0uz

(01) h0P2x18,50 = h2

1P2x17,50 = h1Ph1x21,43 = h1Ph1Px17,50 =

h1P2h1x17,50 = Ph2

1x17,50 = Ph2x22,39 = P 3h1x14,42

30 (10) d0x′P 3d0 = e0P

4Q1 = gP 4x′ = Pd0x′P 2d0 = Pe0P

3Q1 =Q1 P 4e0 = B21P

4d0 = P 2e0P2Q1 = PQ1 P 3e0

(01) d40ij = d3

0e0i2 = d3

0rP2e0 = d3

0kPj = d30Pd0z = d2

0e0rP2d0 =

d20e0jP j = d2

0giP j = d20rPd0Pe0 = d2

0ikPe0 = d20ilPd0 =

d20j

2Pe0 = d20jkPd0 = d2

0mP 2j = d0e20iP j = d0e0rPd2

0 =d0e0ijPe0 = d0e0ikPd0 = d0e0j

2Pd0 = d0e0lP2j = d0e0mP 2i =

d0e0zP 2e0 = d0grP 3e0 = d0gi2Pe0 = d0gijPd0 = d0gkP 2j =d0glP 2i = d0gzP 2d0 = d0imP 2e0 = d0jlP

2e0 = d0jmP 2d0 =d0k

2P 2e0 = d0klP 2d0 = d0lP e0Pj = d0mPd0Pj = d0Pe20z =

e20rP

3e0 = e20i

2Pe0 = e20ijPd0 = e2

0kP 2j = e20lP

2i = e20zP 2d0 =

e0grP 3d0 = e0gi2Pd0 = e0gjP 2j = e0gkP 2i = e0gPj2 =e0rPe0P

2e0 = e0ilP2e0 = e0imP 2d0 = e0jkP 2e0 = e0jlP

2d0 =e0k

2P 2d0 = e0kPe0Pj = e0lPd0Pj = e0Pd0Pe0z = g2iP 2j =g2jP 2i = grPd0P

2e0 = grPe0P2d0 = gikP 2e0 = gilP 2d0 =

gj2P 2e0 = gjkP 2d0 = gjPe0Pj = gkPd0Pj = gmP 3j = gPd20z =

rPe30 = ilPe2

0 = imPd0Pe0 = jkPe20 = jlPd0Pe0 = jmPd2

0 =k2Pd0Pe0 = klPd2

0 = kmP 3e0 = l2P 3e0 = lmP 3d0 = uP 3v =vP 3u = PuP 2v = PvP 2u

(11) d0Pd0x18,20

continued


Stem 105 continued31 (1) h0d0Pd0x18,20 = h0d0x

′P 3d0 = h0e0P4Q1 = h0gP 4x′ =

h0Pd0x′P 2d0 = h0Pe0P

3Q1 = h0Q1 P 4e0 = h0B21P4d0 =

h0P2e0P

2Q1 = h0PQ1 P 3e0 = h2d0P4Q1 = h2e0P

4x′ =h2Pd0P

3Q1 = h2x′P 4e0 = h2Q1 P 4d0 = h2P

2d0P2Q1 =

h2P2e0x18,20 = h2PQ1 P 3d0 = d0Ph2P

3Q1 = d0P2h2P

2Q1 =d0Q1 P 4h2 = d0P

3h2PQ1 = e0P2h2x18,20 = e0x

′P 4h2 =Ph2Pd0P

2Q1 = Ph2Pe0x18,20 = Ph2x′P 3e0 = Ph2Q1 P 3d0 =

Ph2P2d0PQ1 = B2P

5e0 = Pd0P2h2PQ1 = Pd0Q1 P 3h2 =

Pe0x′P 3h2 = P 2h2x

′P 2e0 = P 2h2Q1 P 2d0 = x10,27P5h2 =

x10,28P5h2

32 (1) h20d0Pd0x18,20 = h2

0d0x′P 3d0 = h2

0e0P4Q1 = h2

0gP 4x′ =h2

0Pd0x′P 2d0 = h2

0Pe0P3Q1 = h2

0Q1 P 4e0 = h20B21P

4d0 =h2

0P2e0P

2Q1 = h20PQ1 P 3e0 = h0h2d0P

4Q1 =h0h2e0P

4x′ = h0h2Pd0P3Q1 = h0h2x

′P 4e0 = h0h2Q1 P 4d0 =h0h2P

2d0P2Q1 = h0h2P

2e0x18,20 = h0h2PQ1 P 3d0 =h0d0Ph2P

3Q1 = h0d0P2h2P

2Q1 = h0d0Q1 P 4h2 =h0d0P

3h2PQ1 = h0e0P2h2x18,20 = h0e0x

′P 4h2 =h0Ph2Pd0P

2Q1 = h0Ph2Pe0x18,20 = h0Ph2x′P 3e0 =

h0Ph2Q1 P 3d0 = h0Ph2P2d0PQ1 = h0B2P

5e0 =h0Pd0P

2h2PQ1 = h0Pd0Q1 P 3h2 = h0Pe0x′P 3h2 =

h0P2h2x

′P 2e0 = h0P2h2Q1 P 2d0 = h0x10,27P

5h2 =h0x10,28P

5h2 = h22d0P

4x′ = h22x

′P 4d0 = h22P

2d0x18,20 =h2d0P

2h2x18,20 = h2d0x′P 4h2 = h2Ph2Pd0x18,20 =

h2Ph2x′P 3d0 = h2B2P

5d0 = h2Pd0x′P 3h2 = h2P

2h2x′P 2d0 =

h2B21P5h2 = c0P

4R2 = d0Ph22x18,20 = d0Ph2x

′P 3h2 =d0B2P

5h2 = d0P2h2

2x′ = Ph2

2x′P 2d0 = Ph2B2P

4d0 =Ph2Pd0P

2h2x′ = Ph2B21P

4h2 = Pc0P3R2 = B2Pd0P

4h2 =B2P

2h2P3d0 = B2P

2d0P3h2 = P 2h2B21P

3h2 = P 2c0P2R2 =

R2 P 4c0 = P 3c0PR2

continued


Stem 105 continued33 (10) P 5R2

(01) d30P

3u = d20Pd0P

2u = d20uP 3d0 = d2

0P2d0Pu = d0e0P

4v =d0gP 4u = d0riP

3d0 = d0rPd0P2i = d0i

3Pd0 = d0ijP2j =

d0ikP 2i = d0iP j2 = d0j2P 2i = d0Pd2

0Pu = d0Pd0uP 2d0 =d0Pe0P

3v = d0vP 4e0 = d0wP 4d0 = d0zP 3j = d0P2e0P

2v =d0PvP 3e0 = e2

0P4u = e0rP

4j = e0i2P 2j = e0ijP

2i =e0Pd0P

3v = e0Pe0P3u = e0uP 4e0 = e0vP 4d0 = e0P

2d0P2v =

e0P2e0P

2u = e0PuP 3e0 = e0PvP 3d0 = grP 4i = gi2P 2i =gPd0P

3u = guP 4d0 = gP 2d0P2u = gPuP 3d0 = riPd0P

2d0 =rjP 4e0 = rkP 4d0 = rPe0P

3j = rPjP 3e0 = rP 2e0P2j =

i2jP 2e0 = i2kP 2d0 = i2Pe0Pj = ij2P 2d0 = ijPd0Pj =ilP 3j = izP 3e0 = jkP 3j = jzP 3d0 = kPjP 2j = lP jP 2i =Pd3

0u = Pd0Pe0P2v = Pd0vP 3e0 = Pd0wP 3d0 = Pd0zP 2j =

Pd0P2e0Pv = Pe2

0P2u = Pe0uP 3e0 = Pe0vP 3d0 = Pe0zP 2i =

Pe0P2d0Pv = Pe0P

2e0Pu = uP 2e20 = vP 2d0P

2e0 = wP 2d20 =

zPjP 2d0

34 (1) h0P5R2 = h2P

4R1 = P 2h2x25,24 = P 4h2R1

35 (1) h20P

5R2 = h0h2P4R1 = h0P

2h2x25,24 = h0P4h2R1 =

h1P6Q1 = Ph1P

5Q1 = P 2h1P4Q1 = R1P

6h2 = Q1 P 6h1 =P 3h1P

3Q1 = PQ1 P 5h1 = P 4h1P2Q1


Stem 1066 (1) C1

8 (1) h3x7,84

9 (10) g2H1

(01) h0h3x7,84 = h4x8,75

10 (01) h1x9,99

(11) h3x9,86

12 (10) h4x11,61

(01) h6d0k = h6e0j = h6gi

(11) h23x10,65 = e1G21 = g2x8,32

13 (1) h0h4x11,61 = h0h6d0k = h0h6e0j = h0h6gi = h2h6d0j =h2h6e0i = h2x12,78 = h6f0Pe0 = h6Ph2l = D2B2

14 (10) x14,79

(01) h20h4x11,61 = h2

0h6d0k = h20h6e0j = h2

0h6gi = h0h2h6d0j =h0h2h6e0i = h0h2x12,78 = h0h6f0Pe0 = h0h6Ph2l = h0D2B2 =h2

1x12,80 = h1h4x12,55 = h1h6d30 = h1h6e0Pe0 = h1h6gPd0 =

h1c0x10,76 = h22h6d0i = h2h6f0Pd0 = h2h6Ph2k = h6d0f0Ph2 =

h6d0gPh1 = h6e20Ph1 = Q3u = B1B3

15 (100) g2x7,40 = rx9,51 = A′w = Aw

(010) Ph1x10,76

(001) h0x14,79

16 (1) h20x14,79 = h1x15,68

20 (100) g3N = g2nm = g2rt = nrw = r2N = tm2

(001) d0rx10,27 = d0rx10,28 = d0lB4 = e0rB21 = e0kB4 = grQ1 =gjB4 = mx13,35 = zB23

(011) x′2

21 (1) h0x′2

22 (10) rx16,32 = ix15,41

(01) h20x

′2

(11) d0x18,55 = e0x18,50

23 (100) d0e0g2m = d0e0rw = d0g

3l = d0grv = d0r2l = e3

0gm = e20g

2l =e20rv = e0g

3k = e0gru = e0r2k = g4j = gr2j = gwz = rmz =

jmw = klw = kmv = l2v = lmu

(010) d0ux′ = jx16,37 = kx16,33 = Pd0x15,43 = vPQ1 = zR2 =Q1 Pv = B21Pu

(001) h30x

′2 = h0rx16,32 = h0ix15,41 = xx18,20

(011) rix′ = i2B4

24 (1) h40x

′2 = h20rx16,32 = h2

0ix15,41 = h0xx18,20 = h0rix′ = h0i

2B4 =h3ix16,32 = x9,40P

2i

continued


Stem 106 continued25 (10) P 2x17,52

(01) h50x

′2 = h30rx16,32 = h3

0ix15,41 = h20xx18,20 = h2

0rix′ = h2

0i2B4 =

h0h3ix16,32 = h0x9,40P2i = h3rx18,20 = h3i

2x′ = h3B4P2i

26 (100) d40gr = d3

0e20r = d3

0km = d30l

2 = d20e0gz = d2

0e0jm = d20e0kl =

d20gim = d2

0gjl = d20gk2 = d2

0u2 = d0e

30z = d0e

20im = d0e

20jl =

d0e20k

2 = d0e0grPe0 = d0e0gil = d0e0gjk = d0g2rPd0 = d0g

2ik =d0g

2j2 = d0riu = d0lmPe0 = d0m2Pd0 = d0vPv = d0wPu =

e30rPe0 = e3

0il = e30jk = e2

0grPd0 = e20gik = e2

0gj2 = e0g2ij =

e0gmPj = e0kmPe0 = e0l2Pe0 = e0lmPd0 = e0uPv = e0vPu =

g3i2 = g2lP j = g2Pe0z = gjmPe0 = gklPe0 = gkmPd0 =gl2Pd0 = guPu = rjPv = rkPu = rvPj = ivz = juz = Pd0uw =Pd0v

2 = Pe0uv

(001) h60x

′2 = h40rx16,32 = h4

0ix15,41 = h30xx18,20 = h3

0rix′ =

h30i

2B4 = h20h3ix16,32 = h2

0x9,40P2i = h0h3rx18,20 = h0h3i

2x′ =h0h3B4P

2i = h23P

2x16,32 = g2iP2i = Ph2x21,43 = xrP 2i = xi3 =

x11,35P2i

(101) r2i2

(011) d30PQ1 = d2

0Pd0Q1 = d20Pe0x

′ = d0e0Pd0x′ = d0gP 2Q1 =

d0B21P2e0 = d0x10,27P

2d0 = d0x10,28P2d0 = e2

0P2Q1 =

e0Pe0PQ1 = e0Q1 P 2e0 = e0B21P2d0 = gPd0PQ1 = gx′P 2e0 =

gQ1 P 2d0 = Pd20x10,27 = Pd2

0x10,28 = Pd0Pe0B21 = Pe20Q1 =

B23P3e0

(111) e0gx18,20

continued


Stem 106 continued

27 (1) h70x

′2 = h50rx16,32 = h5

0ix15,41 = h40xx18,20 = h4

0rix′ =

h40i

2B4 = h30h3ix16,32 = h3

0x9,40P2i = h2

0h3rx18,20 = h20h3i

2x′ =h2

0h3B4P2i = h0h

23P

2x16,32 = h0d30PQ1 = h0d

20Pd0Q1 =

h0d20Pe0x

′ = h0d0e0Pd0x′ = h0d0gP 2Q1 = h0d0B21P

2e0 =h0d0x10,27P

2d0 = h0d0x10,28P2d0 = h0e

20P

2Q1 = h0e0gx18,20 =h0e0Pe0PQ1 = h0e0Q1 P 2e0 = h0e0B21P

2d0 = h0gPd0PQ1 =h0gx′P 2e0 = h0gQ1 P 2d0 = h0g2iP

2i = h0Ph2x21,43 =h0xrP 2i = h0xi3 = h0r

2i2 = h0Pd20x10,27 = h0Pd2

0x10,28 =h0Pd0Pe0B21 = h0Pe2

0Q1 = h0B23P3e0 = h0x11,35P

2i =h1P

2x18,50 = h2d20Pd0x

′ = h2d0e0P2Q1 = h2d0gx18,20 =

h2d0Pe0PQ1 = h2d0Q1 P 2e0 = h2d0B21P2d0 = h2e

20x18,20 =

h2e0Pd0PQ1 = h2e0x′P 2e0 = h2e0Q1 P 2d0 = h2gx′P 2d0 =

h2Pd20B21 = h2Pd0Pe0Q1 = h2Pe2

0x′ = h2x10,27P

3e0 =h2x10,28P

3e0 = h2B23P3d0 = h2

3ix18,20 = h23x

′P 2i =h4Pd0x18,20 = h4x

′P 3d0 = c0Pd0x16,32 = d30Ph2x

′ = d20B2P

2d0 =d20P

2h2B21 = d0e0Ph2PQ1 = d0e0P2h2Q1 = d0gP 2h2x

′ =d0Ph2Pd0B21 = d0Ph2Pe0Q1 = d0Pc0x16,32 = d0B2Pd2

0 =d0B23P

3h2 = e20P

2h2x′ = e0Ph2Pd0Q1 = e0Ph2Pe0x

′ =e0B2P

3e0 = e0x10,27P3h2 = e0x10,28P

3h2 = gPh2Pd0x′ =

gB2P3d0 = gB21P

3h2 = Ph1Px18,50 = Ph2x10,27P2e0 =

Ph2x10,28P2e0 = Ph2B23P

2d0 = B2Pe0P2e0 = Q2P

4e0 =B3P

4d0 = Pd0P2h2B23 = Pe0P

2h2x10,27 = Pe0P2h2x10,28 =

P 2h1x18,50 = P 2c0x16,38

28 (1) d0P2x16,32 = P 2d0x16,32

29 (100) d0ix18,20

(010) d40Pv = d3

0e0Pu = d30rPj = d3

0iz = d30Pd0v = d3

0Pe0u =d20e0Pd0u = d2

0gP 2v = d20riPe0 = d2

0rjPd0 = d20i

2l = d20ijk =

d20j

3 = d20wP 2e0 = d0e

20P

2v = d0e0gP 2u = d0e0riPd0 =d0e0i

2k = d0e0ij2 = d0e0Pe0Pv = d0e0vP 2e0 = d0e0wP 2d0 =

d0e0zPj = d0grP 2j = d0gi2j = d0gPd0Pv = d0gPe0Pu =d0guP 2e0 = d0gvP 2d0 = d0rkP 2e0 = d0rlP

2d0 = d0imPj =d0jlP j = d0jPe0z = d0k

2Pj = d0kPd0z = d0Pd0Pe0w =d0Pe2

0v = e30P

2u = e20rP

2j = e20i

2j = e20Pd0Pv = e2

0Pe0Pu =e20uP 2e0 = e2

0vP 2d0 = e0grP 2i = e0gi3 = e0gPd0Pu =e0guP 2d0 = e0rjP

2e0 = e0rkP 2d0 = e0rPe0Pj = e0ilP j =e0iPe0z = e0jkPj = e0jPd0z = e0Pd2

0w = e0Pd0Pe0v =e0Pe2

0u = g2P 3v = griP 2e0 = grjP 2d0 = grPd0Pj = gikPj =giPd0z = gj2Pj = gPd2

0v = gPd0Pe0u = gwP 3e0 = rjPe20 =

rkPd0Pe0 = rlPd20 = rmP 3e0 = i2mPe0 = ijlPe0 = ijmPd0 =

ik2Pe0 = iklPd0 = j2kPe0 = j2lPd0 = jk2Pd0 = kmP 2j =l2P 2j = lmP 2i = lzP 2e0 = mzP 2d0

continued


Stem 106 continued(110) d0x

′P 2i = ix′P 2d0 = jP 3Q1 = B4P4d0 = Q1 P 3j = PjP 2Q1 =

PQ1 P 2j

(001) h0d0P2x16,32 = h0P

2d0x16,32 = h2P3x16,35 = Ph2P

2x16,35 =P 2h2Px16,35 = P 3h2x16,35

(101) gx25,24

(111) d0Pd0R1 = e0P3R2 = Pe0P

2R2 = P 2e0PR2 = R2 P 3e0 =P 2D1P

3d0

30 (10) h0d0ix18,20 = h0d0x′P 2i = h0ix

′P 2d0 = h0jP3Q1 = h0B4P

4d0 =h0Q1 P 3j = h0PjP 2Q1 = h0PQ1 P 2j = h2iP

3Q1 =h2x

′P 3j = h2Pjx18,20 = h2PQ1 P 2i = f0P4Q1 = Ph2iP

2Q1 =Ph2jx18,20 = Ph2x

′P 2j = Ph2Q1 P 2i = iP 2h2PQ1 =iQ1 P 3h2 = jx′P 3h2 = B2P

4j = P 2h2x′Pj = x13,35P

4h2

(01) h20d0P

2x16,32 = h20P

2d0x16,32 = h0h2P3x16,35 = h0Ph2P

2x16,35 =h0P

2h2Px16,35 = h0P3h2x16,35 = h2Ph2P

2x16,32 =h2P

3h2x16,32 = Ph2P2h2x16,32 = x13,34P

4h2

(11) h0d0Pd0R1 = h0e0P3R2 = h0gx25,24 = h0Pe0P

2R2 =h0P

2e0PR2 = h0R2 P 3e0 = h0P2D1P

3d0 = h2d0P3R2 =

h2e0x25,24 = h2Pd0P2R2 = h2P

2d0PR2 = h2P2e0R1 =

h2R2 P 3d0 = d0Ph2P2R2 = d0P

2h2PR2 = d0R1P3d0 =

d0P3h2R2 = e0P

2h2R1 = Ph2Pd0PR2 = Ph2Pe0R1 =Ph2P

2d0R2 = Pd0P2h2R2 = Pd0R1P

2d0

31 (1) h20d0ix18,20 = h2

0d0Pd0R1 = h20d0x

′P 2i = h20e0P

3R2 =h2

0gx25,24 = h20ix

′P 2d0 = h20jP

3Q1 = h20Pe0P

2R2 =h2

0B4P4d0 = h2

0Q1 P 3j = h20PjP 2Q1 = h2

0P2e0PR2 =

h20R2 P 3e0 = h2

0P2D1P

3d0 = h20PQ1 P 2j = h0h2d0P

3R2 =h0h2e0x25,24 = h0h2iP

3Q1 = h0h2Pd0P2R2 = h0h2x

′P 3j =h0h2Pjx18,20 = h0h2P

2d0PR2 = h0h2P2e0R1 = h0h2R2 P 3d0 =

h0h2PQ1 P 2i = h0d0Ph2P2R2 = h0d0P

2h2PR2 =h0d0R1P

3d0 = h0d0P3h2R2 = h0e0P

2h2R1 = h0f0P4Q1 =

h0Ph2iP2Q1 = h0Ph2jx18,20 = h0Ph2Pd0PR2 =

h0Ph2Pe0R1 = h0Ph2x′P 2j = h0Ph2Q1 P 2i = h0Ph2P

2d0R2 =h0iP

2h2PQ1 = h0iQ1 P 3h2 = h0jx′P 3h2 = h0B2P

4j =h0Pd0P

2h2R2 = h0Pd0R1P2d0 = h0P

2h2x′Pj = h0x13,35P

4h2 =h1d0Pd0x18,20 = h1d0x

′P 3d0 = h1e0P4Q1 = h1gP 4x′ =

h1Pd0x′P 2d0 = h1Pe0P

3Q1 = h1Q1 P 4e0 = h1B21P4d0 =

h1P2e0P

2Q1 = h1PQ1 P 3e0 = h22d0x25,24 = h2

2P2d0R1 =

h2d0P2h2R1 = h2f0P

4x′ = h2Ph2ix18,20 = h2Ph2Pd0R1 =h2Ph2x

′P 2i = h2ix′P 3h2 = h2B2P

4i = h2B4P5h2 = h2R1P

4e0 =h2P

2D1P4h2 = d2

0Ph1x18,20 = d20x

′P 3h1 = d0Ph1x′P 2d0 =

(continued)


Stem 106 continued31 (1) (continued) = d0Ph2

2R1 = d0B1P4d0 = d0Pd0P

2h1x′ =

d0B21P4h1 = e0Ph1P

3Q1 = e0P2h1P

2Q1 = e0R1P4h2 =

e0Q1 P 4h1 = e0P3h1PQ1 = f0P

2h2x18,20 = f0x′P 4h2 =

gP 2h1x18,20 = gx′P 4h1 = Ph1Pd20x

′ = Ph1Pe0P2Q1 =

Ph1Q1 P 3e0 = Ph1B21P3d0 = Ph1P

2e0PQ1 = Ph2iP2h2x

′ =Ph2B4P

4h2 = Ph2R1P3e0 = Ph2P

3h2P2D1 = iB2P

4h2 =B1Pd0P

3d0 = B1P2d2

0 = B2P2h2P

2i = Pd0B21P3h1 =

Pe0P2h1PQ1 = Pe0R1P

3h2 = Pe0Q1 P 3h1 = P 2h1Q1 P 2e0 =P 2h1B21P

2d0 = P 2h22P

2D1 = P 2h2B4P3h2 = P 2h2R1P

2e0 =B23P

5h1

32 (1) d60Pd0 = d4

0e0P2e0 = d4

0gP 2d0 = d40Pe2

0 = d30e

20P

2d0 =d30e0Pd0Pe0 = d3

0gPd20 = d2

0e20Pd2

0 = d20e0gP 3e0 = d2

0g2P 3d0 =

d20gPe0P

2e0 = d20iP

2u = d20uP 2i = d0e

30P

3e0 = d0e20gP 3d0 =

d0e20Pe0P

2e0 = d0e0gPd0P2e0 = d0e0gPe0P

2d0 = d0e0Pe30 =

d0g2Pd0P

2d0 = d0gPd0Pe20 = d0riP

2i = d0i4 = d0iPd0Pu =

d0iuP 2d0 = d0jP3v = d0kP 3u = d0vP 3j = d0PjP 2v =

d0PvP 2j = e40P

3d0 = e30Pd0P

2e0 = e30Pe0P

2d0 = e20gPd0P

2d0 =e20Pd0Pe2

0 = e0g2P 4e0 = e0gPd2

0Pe0 = e0iP3v = e0jP

3u =e0uP 3j = e0PjP 2u = e0PuP 2j = e0PvP 2i = g3P 4d0 =g2Pd3

0 = g2Pe0P3e0 = g2P 2e2

0 = giP 3u = gPuP 2i = r2P 4d0 =ri2P 2d0 = rjP 3j = rPjP 2j = i2jP j = iPd2

0u = iPe0P2v =

ivP 3e0 = iwP 3d0 = izP 2j = iP 2e0Pv = jPd0P2v = jPe0P

2u =juP 3e0 = jvP 3d0 = jzP 2i = jP 2d0Pv = jP 2e0Pu = kPd0P

2u =kuP 3d0 = kP 2d0Pu = lP 4v = mP 4u = Pd0vP 2j = Pd0wP 2i =Pd0PjPv = Pe0uP 2j = Pe0vP 2i = Pe0PjPu = uPjP 2e0 =vPjP 2d0


Stem 1075 (1) h4g3 = h6g2

6 (1) h0h4g3 = h0h6g2

7 (10) x7,93

(01) h20h4g3 = h2

0h6g2 = h3h6x

8 (1) h0x7,93

9 (1) x9,102

10 (1) h0x9,102 = h2x9,97

11 (010) h21x9,99

(001) h20x9,102 = h0h2x9,97 = h3x10,82

(101) h1h3x9,86 = d1x7,53 = g2x7,33

(011) h6d0r

(111) D3B1

12 (1) x12,85

13 (1) x13,85

14 (1) gx10,60 = nx9,51 = H1w = rx8,57 = A′N = AN

16 (10) d0x12,60

(01) h1Ph1x10,76 = Gx′ = B1X1

(11) e0x12,55

17 (10) g2x9,39 = grQ2 = x8,33w

(01) h0d0x12,60 = h0e0x12,55 = h2d0x12,55 = h5x16,32 = h6d0P2d0 =

h6Pd20 = Ph2x12,64 = B2B21

18 (10) x18,72

(01) h20d0x12,60 = h2

0e0x12,55 = h0h2d0x12,55 = h0h5x16,32 =h0h6d0P

2d0 = h0h6Pd20 = h0Ph2x12,64 = h0B2B21 = h2

2Px12,60 =h2h6P

3e0 = h2Ph2x12,60 = h2B2Q1 = h6e0P3h2 = h6Ph2P

2e0 =h6Pe0P

2h2 = Pc0x11,61

19 (010) e0rB4 = gx15,47 = vB23 = wx10,27 = wx10,28

(001) h0x18,72 = h2x18,68

(101) P 2x11,61

20 (10) x′R1

(01) h20x18,72 = h0h2x18,68 = h2

2x18,63 = Ph2x15,58

(11) h0P2x11,61

21 (010) h1x′2 = P 2h1x12,55

(110) d0x17,57 = e0x17,52 = gx17,50

(001) h20P

2x11,61 = h0x′R1

continued


Stem 107 continued22 (100) e0g

3r = e0gm2 = e0r3 = e0w

2 = g2lm = gvw = rlw = rmv

(010) d30B23 = d2

0e0x10,27 = d20e0x10,28 = d2

0gB21 = d0e20B21 =

d0e0gQ1 = d0g2x′ = e3

0Q1 = e20gx′ = e0Pe0B23 = gPd0B23 =

gPe0x10,27 = gPe0x10,28 = ix15,43 = uP 2D1 = vR2 = B4Pu

(001) h30P

2x11,61 = h20x

′R1 = xR1 = ix15,42 = B4Q

(011) rx16,33

23 (1) h40P

2x11,61 = h30x

′R1 = h0xR1 = h0rx16,33 = h0ix15,42 =h0B4Q = riR1 = i2X1 = G21 P 2i

24 (10) d20x16,35 = d0e0x16,32 = gPx16,35 = Pd0x16,42 = Pe0x16,38

(01) h50P

2x11,61 = h40x

′R1 = h20xR1 = h2

0rx16,33 = h20ix15,42 =

h20B4Q = h0riR1 = h0i

2X1 = h0G21 P 2i = h3rR1 = h3ix16,33 =h3x

′Q = yx18,20

25 (100) d30gw = d3

0rm = d20e

20w = d2

0e0gv = d20e0rl = d2

0g2u = d2

0grk =d0e

30v = d0e

20gu = d0e

20rk = d0e0grj = d0e0mz = d0g

2ri =d0glz = d0im

2 = d0jlm = d0k2m = d0kl2 = e4

0u = e30rj =

e20gri = e2

0lz = e0g2Pv = e0gkz = e0gPe0w = e0rmPe0 =

e0ilm = e0jkm = e0jl2 = e0k

2l = g3Pu = g2jz = g2Pd0w =g2Pe0v = grlPe0 = grmPd0 = gikm = gil2 = gj2m = gjkl =gk3 = r2Pu = iuw = iv2 = juv = ku2

(001) h60P

2x11,61 = h50x

′R1 = h30xR1 = h3

0rx16,33 = h30ix15,42 =

h30B4Q = h2

0riR1 = h20i

2X1 = h20G21 P 2i = h0h3rR1 =

h0h3ix16,33 = h0h3x′Q = h0yx18,20 = h3i

2R1 = h3X1P2i =

h4P2x16,32 = xiQ = r2Q

(011) d30R2 = d2

0iQ1 = d20jx

′ = d0e0ix′ = d0gPR2 = d0kPQ1 =

d0Pd0x13,35 = d0Pe0P2D1 = d0B4P

2e0 = d0B21Pj = e20PR2 =

e0gR1 = e0jPQ1 = e0Pd0P2D1 = e0Pe0R2 = e0B4P

2d0 =e0Q1 Pj = giPQ1 = gPd0R2 = gx′Pj = iPd0x10,27 =iPd0x10,28 = iPe0B21 = jPd0B21 = jPe0Q1 = kPd0Q1 =kPe0x

′ = lPd0x′ = mP 2Q1 = Pd0Pe0B4 = B23P

2j

continued



0P2x11,61 = h6

0x′R1 = h4

0xR1 = h40rx16,33 = h4

0ix15,42 =h4

0B4Q = h30riR1 = h3

0i2X1 = h3

0G21 P 2i = h20h3rR1 =

h20h3ix16,33 = h2

0h3x′Q = h2

0yx18,20 = h0h3i2R1 = h0h3X1P

2i =h0h4P

2x16,32 = h0d30R2 = h0d

20iQ1 = h0d

20jx

′ = h0d0e0ix′ =

h0d0gPR2 = h0d0kPQ1 = h0d0Pd0x13,35 = h0d0Pe0P2D1 =

h0d0B4P2e0 = h0d0B21Pj = h0e

20PR2 = h0e0gR1 =

h0e0jPQ1 = h0e0Pd0P2D1 = h0e0Pe0R2 = h0e0B4P

2d0 =h0e0Q1 Pj = h0giPQ1 = h0gPd0R2 = h0gx′Pj =h0xiQ = h0r

2Q = h0iPd0x10,27 = h0iPd0x10,28 = h0iPe0B21 =h0jPd0B21 = h0jPe0Q1 = h0kPd0Q1 = h0kPe0x

′ =h0lPd0x

′ = h0mP 2Q1 = h0Pd0Pe0B4 = h0B23P2j =

h2d20ix

′ = h2d0e0PR2 = h2d0gR1 = h2d0jPQ1 =h2d0Pd0P

2D1 = h2d0Pe0R2 = h2d0B4P2d0 = h2d0Q1 Pj =

h2e20R1 = h2e0iPQ1 = h2e0Pd0R2 = h2e0x

′Pj =h2iPd0B21 = h2iPe0Q1 = h2jPd0Q1 = h2jPe0x

′ =h2kPd0x

′ = h2lP2Q1 = h2mx18,20 = h2Pd2

0B4 = h2x10,27P2j =

h2x10,28P2j = h2B23P

2i = h2P2e0x13,35 = h2

3iR1 = h4Pd0R1 =d20Ph2P

2D1 = d20Pe0R1 = d2

0P2h2B4 = d0e0Ph2R2 =

d0e0Pd0R1 = d0f0Pd0x′ = d0Ph2iB21 = d0Ph2jQ1 =

d0Ph2kx′ = d0Ph2Pd0B4 = d0iB2Pd0 = e0f0P2Q1 =

e0Ph2iQ1 = e0Ph2jx′ = e0B2P

2j = e0P2h2x13,35 = f0gx18,20 =

f0Pe0PQ1 = f0Q1 P 2e0 = f0B21P2d0 = gPh2ix

′ =gB2P

2i = gP 2h2P2D1 = gB4P

3h2 = gR1P2e0 = Ph2lPQ1 =

Ph2Pe0x13,35 = Ph2x10,27Pj = Ph2x10,28Pj = D2P4e0 =

AP 4d0 = iP 2h2B23 = jB2P2e0 = jP 2h2x10,27 = jP 2h2x10,28 =

kB2P2d0 = kP 2h2B21 = lP 2h2Q1 = mP 2h2x

′ = B2Pe0Pj =Q2P

3j = B5 P 3e0 = PD2P3e0 = PAP 3d0

continued



0P2x11,61 = h7

0x′R1 = h5

0xR1 = h50rx16,33 = h5

0ix15,42 =h5

0B4Q = h40riR1 = h4

0i2X1 = h4

0G21 P 2i = h30h3rR1 =

h30h3ix16,33 = h3

0h3x′Q = h3

0yx18,20 = h20h3i

2R1 =h2

0h3X1P2i = h2

0h4P2x16,32 = h2

0d30R2 = h2

0d20iQ1 =

h20d

20jx

′ = h20d0e0ix

′ = h20d0gPR2 = h2

0d0kPQ1 =h2

0d0Pd0x13,35 = h20d0Pe0P

2D1 = h20d0B4P

2e0 = h20d0B21Pj =

h20e

20PR2 = h2

0e0gR1 = h20e0jPQ1 = h2

0e0Pd0P2D1 =

h20e0Pe0R2 = h2

0e0B4P2d0 = h2

0e0Q1 Pj = h20giPQ1 =

h20gPd0R2 = h2

0gx′Pj = h20xiQ = h2

0r2Q = h2

0iPd0x10,27 =h2

0iPd0x10,28 = h20iPe0B21 = h2

0jPd0B21 = h20jPe0Q1 =

h20kPd0Q1 = h2

0kPe0x′ = h2

0lPd0x′ = h2

0mP 2Q1 =h2

0Pd0Pe0B4 = h20B23P

2j = h0h2d20ix

′ = h0h2d0e0PR2 =h0h2d0gR1 = h0h2d0jPQ1 = h0h2d0Pd0P

2D1 =h0h2d0Pe0R2 = h0h2d0B4P

2d0 = h0h2d0Q1 Pj = h0h2e20R1 =

h0h2e0iPQ1 = h0h2e0Pd0R2 = h0h2e0x′Pj = h0h2iPd0B21 =

h0h2iPe0Q1 = h0h2jPd0Q1 = h0h2jPe0x′ = h0h2kPd0x

′ =h0h2lP

2Q1 = h0h2mx18,20 = h0h2Pd20B4 = h0h2x10,27P

2j =h0h2x10,28P

2j = h0h2B23P2i = h0h2P

2e0x13,35 = h0h23iR1 =

h0h4Pd0R1 = h0d20Ph2P

2D1 = h0d20Pe0R1 = h0d

20P

2h2B4 =h0d0e0Ph2R2 = h0d0e0Pd0R1 = h0d0f0Pd0x

′ = h0d0Ph2iB21 =h0d0Ph2jQ1 = h0d0Ph2kx′ = h0d0Ph2Pd0B4 = h0d0iB2Pd0 =h0e0f0P

2Q1 = h0e0Ph2iQ1 = h0e0Ph2jx′ = h0e0B2P

2j =h0e0P

2h2x13,35 = h0f0gx18,20 = h0f0Pe0PQ1 = h0f0Q1 P 2e0 =h0f0B21P

2d0 = h0gPh2ix′ = h0gB2P

2i = h0gP 2h2P2D1 =

h0gB4P3h2 = h0gR1P

2e0 = h0Ph2lPQ1 = h0Ph2Pe0x13,35 =h0Ph2x10,27Pj = h0Ph2x10,28Pj = h0D2P

4e0 = h0AP 4d0 =h0iP

2h2B23 = h0jB2P2e0 = h0jP

2h2x10,27 = h0jP2h2x10,28 =

h0kB2P2d0 = h0kP 2h2B21 = h0lP

2h2Q1 = h0mP 2h2x′ =

h0B2Pe0Pj = h0Q2P3j = h0B5 P 3e0 = h0PD2P

3e0 =h0PAP 3d0 = h1d

30PQ1 = h1d

20Pd0Q1 = h1d

20Pe0x

′ =h1d0e0Pd0x

′ = h1d0gP 2Q1 = h1d0B21P2e0 = h1d0x10,27P

2d0 =h1d0x10,28P

2d0 = h1e20P

2Q1 = h1e0gx18,20 = h1e0Pe0PQ1 =h1e0Q1 P 2e0 = h1e0B21P

2d0 = h1gPd0PQ1 = h1gx′P 2e0 =h1gQ1 P 2d0 = h1Pd2

0x10,27 = h1Pd20x10,28 = h1Pd0Pe0B21 =

h1Pe20Q1 = h1B23P

3e0 = h22d

20PR2 = h2

2d0e0R1 = h22d0iPQ1 =

h22d0Pd0R2 = h2

2d0x′Pj = h2

2gP 2R2 = h22iPd0Q1 = h2

2iPe0x′ =

h22jPd0x

′ = h22kP 2Q1 = h2

2lx18,20 = h22B4P

3e0 = h22B21P

2j =h2

2x10,27P2i = h2

2x10,28P2i = h2

2P2d0x13,35 = h2

2P2e0P

2D1 =h2h4P

3R2 = h2d20Ph2R2 = (continued)


Stem 107 continued27 (1) (continued) = h2d

20Pd0R1 = h2d0f0P

2Q1 = h2d0Ph2iQ1 =h2d0Ph2jx

′ = h2d0B2P2j = h2d0P

2h2x13,35 = h2e0f0x18,20 =h2e0Ph2ix

′ = h2e0B2P2i = h2e0P

2h2P2D1 = h2e0B4P

3h2 =h2e0R1P

2e0 = h2f0Pd0PQ1 = h2f0x′P 2e0 = h2f0Q1 P 2d0 =

h2gPh2PR2 = h2gP 2h2R2 = h2gR1P2d0 = h2Ph2kPQ1 =

h2Ph2Pd0x13,35 = h2Ph2Pe0P2D1 = h2Ph2B4P

2e0 =h2Ph2B21Pj = h2D2P

4d0 = h2iB2P2e0 = h2iP

2h2x10,27 =h2iP

2h2x10,28 = h2jB2P2d0 = h2jP

2h2B21 = h2kP 2h2Q1 =h2lP

2h2x′ = h2B2Pd0Pj = h2Pe2

0R1 = h2Pe0P2h2B4 =

h2B5 P 3d0 = h2PD2P3d0 = h2

3R1P2i = h3riQ =

h4Ph2P2R2 = h4P

2h2PR2 = h4R1P3d0 = h4P

3h2R2 =c0rx18,20 = c0i

2x′ = c0jPR2 = c0kR1 = c0Pd0x16,33 =c0B4P

2i = c0PjR2 = d30Ph1Q1 = d3

0Ph2R1 =d20e0Ph1x

′ = d20B1P

2e0 = d20P

2h1x10,27 = d20P

2h1x10,28 =d0e0B1P

2d0 = d0e0P2h1B21 = d0f0Ph2PQ1 = d0f0P

2h2Q1 =d0gPh1PQ1 = d0gP 2h1Q1 = d0gP 2h2R1 = d0Ph1Pd0x10,27 =d0Ph1Pd0x10,28 = d0Ph1Pe0B21 = d0Ph2

2x13,35 = d0Ph2B2Pj =d0D2P

4h2 = d0Pc0x16,33 = d0jB2P2h2 = d0B1Pd0Pe0 =

d0B5 P 3h2 = d0PD2P3h2 = e2

0Ph1PQ1 = e20P

2h1Q1 =e20P

2h2R1 = e0f0P2h2x

′ = e0gP 2h1x′ = e0Ph1Pd0B21 =

e0Ph1Pe0Q1 = e0Ph22P

2D1 = e0Ph2Pe0R1 = e0Ph2P2h2B4 =

e0iB2P2h2 = e0B1Pd2

0 = e0B23P3h1 = f0Ph2Pd0Q1 =

f0Ph2Pe0x′ = f0B2P

3e0 = f0x10,27P3h2 = f0x10,28P

3h2 =gPh1Pd0Q1 = gPh1Pe0x

′ = gPh22R2 = gPh2Pd0R1 =

gB1P3e0 = gx10,27P

3h1 = gx10,28P3h1 = Ph1B23P

2e0 =Ph2

2ix10,27 = Ph22ix10,28 = Ph2

2jB21 = Ph22kQ1 = Ph2

2lx′ =

Ph22Pe0B4 = Ph2D2P

3d0 = Ph2iB2Pe0 = Ph2jB2Pd0 =Ph2Q2P

2i = Ph2B5 P 2d0 = Ph2PD2P2d0 = ryP 2i = rx′P 2c0 =

yi3 = D2Pd0P3h2 = D2P

2h2P2d0 = A′′P 5h2 = Pc0iP

2D1 =Pc0jR2 = iQ2P

3h2 = iB4P2c0 = lB2P

3h2 = Pd0P2h2B5 =

Pd0P2h2PD2 = Pe0P

2h1B23

continued


Stem 107 continued28 (10) d0iR1 = jP 2R2 = PjPR2 = P 2d0x16,33 = R2 P 2j = P 2D1P

2i

(01) d50e0g = d4

0e30 = d3

0g2Pe0 = d3

0iv = d30ju = d2

0e20gPe0 =

d20e0g

2Pd0 = d20e0iu = d2

0rij = d20kPv = d2

0lPu = d20wPj =

d0e40Pe0 = d0e

30gPd0 = d0e0ri

2 = d0e0jPv = d0e0kPu =d0e0vPj = d0g

3P 2e0 = d0giPv = d0gjPu = d0guPj =d0r

2P 2e0 = d0rkPj = d0rPd0z = d0ikz = d0iPe0w = d0j2z =

d0jPd0w = d0jPe0v = d0kPd0v = d0kPe0u = d0lPd0u =d0mP 2v = e5

0Pd0 = e20g

2P 2e0 = e20iPv = e2

0jPu = e20uPj =

e0g3P 2d0 = e0g

2Pe20 = e0giPu = e0r

2P 2d0 = e0rjPj = e0ijz =e0iPd0w = e0iPe0v = e0jPd0v = e0jPe0u = e0kPd0u =e0lP

2v = e0mP 2u = g3Pd0Pe0 = griP j = gi2z = giPd0v =giPe0u = gjPd0u = gkP 2v = glP 2u = gwP 2j = r2Pd0Pe0 =rikPe0 = rilPd0 = rj2Pe0 = rjkPd0 = rmP 2j = i2jm = i2kl =ij2l = ijk2 = j3k = kwP 2e0 = lP e0Pv = lvP 2e0 = lwP 2d0 =lzP j = mPd0Pv = mPe0Pu = muP 2e0 = mvP 2d0 = Pe0z

2

29 (1) h0d0iR1 = h0jP2R2 = h0PjPR2 = h0P

2d0x16,33 = h0R2 P 2j =h0P

2D1P2i = h1d0P

2x16,32 = h1P2d0x16,32 = h2iP

2R2 =h2PjR1 = h2R2 P 2i = d0P

2h1x16,32 = d0R1P2i = f0P

3R2 =Ph1Pd0x16,32 = Ph2iPR2 = Ph2jR1 = iP 2h2R2 = iR1P

2d0 =P 3h1x16,38 = P 3h2x16,37 = W1P

3d0

31 (1) d60i = d4

0e0Pj = d40jPe0 = d4

0kPd0 = d30e0iPe0 = d3

0e0jPd0 =d30giPd0 = d3

0lP2e0 = d3

0mP 2d0 = d20e

20iPd0 = d2

0e0gP 2j =d20e0kP 2e0 = d2

0e0lP2d0 = d2

0g2P 2i = d2

0gjP 2e0 = d20gkP 2d0 =

d20gPe0Pj = d2

0kPe20 = d2

0lPd0Pe0 = d20mPd2

0 = d0e30P

2j =d0e

20gP 2i = d0e

20jP

2e0 = d0e20kP 2d0 = d0e

20Pe0Pj =

d0e0giP 2e0 = d0e0gjP 2d0 = d0e0gPd0Pj = d0e0jPe20 =

d0e0kPd0Pe0 = d0e0lPd20 = d0e0mP 3e0 = d0g

2iP 2d0 =d0giPe2

0 = d0gjPd0Pe0 = d0gkPd20 = d0glP 3e0 = d0gmP 3d0 =

d0rP3u = d0i

2Pu = d0mPe0P2e0 = e4

0P2i = e3

0iP2e0 =

e30jP

2d0 = e30Pd0Pj = e2

0giP 2d0 = e20iPe2

0 = e20jPd0Pe0 =

e20kPd2

0 = e20lP

3e0 = e20mP 3d0 = e0g

2P 3j = e0giPd0Pe0 =e0gjPd2

0 = e0gkP 3e0 = e0glP 3d0 = e0lP e0P2e0 = e0mPd0P

2e0 =e0mPe0P

2d0 = g2iPd20 = g2jP 3e0 = g2kP 3d0 = g2Pe0P

2j =g2PjP 2e0 = gkPe0P

2e0 = glPd0P2e0 = glPe0P

2d0 =gmPd0P

2d0 = rPd0P2u = ruP 3d0 = rP 2d0Pu = i2Pd0u =

ijP 2v = ikP 2u = ivP 2j = iwP 2i = iP jPv = j2P 2u = juP 2j =jvP 2i = jP jPu = kuP 2i = lP e3

0 = mPd0Pe20 = uPj2 = zP 3v


Stem 1086 (10) x6,89

(01) h1h4g3 = h1h6g2 = h3h6e1

7 (1) h0x6,89

9 (1) h3x8,93

10 (10) h1x9,102 = h2x9,99 = h6w

(01) h0h3x8,93 = g2A′′

(11) h23x8,80

11 (10) x11,91

(01) h20h3x8,93 = h0h

23x8,80 = h0g2A

′′ = h2g2A′ = h3f1A

′ = px7,53 =xx6,47

13 (1) h1x12,85 = h4x12,60 = h6d20e0 = h6gPe0

14 (1) x14,82

15 (10) e0x11,61

(01) x15,74

16 (100) e0rA′ = e0rA = g2G21 = gnQ2 = grD2 = lx9,51 = x7,34w =

x7,40v = Nx8,33

(010) h0e0x11,61 = h2d0x11,61 = f0x12,55 = B2B4

(001) h0x15,74 = h2x15,68 = h6iPd0

17 (100) x17,76

(010) h20e0x11,61 = h0h2d0x11,61 = h0f0x12,55 = h0B2B4 = h1d0x12,60 =

h1e0x12,55 = h22x15,65 = h5x16,33 = B1x10,27 = B1x10,28

(001) h20x15,74 = h0h2x15,68 = h0h6iPd0 = h2h6P

2j = h6Ph2Pj =h6jP

2h2

18 (1) h0x17,76

19 (10) h1x18,72 = d0x15,56

(01) h20x17,76

(11) h3x18,63

20 (10) gx16,48

(01) h30x17,76 = h0h3x18,63 = ix13,46 = R2

1

21 (10) d20gB4 = d0e

20B4 = d0kB23 = d0lx10,27 = d0lx10,28 = d0mB21 =

e0gx13,35 = e0jB23 = e0kx10,27 = e0kx10,28 = e0lB21 = e0mQ1 =g2P 2D1 = giB23 = gjx10,27 = gjx10,28 = gkB21 = glQ1 = gmx′

(01) h40x17,76 = h2

0h3x18,63 = h0ix13,46 = h0R21

22 (10) h21x

′2 = h1P2h1x12,55 = Ph2

1x12,55 = Ph1B1x′ = qx16,32 = uW1 =

X1Pu

(01) h50x17,76 = h3

0h3x18,63 = h20ix13,46 = h2

0R21

(11) X1Q

23 (1) d0x19,49 = ix16,42 = jx16,38 = kx16,35 = lx16,32 = Pe0x15,41

continued



0g4 = d2

0gr2 = d20mw = d0e

20g

3 = d0e20r

2 = d0e0lw = d0e0mv =d0gkw = d0glv = d0gmu = d0rkm = d0rl

2 = e40g

2 = e20kw =

e20lv = e2

0mu = e0grz = e0gjw = e0gkv = e0glu = e0rjm =e0rkl = g2iw = g2jv = g2ku = grim = grjl = grk2 = ru2 = lmz

(01) d20x16,37 = d0e0x16,33 = d0rPQ1 = d0ix13,35 = d0jP

2D1 =d0kR2 = d0B4Pj = d0zx′ = e0iP

2D1 = e0jR2 = giR2 =rPd0Q1 = rPe0x

′ = i2x10,27 = i2x10,28 = ijB21 = ikQ1 = ilx′ =iPe0B4 = j2Q1 = jkx′ = jPd0B4 = mPR2

26 (1) d0x22,39

27 (10) d40e0m = d4

0gl = d30e

20l = d3

0e0gk = d30g

2j = d20e

30k = d2

0e20gj =

d20e0g

2i = d20gmPe0 = d2

0rPv = d20uz = d0e

40j = d0e

30gi =

d0e20mPe0 = d0e0glPe0 = d0e0gmPd0 = d0e0rPu = d0g

3Pj =d0g

2kPe0 = d0g2lPd0 = d0r

2Pj = d0riz = d0rPd0v = d0rPe0u =d0ijw = d0ikv = d0ilu = d0j

2v = d0jku = e50i = e3

0lP e0 =e30mPd0 = e2

0g2Pj = e2

0gkPe0 = e20glPd0 = e0g

2jPe0 =e0g

2kPd0 = e0rPd0u = e0i2w = e0ijv = e0iku = e0j

2u =e0zPv = g3iPe0 = g3jPd0 = g2mP 2e0 = grP 2v = gi2v = giju =gzPu = r2iPe0 = r2jPd0 = ri2l = rijk = rj3 = rwP 2e0 =imPv = jlPv = jmPu = jz2 = k2Pv = klPu = kwPj = lvP j =muPj = Pd0wz = Pe0vz

(01) x′P 2u

(11) ux18,20

continued



0P3Q1 = d0Pd0P

2Q1 = d0x′P 3e0 = d0Q1 P 3d0 =

d0P2d0PQ1 = e0x

′P 3d0 = gP 4Q1 = Pd20PQ1 = Pd0x

′P 2e0 =Pd0Q1 P 2d0 = Pe0x

′P 2d0 = B21P4e0 = x10,27P

4d0 = x10,28P4d0

(01) d40rPd0 = d4

0ik = d40j

2 = d30e0ij = d3

0gi2 = d30lP j = d3

0Pe0z =d20e

20i

2 = d20e0rP

2e0 = d20e0kPj = d2

0e0Pd0z = d20grP 2d0 =

d20gjPj = d2

0rPe20 = d2

0ilPe0 = d20imPd0 = d2

0jkPe0 = d20jlPd0 =

d20k

2Pd0 = d0e20rP

2d0 = d0e20jP j = d0e0giP j = d0e0rPd0Pe0 =

d0e0ikPe0 = d0e0ilPd0 = d0e0j2Pe0 = d0e0jkPd0 = d0e0mP 2j =

d0grPd20 = d0gijPe0 = d0gikPd0 = d0gj2Pd0 = d0glP 2j =

d0gmP 2i = d0gzP 2e0 = d0jmP 2e0 = d0klP 2e0 = d0kmP 2d0 =d0l

2P 2d0 = d0mPe0Pj = d0uP 2u = d0Pu2 = e30iP j = e2

0rPd20 =

e20ijPe0 = e2

0ikPd0 = e20j

2Pd0 = e20lP

2j = e20mP 2i = e2

0zP 2e0 =e0grP 3e0 = e0gi2Pe0 = e0gijPd0 = e0gkP 2j = e0glP 2i =e0gzP 2d0 = e0imP 2e0 = e0jlP

2e0 = e0jmP 2d0 = e0k2P 2e0 =

e0klP 2d0 = e0lP e0Pj = e0mPd0Pj = e0Pe20z = g2rP 3d0 =

g2i2Pd0 = g2jP 2j = g2kP 2i = g2Pj2 = grPe0P2e0 = gilP 2e0 =

gimP 2d0 = gjkP 2e0 = gjlP 2d0 = gk2P 2d0 = gkPe0Pj =glPd0Pj = gPd0Pe0z = riP 2u = ruP 2i = i3u = imPe2

0 =jlPe2

0 = jmPd0Pe0 = k2Pe20 = klPd0Pe0 = kmPd2

0 = l2Pd20 =

lmP 3e0 = m2P 3d0 = Pd0uPu = u2P 2d0 = vP 3v = wP 3u =PvP 2v

(11) d0Pe0x18,20 = e0Pd0x18,20

31 (1) h0d20P

3Q1 = h0d0Pd0P2Q1 = h0d0Pe0x18,20 = h0d0x

′P 3e0 =h0d0Q1 P 3d0 = h0d0P

2d0PQ1 = h0e0Pd0x18,20 = h0e0x′P 3d0 =

h0gP 4Q1 = h0Pd20PQ1 = h0Pd0x

′P 2e0 = h0Pd0Q1 P 2d0 =h0Pe0x

′P 2d0 = h0B21P4e0 = h0x10,27P

4d0 = h0x10,28P4d0 =

h2d0Pd0x18,20 = h2d0x′P 3d0 = h2e0P

4Q1 = h2gP 4x′ =h2Pd0x

′P 2d0 = h2Pe0P3Q1 = h2Q1 P 4e0 = h2B21P

4d0 =h2P

2e0P2Q1 = h2PQ1 P 3e0 = d2

0Ph2x18,20 = d20x

′P 3h2 =d0Ph2x

′P 2d0 = d0B2P4d0 = d0Pd0P

2h2x′ = d0B21P

4h2 =e0Ph2P

3Q1 = e0P2h2P

2Q1 = e0Q1 P 4h2 = e0P3h2PQ1 =

gP 2h2x18,20 = gx′P 4h2 = Ph2Pd20x

′ = Ph2Pe0P2Q1 =

Ph2Q1 P 3e0 = Ph2B21P3d0 = Ph2P

2e0PQ1 = Pc0P2x16,32 =

B2Pd0P3d0 = B2P

2d20 = Pd0B21P

3h2 = Pe0P2h2PQ1 =

Pe0Q1 P 3h2 = P 2h2Q1 P 2e0 = P 2h2B21P2d0 = B23P

5h2 =P 3c0x16,32

32 (1) P 4x16,32


Stem 1095 (1) D11

8 (1) h6B1

9 (10) h6N

(01) h23x7,79

(11) h4x8,80

10 (10) x10,100

(01) h0h23x7,79 = h0h4x8,80 = h1h3x8,93 = h2g2H1 = h3c2A

′ =h3f1H1 = px6,53 = e1x6,47

12 (10) x12,86

(01) h6d0l = h6e0k = h6gj

13 (1) x13,87

14 (01) x14,84

(11) y14,83

15 (100) h1x14,82 = h6i2 = f0x11,61

(010) h0y14,83

(001) h0x14,84

(101) h2x14,79

16 (1) h20x14,84 = h0h2x14,79 = h1x15,74 = h4x15,56

17 (10) x17,79

(01) x17,80

18 (10) h0x17,79

(01) h0x17,80

19 (100) rx13,42

(010) h20x17,79

(001) h20x17,80

20 (0011) h3x19,58

(0100) d0rB23 = d0mB4 = e0rx10,27 = e0rx10,28 = e0lB4 = grB21 =gkB4

(0010) h30x17,79

(0001) h30x17,80

(1001) x′Q1

21 (100) h0x′Q1 = h2x

′2 = P 2h2x12,55

(010) h0h3x19,58 = iP 3h25

(110) c0x18,63

(001) h40x17,80

(011) h40x17,79

continued


Stem 109 continued22 (100) rx16,35 = jx15,41

(010) h20h3x19,58 = h2

0x′Q1 = h0h2x

′2 = h0iP3h2

5 = h0P2h2x12,55

(110) d0x18,57 = e0x18,55 = gx18,50

(001) h50x17,80

(011) h50x17,79

23 (0011) h60x17,79 = h4x22,39 = x10,27Q

(1000) d0g3m = d0grw = d0r

2m = e20g

2m = e20rw = e0g

3l = e0grv =e0r

2l = g4k = g2ru = gr2k = kmw = l2w = lmv = m2u

(0100) d0rR2 = d0uQ1 = d0vx′ = kx16,37 = lx16,33 = Pd0x15,47 =wPQ1 = zP 2D1 = B21Pv = x10,27Pu

(0010) h30h3x19,58 = h3

0x′Q1 = h2

0h2x′2 = h2

0iP3h2

5 = h20P

2h2x12,55 =

h0rx16,35 = h0jx15,41 = h31x

′2 = h21P

2h1x12,55 = h1Ph21x12,55 =

h1Ph1B1x′ = h1qx16,32 = h1uW1 = h1X1Q = h1X1Pu =

h2rx16,32 = h2ix15,41 = h23x21,43 = Ph1uX1 = xP 2Q1 = GP 2u =

x6,53P4h1 = B2

1P 2h1 = Pe0x15,42 = x10,28Q = Px6,53P3h1

(0110) e0ux′ = riQ1 = rjx′ = ijB4 = Pe0x15,43 = x10,28Pu

(0001) h60x17,80

24 (1) h70x17,79 = h7

0x17,80 = h0h4x22,39 = h0x10,27Q

25 (10) d0Px17,50 = Pd0x17,50

(01) h80x17,79 = h8

0x17,80 = h20h4x22,39 = h2

0x10,27Q

26 (010) d40x

′ = d20e0PQ1 = d2

0Pd0B21 = d20Pe0Q1 = d0e0Pd0Q1 =

d0e0Pe0x′ = d0gPd0x

′ = d0x10,27P2e0 = d0x10,28P

2e0 =d0B23P

2d0 = e20Pd0x

′ = e0gP 2Q1 = e0B21P2e0 =

e0x10,27P2d0 = e0x10,28P

2d0 = gPe0PQ1 = gQ1 P 2e0 =gB21P

2d0 = Pd20B23 = Pd0Pe0x10,27 = Pd0Pe0x10,28 =

Pe20B21 = uR1

(001) h90x17,79 = h9

0x17,80 = h30h4x22,39 = h3

0x10,27Q

(101) d30e0gr = d3

0lm = d20e

30r = d2

0e0km = d20e0l

2 = d20g

2z = d20gjm =

d20gkl = d2

0uv = d0e20gz = d0e

20jm = d0e

20kl = d0e0gim =

d0e0gjl = d0e0gk2 = d0e0u2 = d0g

2rPe0 = d0g2il = d0g

2jk =d0riv = d0rju = d0m

2Pe0 = d0wPv = e40z = e3

0im = e30jl =

e30k

2 = e20grPe0 = e2

0gil = e20gjk = e0g

2rPd0 = e0g2ik = e0g

2j2 =e0riu = e0lmPe0 = e0m

2Pd0 = e0vPv = e0wPu = g3ij =g2mPj = gkmPe0 = gl2Pe0 = glmPd0 = guPv = gvPu = r2ij =rkPv = rlPu = rwPj = iwz = jvz = kuz = Pd0vw = Pe0uw =Pe0v

2

(111) g2x18,20

27 (1) h100 x17,79 = h10

0 x17,80 = h40h4x22,39 = h4

0x10,27Q = h4Q2

continued


Stem 109 continued28 (010) h1ux18,20 = h1x

′P 2u = Ph1x′Q = Ph1x

′Pu = B1P3u =

P 2h1ux′ = P 3h1x15,42 = P 3h1x15,43

(001) h110 x17,79 = h11

0 x17,80 = h50h4x22,39 = h5

0x10,27Q = h0h4Q2

(101) d0P2x16,35 = Pd0Px16,35 = P 2d0x16,35

(111) e0P2x16,32 = P 2e0x16,32

29 (100) d0iP2Q1 = d0x

′P 2j = d0Q1 P 2i = e0x′P 2i = iPd0PQ1 =

ix′P 2e0 = iQ1 P 2d0 = jx′P 2d0 = kP 3Q1 = Pd0x′Pj =

B4P4e0 = B21P

3j = x13,35P3d0

(010) d50u = d4

0ri = d30e0Pv = d3

0gPu = d30jz = d3

0Pd0w = d30Pe0v =

d20e

20Pu = d2

0e0rPj = d20e0iz = d2

0e0Pd0v = d20e0Pe0u =

d20gPd0u = d2

0rjPe0 = d20rkPd0 = d2

0i2m = d2

0ijl = d20ik

2 =d20j

2k = d0e20Pd0u = d0e0gP 2v = d0e0riPe0 = d0e0rjPd0 =

d0e0i2l = d0e0ijk = d0e0j

3 = d0e0wP 2e0 = d0g2P 2u =

d0griPd0 = d0gi2k = d0gij2 = d0gPe0Pv = d0gvP 2e0 =d0gwP 2d0 = d0gzPj = d0rlP

2e0 = d0rmP 2d0 = d0jmPj =d0klP j = d0kPe0z = d0lPd0z = d0Pe2

0w = e30P

2v = e20gP 2u =

e20riPd0 = e2

0i2k = e2

0ij2 = e2

0Pe0Pv = e20vP 2e0 = e2

0wP 2d0 =e20zPj = e0grP 2j = e0gi2j = e0gPd0Pv = e0gPe0Pu =

e0guP 2e0 = e0gvP 2d0 = e0rkP 2e0 = e0rlP2d0 = e0imPj =

e0jlP j = e0jPe0z = e0k2Pj = e0kPd0z = e0Pd0Pe0w =

e0Pe20v = g2rP 2i = g2i3 = g2Pd0Pu = g2uP 2d0 = grjP 2e0 =

grkP 2d0 = grPe0Pj = gilP j = giPe0z = gjkPj = gjPd0z =gPd2

0w = gPd0Pe0v = gPe20u = rkPe2

0 = rlPd0Pe0 = rmPd20 =

ijmPe0 = iklPe0 = ikmPd0 = il2Pd0 = iuPu = j2lP e0 =j2mPd0 = jk2Pe0 = jklPd0 = k3Pd0 = lmP 2j = m2P 2i =mzP 2e0

(110) d0jx18,20 = e0ix18,20

(001) h120 x17,79 = h12

0 x17,80 = h60h4x22,39 = h6

0x10,27Q = h20h4Q

2 =h0d0P

2x16,35 = h0e0P2x16,32 = h0Pd0Px16,35 = h0P

2d0x16,35 =h0P

2e0x16,32 = h2d0P2x16,32 = h2P

2d0x16,32 = d0P2h2x16,32 =

Ph2Pd0x16,32 = P 3h2x16,38 = x13,34P3d0

(101) d20P

2R2 = d0Pd0PR2 = d0Pe0R1 = d0P2d0R2 = e0Pd0R1 =

gP 3R2 = Pd20R2 = P 2D1P

3e0

continued


Stem 109 continued30 (10) h0d0iP

2Q1 = h0d0jx18,20 = h0d0x′P 2j = h0d0Q1 P 2i =

h0e0ix18,20 = h0e0x′P 2i = h0iPd0PQ1 = h0ix

′P 2e0 =h0iQ1 P 2d0 = h0jx

′P 2d0 = h0kP 3Q1 = h0Pd0x′Pj =

h0B4P4e0 = h0B21P

3j = h0x13,35P3d0 = h2d0ix18,20 =

h2d0x′P 2i = h2ix

′P 2d0 = h2jP3Q1 = h2B4P

4d0 = h2Q1 P 3j =h2PjP 2Q1 = h2PQ1 P 2j = d0iP

2h2x′ = d0B4P

4h2 =f0Pd0x18,20 = f0x

′P 3d0 = Ph2iPd0x′ = Ph2jP

2Q1 =Ph2kx18,20 = Ph2B4P

3d0 = Ph2Q1 P 2j = Ph2B21P2i =

Ph2PjPQ1 = iB2P3d0 = iB21P

3h2 = jP 2h2PQ1 = jQ1 P 3h2 =kx′P 3h2 = B2Pd0P

2i = Pd0B4P3h2 = P 2h2B4P

2d0 =P 2h2Q1 Pj

(01) h130 x17,79 = h13

0 x17,80 = h70h4x22,39 = h7

0x10,27Q = h30h4Q

2 =h2

0d0P2x16,35 = h2

0e0P2x16,32 = h2

0Pd0Px16,35 = h20P

2d0x16,35 =h2

0P2e0x16,32 = h0h2d0P

2x16,32 = h0h2P2d0x16,32 =

h0d0P2h2x16,32 = h0Ph2Pd0x16,32 = h0P

3h2x16,38 =h0x13,34P

3d0 = h22P

3x16,35 = h2Ph2P2x16,35 = h2P

2h2Px16,35 =h2P

3h2x16,35 = Ph22Px16,35 = Ph2P

2h2x16,35

(11) h0d20P

2R2 = h0d0Pd0PR2 = h0d0Pe0R1 = h0d0P2d0R2 =

h0e0Pd0R1 = h0gP 3R2 = h0Pd20R2 = h0P

2D1P3e0 =

h2d0Pd0R1 = h2e0P3R2 = h2gx25,24 = h2Pe0P

2R2 =h2P

2e0PR2 = h2R2 P 3e0 = h2P2D1P

3d0 = d20Ph2R1 =

d0R1P3e0 = d0P

3h2P2D1 = e0Ph2P

2R2 = e0P2h2PR2 =

e0R1P3d0 = e0P

3h2R2 = gP 2h2R1 = Ph2Pe0PR2 =Ph2P

2d0P2D1 = Ph2P

2e0R2 = Pd0P2h2P

2D1 = Pd0R1P2e0 =

Pe0P2h2R2 = Pe0R1P

2d0

31 (1) h20d

20P

2R2 = h20d0iP

2Q1 = h20d0jx18,20 = h2

0d0Pd0PR2 =h2

0d0Pe0R1 = h20d0x

′P 2j = h20d0Q1 P 2i = h2

0d0P2d0R2 =

h20e0ix18,20 = h2

0e0Pd0R1 = h20e0x

′P 2i = h20gP 3R2 =

h20iPd0PQ1 = h2

0ix′P 2e0 = h2

0iQ1 P 2d0 = h20jx

′P 2d0 =h2

0kP 3Q1 = h20Pd2

0R2 = h20Pd0x

′Pj = h20B4P

4e0 =h2

0B21P3j = h2

0P2D1P

3e0 = h20x13,35P

3d0 = h0h2d0ix18,20 =h0h2d0Pd0R1 = h0h2d0x

′P 2i = h0h2e0P3R2 = h0h2gx25,24 =

h0h2ix′P 2d0 = h0h2jP

3Q1 = h0h2Pe0P2R2 = h0h2B4P

4d0 =h0h2Q1 P 3j = h0h2PjP 2Q1 = h0h2P

2e0PR2 =h0h2R2 P 3e0 = h0h2P

2D1P3d0 = h0h2PQ1 P 2j = h0d

20Ph2R1 =

h0d0iP2h2x

′ = h0d0B4P4h2 = h0d0R1P

3e0 = h0d0P3h2P

2D1 =h0e0Ph2P

2R2 = h0e0P2h2PR2 = h0e0R1P

3d0 = h0e0P3h2R2 =

h0f0Pd0x18,20 = h0f0x′P 3d0 = h0gP 2h2R1 = h0Ph2iPd0x

′ =h0Ph2jP

2Q1 = h0Ph2kx18,20 = h0Ph2Pe0PR2 =h0Ph2B4P

3d0 = h0Ph2Q1 P 2j = (continued)


Stem 109 continued31 (1) (continued) = h0Ph2B21P

2i = h0Ph2PjPQ1 =h0Ph2P

2d0P2D1 = h0Ph2P

2e0R2 = h0iB2P3d0 =

h0iB21P3h2 = h0jP

2h2PQ1 = h0jQ1 P 3h2 = h0kx′P 3h2 =h0B2Pd0P

2i = h0Pd0P2h2P

2D1 = h0Pd0B4P3h2 =

h0Pd0R1P2e0 = h0Pe0P

2h2R2 = h0Pe0R1P2d0 =

h0P2h2B4P

2d0 = h0P2h2Q1 Pj = h1d

20P

3Q1 = h1d0Pd0P2Q1 =

h1d0Pe0x18,20 = h1d0x′P 3e0 = h1d0Q1 P 3d0 = h1d0P

2d0PQ1 =h1e0Pd0x18,20 = h1e0x

′P 3d0 = h1gP 4Q1 = h1Pd20PQ1 =

h1Pd0x′P 2e0 = h1Pd0Q1 P 2d0 = h1Pe0x

′P 2d0 = h1B21P4e0 =

h1x10,27P4d0 = h1x10,28P

4d0 = h22d0P

3R2 = h22e0x25,24 =

h22iP

3Q1 = h22Pd0P

2R2 = h22x

′P 3j = h22Pjx18,20 =

h22P

2d0PR2 = h22P

2e0R1 = h22R2 P 3d0 = h2

2PQ1 P 2i =h2d0Ph2P

2R2 = h2d0P2h2PR2 = h2d0R1P

3d0 =h2d0P

3h2R2 = h2e0P2h2R1 = h2f0P

4Q1 = h2Ph2iP2Q1 =

h2Ph2jx18,20 = h2Ph2Pd0PR2 = h2Ph2Pe0R1 =h2Ph2x

′P 2j = h2Ph2Q1 P 2i = h2Ph2P2d0R2 =

h2iP2h2PQ1 = h2iQ1 P 3h2 = h2jx

′P 3h2 = h2B2P4j =

h2Pd0P2h2R2 = h2Pd0R1P

2d0 = h2P2h2x

′Pj = h2x13,35P4h2 =

d20Ph1P

2Q1 = d20P

2h1PQ1 = d20R1P

3h2 = d20Q1 P 3h1 =

d0e0Ph1x18,20 = d0e0x′P 3h1 = d0Ph1Pd0PQ1 = d0Ph1x

′P 2e0 =d0Ph1Q1 P 2d0 = d0Ph2

2PR2 = d0Ph2P2h2R2 =

d0Ph2R1P2d0 = d0B1P

4e0 = d0Pd0P2h1Q1 = d0Pd0P

2h2R1 =d0Pe0P

2h1x′ = d0x10,27P

4h1 = d0x10,28P4h1 = e0Ph1x

′P 2d0 =e0Ph2

2R1 = e0B1P4d0 = e0Pd0P

2h1x′ = e0B21P

4h1 =f0Ph2P

3Q1 = f0P2h2P

2Q1 = f0Q1 P 4h2 = f0P3h2PQ1 =

gPh1P3Q1 = gP 2h1P

2Q1 = gR1P4h2 = gQ1 P 4h1 =

gP 3h1PQ1 = Ph1Pd20Q1 = Ph1Pd0Pe0x

′ = Ph1B21P3e0 =

Ph1x10,27P3d0 = Ph1x10,28P

3d0 = Ph22iPQ1 = Ph2

2Pd0R2 =Ph2

2x′Pj = Ph2iP

2h2Q1 = Ph2jP2h2x

′ = Ph2B2P3j =

Ph2Pd20R1 = Ph2P

3h2x13,35 = D2P6h2 = Pc0iR1 = jB2P

4h2 =B1Pd0P

3e0 = B1Pe0P3d0 = B1P

2d0P2e0 = B2P

2h2P2j =

B2PjP 3h2 = Pd0x10,27P3h1 = Pd0x10,28P

3h1 = Pe0B21P3h1 =

P 2h1B21P2e0 = P 2h1x10,27P

2d0 = P 2h1x10,28P2d0 =

P 2h22x13,35 = B5 P 5h2 = PD2P

5h2 = P 3c0x16,33


Stem 1106 (1) h2h4g3 = h2h6g2 = h3h6f1 = h2

4e2

7 (1) h0h2h4g3 = h0h2h6g2 = h0h3h6f1 = h0h24e2 = h2

3h6p = c2p′

8 (1) h3x7,90 = h4x7,79

9 (1) h1h6B1

10 (100) x10,102

(001) h2x9,102

(011) h23x8,83 = g2r1

11 (10) h1x10,100 = h4x10,73 = c1x8,75 = g2x7,40 = D1D2

(01) h0h2x9,102 = h22x9,97 = h6e0r

(11) h0h23x8,83 = h0g2r1 = pm1

13 (10) x13,88

(01) h1x12,86

14 (100) h2x13,85 = h5x13,42 = c1x11,61 = f0x10,65

(001) h1x13,87 = h6Pu

(011) h6Q

15 (10) x15,78

(01) h0h6Q

16 (1000) x16,77

(0100) x16,78

(0010) d0x12,64 = e0x12,60 = gx12,55

(0001) h20h6Q

17 (10) h0d0x12,64 = h0e0x12,60 = h0gx12,55 = h2d0x12,60 = h2e0x12,55 =h5x16,35 = h6d0P

2e0 = h6e0P2d0 = h6Pd0Pe0 = B2x10,27 =

B2x10,28 = Q2x′

(01) h30h6Q = h0x16,78

18 (1000) x18,77

(0100) x18,78

(0010) h1x17,79

(0001) h40h6Q = h2

0d0x12,64 = h20e0x12,60 = h2

0gx12,55 = h20x16,78 =

h0h2d0x12,60 = h0h2e0x12,55 = h0h5x16,35 = h0h6d0P2e0 =

h0h6e0P2d0 = h0h6Pd0Pe0 = h0B2x10,27 = h0B2x10,28 =

h0Q2x′ = h2

2d0x12,55 = h2h5x16,32 = h2h6d0P2d0 = h2h6Pd2

0 =h2Ph2x12,64 = h2B2B21 = h5d0R2 = h6d

20P

2h2 = h6d0Ph2Pd0 =h6gP 3h2 = c0x15,65 = d0B

22

19 (1000) grB4 = wB23

(0100) Px15,65

(0010) h0x18,77

(0001) h0x18,78 = h2x18,72 = d0x15,58

continued


Stem 110 continued20 (100) h0Px15,65 = h2P

2x11,61 = P 2h2x11,61

(010) h20x18,77

(001) h20x18,78 = h0h2x18,72 = h0d0x15,58 = h2

2x18,68

(101) R1Q1

21 (100) e0x17,57 = gx17,52

(010) h20Px15,65 = h0h2P

2x11,61 = h0P2h2x11,61 = h0R1Q1 =

h1x′Q1 = h2x

′R1 = Ph1Px12,60 = B1PQ1 = P 2h1x12,60

(001) h30x18,77

22 (100) g4r = g2m2 = gr3 = gw2 = rmw

(010) d20e0B23 = d2

0gx10,27 = d20gx10,28 = d0e

20x10,27 = d0e

20x10,28 =

d0e0gB21 = d0g2Q1 = e3

0B21 = e20gQ1 = e0g

2x′ = gPe0B23 =rx16,37 = ix15,47 = jx15,43 = ux13,35 = vP 2D1 = wR2 = B4Pv

(001) h40x18,77 = h4x21,43

23 (10) Ph1x18,63

(01) h50x18,77 = h0h4x21,43

24 (10) d20x16,38 = d0e0x16,35 = d0gx16,32 = e2

0x16,32 = ix17,50 =Pd0x16,48 = Pe0x16,42

(01) h60x18,77 = h2

0h4x21,43

25 (100) d20e0gw = d2

0e0rm = d20g

2v = d20grl = d0e

30w = d0e

20gv = d0e

20rl =

d0e0g2u = d0e0grk = d0g

2rj = d0gmz = d0jm2 = d0klm = d0l

3 =e40v = e3

0gu = e30rk = e2

0grj = e20mz = e0g

2ri = e0glz = e0im2 =

e0jlm = e0k2m = e0kl2 = g3Pv = g2kz = g2Pe0w = grmPe0 =

gilm = gjkm = gjl2 = gk2l = r2Pv = ruz = ivw = juw = jv2 =kuv = lu2

(010) d30P

2D1 = d20e0R2 = d2

0iB21 = d20jQ1 = d2

0kx′ = d20Pd0B4 =

d0e0iQ1 = d0e0jx′ = d0gix′ = d0lPQ1 = d0Pe0x13,35 =

d0x10,27Pj = d0x10,28Pj = e20ix

′ = e0gPR2 = e0kPQ1 =e0Pd0x13,35 = e0Pe0P

2D1 = e0B4P2e0 = e0B21Pj = g2R1 =

gjPQ1 = gPd0P2D1 = gPe0R2 = gB4P

2d0 = gQ1 Pj =iPd0B23 = iPe0x10,27 = iPe0x10,28 = jPd0x10,27 = jPd0x10,28 =jPe0B21 = kPd0B21 = kPe0Q1 = lPd0Q1 = lP e0x

′ =mPd0x

′ = Pe20B4

(001) h70x18,77 = h3

0h4x21,43

26 (1) h80x18,77 = h4

0h4x21,43

27 (01) h90x18,77 = h5

0h4x21,43

(11) iPx16,35 = Pjx16,32

continued


Stem 110 continued28 (100) zx18,20

(010) rP 3Q1 = i2PQ1 = ix′Pj = B4P3j = x13,35P

2i

(110) d50g

2 = d40e

20g = d3

0e40 = d3

0iw = d30jv = d3

0ku = d20e0g

2Pe0 =d20e0iv = d2

0e0ju = d20g

3Pd0 = d20giu = d2

0r2Pd0 = d2

0rik =d20rj

2 = d20lPv = d2

0mPu = d20z

2 = d0e30gPe0 = d0e

20g

2Pd0 =d0e

20iu = d0e0rij = d0e0kPv = d0e0lPu = d0e0wPj = d0gri2 =

d0gjPv = d0gkPu = d0gvPj = d0rlP j = d0rPe0z = d0ilz =d0jkz = d0jPe0w = d0kPd0w = d0kPe0v = d0lPd0v =d0lP e0u = d0mPd0u = e5

0Pe0 = e40gPd0 = e2

0ri2 = e2

0jPv =e20kPu = e2

0vPj = e0g3P 2e0 = e0giPv = e0gjPu = e0guPj =

e0r2P 2e0 = e0rkPj = e0rPd0z = e0ikz = e0iPe0w = e0j

2z =e0jPd0w = e0jPe0v = e0kPd0v = e0kPe0u = e0lPd0u =e0mP 2v = g4P 2d0 = g3Pe2

0 = g2iPu = gr2P 2d0 = grjPj =gijz = giPd0w = giPe0v = gjPd0v = gjPe0u = gkPd0u =glP 2v = gmP 2u = r2Pe2

0 = rilPe0 = rimPd0 = rjkPe0 =rjlPd0 = rk2Pd0 = i2km = i2l2 = ij2m = ijkl = ik3 = j3l =j2k2 = lwP 2e0 = mPe0Pv = mvP 2e0 = mwP 2d0 = mzPj

(001) h100 x18,77 = h6

0h4x21,43 = h0iPx16,35 = h0Pjx16,32 = f0P2x16,32 =

Ph2ix16,32 = P 3h2x15,41 = x13,34P2i

(011) d0iPR2 = d0jR1 = e0iR1 = iPd0R2 = kP 2R2 = P 2d0x16,37 =P 2e0x16,33 = P 2D1P

2j

29 (10) h0rP3Q1 = h0i

2PQ1 = h0ix′Pj = h0B4P

3j = h0zx18,20 =h0x13,35P

2i = h21ux18,20 = h2

1x′P 2u = h1Ph1x

′Q = h1Ph1x′Pu =

h1B1P3u = h1P

2h1ux′ = h1P3h1x15,42 = h1P

3h1x15,43 =h3P

3x16,35 = f0ix18,20 = f0x′P 2i = D3P

6h1 = Ph21ux′ =

Ph1qx18,20 = Ph1B1P2u = Ph1P

2h1x15,42 = Ph1P2h1x15,43 =

Ph2rx18,20 = Ph2i2x′ = Ph2B4P

2i = rx′P 3h2 = qx′P 3h1 =iB2P

2i = iB4P3h2 = B1P

2h1Q = B1P2h1Pu = B1uP 3h1 =

PD3P5h1 = X1P

4e0 = P 2D3P4h1

(01) h110 x18,77 = h7

0h4x21,43 = h20iPx16,35 = h2

0Pjx16,32 =h0f0P

2x16,32 = h0Ph2ix16,32 = h0P3h2x15,41 = h0x13,34P

2i =h1e0P

2x16,32 = h1P2e0x16,32 = e0P

2h1x16,32 = Ph1Pe0x16,32 =W1P

3e0

(11) h0d0iPR2 = h0d0jR1 = h0e0iR1 = h0iPd0R2 = h0kP 2R2 =h0P

2d0x16,37 = h0P2e0x16,33 = h0P

2D1P2j = h1d0P

2x16,35 =h1Pd0Px16,35 = h1P

2d0x16,35 = h2d0iR1 = h2jP2R2 =

h2PjPR2 = h2P2d0x16,33 = h2R2 P 2j = h2P

2D1P2i =

d0Ph1Px16,35 = d0P2h1x16,35 = d0P

2h2x16,33 = d0R1P2j =

e0R1P2i = f0Pd0R1 = Ph1Pd0x16,35 = Ph2jPR2 = Ph2kR1 =

Ph2Pd0x16,33 = Ph2PjR2 = Pc0x22,39 = iP 2h2P2D1 =

iR1P2e0 = jP 2h2R2 = jR1P

2d0 = Pd0R1Pj = P 3h1x16,42


Stem 1115 (1) h3h6c2 = h5e2

8 (1) h6B2

9 (1000) x9,107

(0010) x9,109

(0001) h0h6B2

(0101) h23x7,81 = h4x8,83 = g2n1 = g2Q3

10 (10) h0x9,107

(01) h20h6B2 = h0x9,109 = h2

1h6B1

(11) h3x9,97

11 (10) h1x10,102

(01) h20x9,107 = h0h3x9,97

12 (10) h2x11,91 = f0x8,78 = gx8,75 = CA′ = CA

(01) h30x9,107 = h2

0h3x9,97 = h23x10,76

13 (1) h40x9,107 = h3

0h3x9,97 = h0h23x10,76 = h3x12,80 = h4x12,64 =

h6d20g = h6d0e

20 = g2x9,40 = xx8,51

14 (10) d0x10,76

(01) h1x13,88

15 (1000) gx11,61

(0100) x15,81

(0010) x15,82

(0001) h0d0x10,76 = h21x13,87 = h1h6Q = h1h6Pu = h2x14,82 = h5x14,42 =

h6Ph1u = c0x12,78

16 (0011) h2x15,74 = h6d0Pj = h6iPe0 = h6jPd0 = D2x′

(1000) grA′ = grA = mx9,51 = x7,40w

(0100) h1x15,78

(0010) h0gx11,61 = h2e0x11,61 = f0x12,60

(0001) h0x15,81 = h0x15,82 = h4x15,58

17 (010) h20gx11,61 = h0h2e0x11,61 = h0f0x12,60 = h1d0x12,64 =

h1e0x12,60 = h1gx12,55 = h22d0x11,61 = h2f0x12,55 = h2B2B4 =

h5x16,37 = B1B23

(110) h1x16,77

(001) h20x15,81 = h2

0x15,82 = h0h4x15,58

(011) h0h2x15,74 = h0h6d0Pj = h0h6iPe0 = h0h6jPd0 = h0D2x′ =

h22x15,68 = h2h6iPd0 = h6d0Ph2i = h6f0P

2d0 = h6kP 2h2 = Q2R1

18 (1) h2x17,76

19 (10) h21x17,79 = h3x18,68 = Ph1x14,74

(01) h0h2x17,76 = h1x18,78 = e0x15,56

continued


Stem 111 continued21 (10) g4n = g2tm = gnr2 = gNw = nmw = rtw = rmN

(01) d0e0gB4 = d0lB23 = d0mx10,27 = d0mx10,28 = e30B4 = e0kB23 =

e0lx10,27 = e0lx10,28 = e0mB21 = g2x13,35 = gjB23 = gkx10,27 =gkx10,28 = glB21 = gmQ1

23 (1) d20x15,41 = e0x19,49 = ix16,48 = jx16,42 = kx16,38 = lx16,35 =

mx16,32

24 (100) d0e0g4 = d0e0gr2 = d0e0mw = d0glw = d0gmv = d0rlm = e3

0g3 =

e30r

2 = e20lw = e2

0mv = e0gkw = e0glv = e0gmu = e0rkm =e0rl

2 = g2rz = g2jw = g2kv = g2lu = grjm = grkl = ruv = m2z

(010) d20rx

′ = d20iB4 = d0e0x16,37 = d0gx16,33 = d0jx13,35 = d0kP 2D1 =

d0lR2 = d0zQ1 = e20x16,33 = e0rPQ1 = e0ix13,35 = e0jP

2D1 =e0kR2 = e0B4Pj = e0zx′ = giP 2D1 = gjR2 = rPd0B21 =rPe0Q1 = i2B23 = ijx10,27 = ijx10,28 = ikB21 = ilQ1 = imx′ =j2B21 = jkQ1 = jlx′ = jPe0B4 = k2x′ = kPd0B4

(001) h1Ph1x18,63 = P 2h1x15,56

26 (1) d0Px18,50 = e0x22,39 = Pd0x18,50

27 (10) d40gm = d3

0e20m = d3

0e0gl = d30g

2k = d30ru = d2

0e30l = d2

0e20gk =

d20e0g

2j = d20g

3i = d20r

2i = d20vz = d0e

40k = d0e

30gj = d0e

20g

2i =d0e0gmPe0 = d0e0rPv = d0e0uz = d0g

2lP e0 = d0g2mPd0 =

d0grPu = d0rjz = d0rPd0w = d0rPe0v = d0ikw = d0ilv =d0imu = d0j

2w = d0jkv = d0jlu = d0k2u = e5

0j = e40gi =

e30mPe0 = e2

0glPe0 = e20gmPd0 = e2

0rPu = e0g3Pj = e0g

2kPe0 =e0g

2lPd0 = e0r2Pj = e0riz = e0rPd0v = e0rPe0u = e0ijw =

e0ikv = e0ilu = e0j2v = e0jku = g3jPe0 = g3kPd0 = grPd0u =

gi2w = gijv = giku = gj2u = gzPv = r2jPe0 = r2kPd0 =ri2m = rijl = rik2 = rj2k = jmPv = klPv = kmPu = kz2 =l2Pu = lwPj = mvPj = Pe0wz

(01) rP 2R2 = i2R2 = uP 2Q1 = zR1 = x′P 2v = Q1 P 2u =Pjx16,33 = PuPQ1

(11) vx18,20

29 (1) P 3x17,50


Stem 1127 (1) x7,97

8 (100) x8,105

(001) h0x7,97

(111) h3x7,92 = h4x7,81 = g2d2

10 (10) x10,107

(01) h1x9,107 = h3x9,99

11 (10) h4x10,76

(01) h0x10,107 = h2x10,100 = c1x8,78 = e0x7,79 = H1C

12 (1) h0h4x10,76 = h21x10,102 = h6d0m = h6e0l = h6gk = c0x9,97 =

g2G21

13 (10) x13,91

(01) h2x12,86

14 (10) gx10,65

(01) x14,91

15 (1000) gnA′ = gnA = gH1r = tx9,51 = mx8,57 = x7,40N

(0100) h2y14,83

(0010) h1d0x10,76 = h6ij = c0x12,80

(0001) h0x14,91

(0101) h2x14,84

16 (0011) h0h2y14,83 = gx12,58 = d1x12,44 = D2R1

(0100) Px12,80

(0010) h0h2x14,84 = h1x15,82 = h22x14,79

(0001) h20x14,91 = h1x15,81

(1001) h3x15,68

17 (10) h0h3x15,68

(01) h0Px12,80 = h21x15,78 = Ph1x12,78

18 (100) grx8,33 = gmQ2 = wx9,39

(010) x18,83

(001) h20h3x15,68 = h2

1x16,77 = d1x14,42 = qx12,44

20 (01) Pd0x12,55 = x′B21 = Q12

(11) e0rB23 = e0mB4 = grx10,27 = grx10,28 = glB4

21 (1) h0Pd0x12,55 = h0x′B21 = h0Q1

2 = h2x′Q1 = c0x18,68 =

Ph2Px12,60 = B2PQ1 = P 2h2x12,60

22 (10) Px18,68

(01) d0x18,60 = e0x18,57 = gx18,55 = rx16,38 = kx15,41

continued



0x15,43 = d0rP2D1 = d0uB21 = d0vQ1 = d0wx′ = e0rR2 =

e0uQ1 = e0vx′ = gux′ = riB21 = rjQ1 = rkx′ = rPd0B4 =ikB4 = j2B4 = lx16,37 = mx16,33 = Pe0x15,47 = zx13,35 =x10,27Pv = x10,28Pv = B23Pu

(110) e0g3m = e0grw = e0r

2m = g4l = g2rv = gr2l = lmw = m2v

(001) h0Px18,68 = Ph2x18,63

24 (1) h20Px18,68 = h0Ph2x18,63

25 (10) e0Px17,50 = ix18,50 = Pe0x17,50

(01) h30Px18,68 = h2

0Ph2x18,63 = h21Ph1x18,63 = h1P

2h1x15,56 =e0x21,43 = Ph2

1x15,56

(11) d0Px17,52 = Pd0x17,52

26 (10) d30g

2r = d30m

2 = d20e

20gr = d2

0e0lm = d20gkm = d2

0gl2 = d20uw =

d20v

2 = d0e40r = d0e

20km = d0e

20l

2 = d0e0g2z = d0e0gjm =

d0e0gkl = d0e0uv = d0g2im = d0g

2jl = d0g2k2 = d0gu2 =

d0riw = d0rjv = d0rku = e30gz = e3

0jm = e30kl = e2

0gim = e20gjl =

e20gk2 = e2

0u2 = e0g

2rPe0 = e0g2il = e0g

2jk = e0riv = e0rju =e0m

2Pe0 = e0wPv = g3rPd0 = g3ik = g3j2 = griu = glmPe0 =gm2Pd0 = gvPv = gwPu = r3Pd0 = r2ik = r2j2 = rlPv =rmPu = rz2 = jwz = kvz = luz = Pd0w

2 = Pe0vw

(01) d40Q1 = d3

0e0x′ = d2

0gPQ1 = d20Pd0x10,27 = d2

0Pd0x10,28 =d20Pe0B21 = d0e

20PQ1 = d0e0Pd0B21 = d0e0Pe0Q1 =

d0gPd0Q1 = d0gPe0x′ = d0B23P

2e0 = e20Pd0Q1 = e2

0Pe0x′ =

e0gPd0x′ = e0x10,27P

2e0 = e0x10,28P2e0 = e0B23P

2d0 =g2P 2Q1 = gB21P

2e0 = gx10,27P2d0 = gx10,28P

2d0 =Pd0Pe0B23 = Pe2

0x10,27 = Pe20x10,28 = uPR2 = vR1 = PuR2

28 (1) d0Pd0x16,32 = e0P2x16,35 = gP 2x16,32 = Pe0Px16,35 =

P 2d0x16,38 = P 2e0x16,35


Stem 1137 (01) h6C

(11) h3C1

9 (1) x9,111

10 (1) x10,109

11 (10) h6gr

(01) h21x9,107 = h1h3x9,99 = h2

3x9,86 = c1x8,80 = e1x7,53

(11) h1x10,107 = h22x9,102 = f0x7,79 = D1A

′ = D1A

12 (1) gx8,78

13 (10) x13,93

(01) Px9,99

14 (10) h2x13,88

(01) h0Px9,99 = h1x13,91 = h6Pv = Ph1x9,97

15 (01) h1gx10,65 = h22x13,85 = h2h5x13,42 = h2c1x11,61 = h2f0x10,65 =

h4x14,67

(11) h3x14,79

16 (01) h0h3x14,79

(11) e0x12,64 = gx12,60

17 (0011) Q2Q1

(1011) h2x16,77

(0100) e0gx9,51 = e0rx7,40 = e0A′m = e0Am = gnx8,33 = grx7,34 =

gtQ2 = gD2m = gA′l = gAl = Nx9,39 = G21 w

(0010) h0e0x12,64 = h0gx12,60 = h1Px12,80 = h2d0x12,64 = h2e0x12,60 =h2gx12,55 = h5x16,38 = h6d

20Pd0 = h6e0P

2e0 = h6gP 2d0 =h6Pe2

0 = Ph1x12,80 = Pc0x10,76 = B2B23 = B3x′

(1010) h2x16,78

(0001) h20h3x14,79 = h1h3x15,68

18 (10) x18,85

(01) P 2x10,76

19 (1000) Pd0x11,61

(0100) h1x18,83

(0010) h0x18,85 = h2x18,78 = e0x15,58

(0001) h0P2x10,76

(1001) ix12,55 = B4x′

20 (0011) h20x18,85 = h0h2x18,78 = h0e0x15,58 = h2

2x18,72 = h2d0x15,58

(1000) h6P3j

(0100) B2R2 = R1B21

(0111) h0Pd0x11,61 = h2Px15,65 = Ph2x15,65

(0110) h0ix12,55 = h0B4x′

(0001) h20P

2x10,76

continued


Stem 113 continued21 (100) gx17,57

(010) h20Pd0x11,61 = h0h2Px15,65 = h0Ph2x15,65 = h0B2R2 =

h0R1B21 = h1Pd0x12,55 = h1x′B21 = h1Q1

2 = h22P

2x11,61 =h2P

2h2x11,61 = h2R1Q1 = d0Ph1x12,55 = d0B1x′ = Ph2

2x11,61 =P 2h1x12,64

(001) h30P

2x10,76 = h3x′2 = xx16,32

(011) h20ix12,55 = h2

0B4x′

(111) rx15,41

22 (100) x22,71

(010) d20gB23 = d0e

20B23 = d0e0gx10,27 = d0e0gx10,28 = d0g

2B21 =d0uB4 = e3

0x10,27 = e30x10,28 = e2

0gB21 = e0g2Q1 = g3x′ =

jx15,47 = kx15,43 = vx13,35 = wP 2D1

(001) h40P

2x10,76 = h30ix12,55 = h3

0B4x′ = h0h3x

′2 = h0xx16,32 =h0rx15,41 = g2x18,20 = xix′

(011) r2x′ = riB4

23 (10) h0x22,71

(01) h50P

2x10,76 = h40ix12,55 = h4

0B4x′ = h2

0h3x′2 = h2

0xx16,32 =h2

0rx15,41 = h0g2x18,20 = h0xix′ = h0r2x′ = h0riB4 = h3rx16,32 =

h3ix15,41 = i2x9,40 = x8,51P2i

(11) h1Px18,68 = Ph1x18,68

24 (10) d20x16,42 = d0e0x16,38 = d0gx16,35 = e2

0x16,35 = e0gx16,32 =ix17,52 = jx17,50 = Pe0x16,48

(01) h60P

2x10,76 = h50ix12,55 = h5

0B4x′ = h3

0h3x′2 = h3

0xx16,32 =h3

0rx15,41 = h20g2x18,20 = h2

0xix′ = h20r

2x′ = h20riB4 = h2

0x22,71 =h0h3rx16,32 = h0h3ix15,41 = h0i

2x9,40 = h0x8,51P2i = h3xx18,20 =

h3rix′ = h3i

2B4 = Ph2x19,58

25 (10) d20g

2w = d20grm = d0e

20gw = d0e

20rm = d0e0g

2v = d0e0grl =d0g

3u = d0g2rk = d0r

2u = d0km2 = d0l2m = e4

0w = e30gv =

e30rl = e2

0g2u = e2

0grk = e0g2rj = e0gmz = e0jm

2 = e0klm =e0l

3 = g3ri = g2lz = gim2 = gjlm = gk2m = gkl2 = r3i = rvz =iw2 = jvw = kuw = kv2 = luv = mu2

(01) d30x13,35 = d2

0e0P2D1 = d2

0gR2 = d20ix10,27 = d2

0ix10,28 =d20jB21 = d2

0kQ1 = d20lx

′ = d20Pe0B4 = d0e

20R2 = d0e0iB21 =

d0e0jQ1 = d0e0kx′ = d0e0Pd0B4 = d0giQ1 = d0gjx′ =d0mPQ1 = d0B23Pj = e2

0iQ1 = e20jx

′ = e0gix′ =e0lPQ1 = e0Pe0x13,35 = e0x10,27Pj = e0x10,28Pj = g2PR2 =gkPQ1 = gPd0x13,35 = gPe0P

2D1 = gB4P2e0 = gB21Pj =

iPe0B23 = jPd0B23 = jPe0x10,27 = jPe0x10,28 = kPd0x10,27 =kPd0x10,28 = kPe0B21 = lPd0B21 = lP e0Q1 = mPd0Q1 =mPe0x

′

27 (1) d0ix16,32 = jPx16,35 = Pjx16,35 = P 2d0x15,41


Stem 1146 (1) G1

9 (10) x9,112

(11) h2h6B2

10 (10) h2x9,107 = h3x9,102 = h6gn

(01) h1x9,111 = h2x9,109 = c1x7,79 = D1H1

(11) h4x9,86

12 (10) gx8,80

(01) x12,93

14 (100) Q22

(010) e0x10,76

(001) h1Px9,99 = D3x′ = Ph1x9,99

15 (10) x15,90

(01) h0Q22

16 (10) h2gx11,61 = h5x15,41 = h6d20i = h6e0Pj = h6jPe0 = h6kPd0 =

f0x12,64 = D2Q1 = Ax′

(01) h0x15,90 = h2x15,82

17 (1) h0h2gx11,61 = h0h5x15,41 = h0h6d20i = h0h6e0Pj = h0h6jPe0 =

h0h6kPd0 = h0f0x12,64 = h0D2Q1 = h0Ax′ = h1e0x12,64 =h1gx12,60 = h2

2e0x11,61 = h22x15,74 = h2h6d0Pj = h2h6iPe0 =

h2h6jPd0 = h2f0x12,60 = h2D2x′ = h6d0Ph2j = h6e0Ph2i =

h6f0P2e0 = h6lP

2h2 = c0x14,79 = Ph2x12,78 = B2B5 =B2PD2 = B3R1

18 (100) x18,87

(010) ix11,61

(011) Px14,79

19 (0011) h0ix11,61

(1000) h1P2x10,76 = P 2h1x10,76

(1011) X1x′

(0010) h0Px14,79

(0110) h1x18,85 = h22x17,76 = f0x15,58 = gx15,56

(0101) h0x18,87 = B4R1

20 (010) h20Px14,79 = h2

1x18,83 = Ph1x15,68

(101) gx16,54 = nx15,41 = rx14,46 = mx13,42

(011) h20ix11,61 = h2

0x18,87 = h0B4R1 = h0X1x′ = h3P

2x11,61

21 (10) d0g2B4 = d0mB23 = e2

0gB4 = e0lB23 = e0mx10,27 = e0mx10,28 =gkB23 = glx10,27 = glx10,28 = gmB21 = rx15,43

(01) h30ix11,61 = h3

0x18,87 = h20B4R1 = h2

0X1x′ = h0h3P

2x11,61 =h3x

′R1 = g2R1 = xx16,33 = rx15,42

continued



0ix11,61 = h40x18,87 = h3

0B4R1 = h30X1x

′ = h20h3P

2x11,61 =h0h3x

′R1 = h0g2R1 = h0xx16,33 = h0rx15,42 = xiR1 = r2R1 =riX1 = yx16,32 = i2G21 = x9,40Q

23 (01) h50ix11,61 = h5

0x18,87 = h40B4R1 = h4

0X1x′ = h3

0h3P2x11,61 =

h20h3x

′R1 = h20g2R1 = h2

0xx16,33 = h20rx15,42 = h0xiR1 =

h0r2R1 = h0riX1 = h0yx16,32 = h0i

2G21 = h0x9,40Q =

h1x22,71 = h3xR1 = h3rx16,33 = h3ix15,42 = h3B4Q = c0x′2 =

yix′ = P 2c0x12,55

(11) d0e0x15,41 = gx19,49 = jx16,48 = kx16,42 = lx16,38 = mx16,35

24 (01) d20rQ1 = d2

0jB4 = d0e0rx′ = d0e0iB4 = d0gx16,37 = d0kx13,35 =

d0lP2D1 = d0mR2 = d0zB21 = e2

0x16,37 = e0gx16,33 =e0jx13,35 = e0kP 2D1 = e0lR2 = e0zQ1 = grPQ1 = gix13,35 =gjP 2D1 = gkR2 = gB4Pj = gzx′ = rPd0x10,27 = rPd0x10,28 =rPe0B21 = ijB23 = ikx10,27 = ikx10,28 = ilB21 = imQ1 =j2x10,27 = j2x10,28 = jkB21 = jlQ1 = jmx′ = k2Q1 = klx′ =kPe0B4 = lPd0B4

(11) d0g5 = d0g

2r2 = d0gmw = d0rm2 = e2

0g4 = e2

0gr2 = e20mw =

e0glw = e0gmv = e0rlm = g2kw = g2lv = g2mu = grkm =grl2 = ruw = rv2

26 (1) d0Px18,55 = e0Px18,50 = gx22,39 = Pd0x18,55 = Pe0x18,50


Stem 1156 (1) h6D1

8 (1) h2x7,97

9 (1) h2x8,105 = h6gd1

10 (1) h1x9,112 = h23x8,93 = g2x6,47 = D3G

11 (1) x11,101

13 (10) x13,95

(01) D2Q2

14 (10) h0x13,95

(01) h0D2Q2 = h22x12,86 = h4x13,73 = gx10,73 = D3R1

15 (10) h21Px9,99 = h1D3x

′ = h1Ph1x9,99 = h3x14,82 = h6rPd0 = h6ik =h6j

2 = c0x12,85 = d0x11,80 = H1x′ = GX1 = x6,53u = B1PD3

(01) h20x13,95 = h2x14,91

16 (10) Px12,85

(01) h1x15,90 = h22y14,83 = h2

2x14,84 = A′R1 = AR1

17 (10) x17,93

(01) x17,94

18 (1) h0x17,94 = h3x17,76

19 (10) x19,86

(01) h20x17,94 = h0h3x17,76 = rx13,46 = ix12,58 = X1R1

20 (1000) grB23 = gmB4

(0100) x′x10,27

(0111) Pe0x12,55 = x′x10,28

(0010) h21P

2x10,76 = h1P2h1x10,76 = h1X1x

′ = Ph21x10,76 = B1W1

(0001) h30x17,94 = h2

0h3x17,76 = h0rx13,46 = h0ix12,58 = h0X1R1 =h2

3x18,63

(0101) d0Px12,60 = Pd0x12,60 = Q1 B21

21 (1) h40x17,94 = h3

0h3x17,76 = h20rx13,46 = h2

0ix12,58 = h20X1R1 =

h0h23x18,63 = h0d0Px12,60 = h0Pd0x12,60 = h0Pe0x12,55 =

h0x′x10,28 = h0Q1 B21 = h2Pd0x12,55 = h2x

′B21 = h2Q12 =

h3ix13,46 = h3R21 = c0x18,72 = d0Ph2x12,55 = d0B2x

′ = G21 Q =P 2h2x12,64

22 (10) d0x18,63

(01) e0x18,60 = gx18,57 = rx16,42 = lx15,41

23 (100) g4m = g2rw = gr2m = m2w

(010) d20x15,47 = d0e0x15,43 = d0rx13,35 = d0ux10,27 = d0ux10,28 =

d0vB21 = d0wQ1 = d0B4z = e0rP2D1 = e0uB21 = e0vQ1 =

e0wx′ = grR2 = guQ1 = gvx′ = rix10,27 = rix10,28 = rjB21 =rkQ1 = rlx′ = rPe0B4 = ilB4 = jkB4 = mx16,37 = B23Pv

(001) h0d0x18,63 = h2Px18,68 = Ph2x18,68

continued



0d0x18,63 = h0h2Px18,68 = h0Ph2x18,68 = h2Ph2x18,63 =P 2h2x15,58

25 (10) d20x17,50 = e0Px17,52 = gPx17,50 = ix18,55 = jx18,50 =

Pd0x17,57 = Pe0x17,52

(01) Ph1x′2 = B1x18,20 = x12,55P

3h1

(11) ux16,32

Stem 1168 (1) h2h6C

11 (1) h6x′

12 (10) D22

(01) h0h6x′

13 (100) x13,97

(010) h0D22 = h3x12,86

(001) h20h6x

′

14 (1) h1x13,95

15 (1000) h22x13,88 = h3x14,84 = H1R1

(1100) h3y14,83

(0010) x15,96

(0001) x15,97

16 (1000) x16,95

(0100) gx12,64

(0010) h0h3y14,83

(0001) h0x15,96

17 (1000) g2x9,51 = grx7,40 = gA′m = gAm

(0100) h0x16,95

(0010) h0gx12,64 = h1Px12,85 = h2e0x12,64 = h2gx12,60 = h4Px12,60 =h5x16,42 = h6d

20Pe0 = h6d0e0Pd0 = h6gP 2e0 = c0x14,82 =

Ph1x12,85 = Q2B21 = B3Q1 = x7,33x′ = x7,34x

′

(0001) h20x15,96

18 (1000) Px14,82

(0100) h1x17,93 = h22x16,77 = h2

2x16,78 = f0x14,67 = d1x14,46 = rx12,48 =tx12,44 = x8,32R1 = x8,33R1

(0111) h3x17,79

(0010) h20x16,95

(0001) h30x15,96 = h3x17,80

19 (0011) h0h3x17,79

(1000) ix12,60 = jx12,55 = B4Q1

(0010) h30x16,95

(0110) h4x18,63

(0001) h40x15,96 = h0h3x17,80 = h2P

2x10,76 = P 2h2x10,76

(1001) d0x15,65 = Pe0x11,61

(0101) h2x18,85 = gx15,58

continued



0h3x17,79

(1011) h0ix12,60 = h0jx12,55 = h0B4Q1 = h2ix12,55 = h2B4x′

(1100) Ph2x15,68 = B2P2D1 = R1x10,28

(0010) h40x16,95 = rP 3h2

5

(1111) h6d0P2i = h6iP

2d0 = R1x10,27

(1010) h0d0x15,65 = h0Pe0x11,61 = h2Pd0x11,61 = d0Ph2x11,61

(0110) h0h2x18,85 = h0gx15,58 = h22x18,78 = h2e0x15,58 = c0x17,76

(0001) h50x15,96 = h2

0h3x17,80 = h0h2P2x10,76 = h0P

2h2x10,76

(0101) h0h4x18,63

21 (100) h20d0x15,65 = h2

0Pe0x11,61 = h0h2Pd0x11,61 = h0d0Ph2x11,61 =h0Ph2x15,68 = h0B2P

2D1 = h0R1x10,28 = h1d0Px12,60 =h1Pd0x12,60 = h1x

′x10,27 = h1Q1 B21 = h22Px15,65 =

h2Ph2x15,65 = h2B2R2 = h2R1B21 = d0Ph1x12,60 = d0B1Q1 =d0B2R1

(010) h50x16,95 = h0rP

3h25 = h2

3x19,58

(001) h60x15,96 = h3

0h3x17,80 = h20h2P

2x10,76 = h20P

2h2x10,76 =h3

1P2x10,76 = h2

1P2h1x10,76 = h2

1X1x′ = h1Ph2

1x10,76 = h1B1W1 =h3x

′Q1 = D3P2u = Ph1Gx′ = Ph1B1X1 = xx16,35 = qx15,42 =

qx15,43 = PD3Q = PD3Pu = x8,75P3h1 = uP 2D3

(101) h20ix12,60 = h2

0jx12,55 = h20B4Q1 = h0h2ix12,55 = h0h2B4x

′ =h1Pe0x12,55 = h1x

′x10,28 = e0Ph1x12,55 = e0B1x′

(011) h30h3x17,79 = h2

0h4x18,63

(111) h0h6d0P2i = h0h6iP

2d0 = h0R1x10,27 = h2h6P3j = h6Ph2P

2j =h6jP

3h2 = h6P2h2Pj

22 (100) g4t = g2nw = g2rN = gnrm = gr2t = tmw = m2N

(010) x22,78

(001) d0e0gB23 = d0g2x10,27 = d0g

2x10,28 = d0vB4 = e30B23 =

e20gx10,27 = e2

0gx10,28 = e0g2B21 = e0uB4 = g3Q1 = r2Q1 =

rjB4 = kx15,47 = lx15,43 = wx13,35

23 (1) h0x22,78 = h1d0x18,63 = h2x22,71 = d0x19,58 = Ph1x18,72 =Pd0x15,56

24 (1) d20x16,48 = d0e0x16,42 = d0gx16,38 = e2

0x16,38 = e0gx16,35 =g2x16,32 = ix17,57 = jx17,52 = kx17,50


Stem 1177 (1) h2G1 = h6G

10 (10) x10,113

(01) x10,114

11 (100) x11,103

(010) h0x10,113

(001) h0x10,114 = h6R1

12 (1000) x12,96

(0100) h1h6x′

(0010) h20x10,113

(0001) h20x10,114 = h0h6R1

13 (10) h30x10,113

(01) h30x10,114 = h2

0h6R1 = h0x12,96

14 (0010) h40x10,113

(1010) gx10,76

(0110) h3x13,88

(0001) h40x10,114 = h3

0h6R1 = h20x12,96

15 (100) x15,98

(010) h50x10,113 = h2

1x13,95 = h4x14,74 = c0x12,86

(001) h50x10,114 = h4

0h6R1 = h30x12,96 = h3h6Q = h5P

3h25

16 (10000) g2x8,57 = gnx7,40 = gH1m = gtA′ = gtA = rx10,60

(01000) h2x15,90

(00011) h4x15,65 = h6d20j = h6d0e0i = h6gPj = h6kPe0 = h6lPd0 =

D2B21 = AQ1 = A′′x′

(10011) Q2B4

(00100) Px12,86

(00001) h60x10,114 = h5

0h6R1 = h40x12,96 = h0h3h6Q = h0h5P

3h25 = d0x12,78

(00010) h1x15,96 = h1x15,97 = h3x15,78 = c0x13,87

continued


Stem 117 continued17 (0011) h3x16,78 = x7,34R1

(1000) Px13,87

(0100) h1x16,95

(0010) h0h2x15,90 = h22x15,82 = c0y14,83 = c0x14,84 = c1x14,67 =

e0x13,73 = e1x13,42 = nx12,48 = Cx11,35

(0110) h3x16,77

(0001) h70x10,114 = h6

0h6R1 = h50x12,96 = h2

0h3h6Q = h20h5P

3h25 =

h0h4x15,65 = h0h6d20j = h0h6d0e0i = h0h6gPj = h0h6kPe0 =

h0h6lPd0 = h0d0x12,78 = h0D2B21 = h0AQ1 = h0A′′x′ =

h0Q2B4 = h1gx12,64 = h22gx11,61 = h2h5x15,41 = h2h6d

20i =

h2h6e0Pj = h2h6jPe0 = h2h6kPd0 = h2f0x12,64 = h2D2Q1 =h2Ax′ = h4Ph2x11,61 = h6d0f0Pd0 = h6d0Ph2k = h6e0Ph2j =h6gPh2i = h6mP 2h2 = B2PA = x7,33R1

18 (10) jx11,61

(01) Px14,84

19 (0011) h2Px14,79 = Ph2x14,79

(1000) g3Q2 = grx9,39 = gmx8,33 = r2Q2

(0010) h0jx11,61 = h1Px14,82 = h2ix11,61 = Ph1x14,82

(0110) h2x18,87

(0001) h0Px14,84

(0101) h3x18,77

21 (10) e0g2B4 = e0mB23 = glB23 = gmx10,27 = gmx10,28 = rx15,47

(01) x21,84

23 (1) d0gx15,41 = e20x15,41 = rx17,50 = kx16,48 = lx16,42 = mx16,38


Stem 1189 (10) x9,115

(01) x9,116

10 (100) h3x9,107

(010) x10,116

(001) h0x9,116

11 (100) x11,106

(010) h0h3x9,107 = h23x9,97

(001) h20x9,116 = h0x10,116

12 (100) x12,100

(010) h1x11,103

(001) h30x9,116 = h2

0x10,116

13 (0011) h0x12,100

(1000) AQ2

(0100) h21h6x

′ = h6Ph1B1 = c0x10,102 = d0x9,97

(1010) A′Q2

(0001) h40x9,116 = h3

0x10,116

14 (0011) h20x12,100

(1000) x14,104

(0010) h0A′Q2

(1111) Px10,102

(0001) h50x9,116 = h4

0x10,116 = h2x13,95

15 (10) h1h3x13,88 = H1Q1

(01) h60x9,116 = h5

0x10,116 = h30x12,100 = h0h2x13,95 = h0x14,104

16 (10) d0x12,80

(01) h1x15,98 = h3x15,81 = d1x12,48 = e1x12,44 = Q2X1

17 (1) h1Px12,86 = Ph1x12,86

18 (010) h1Px13,87 = h5x17,50 = h6P2u = c0x15,78 = Ph1x13,87

(110) e0g2A′ = e0g

2A = e0mx7,40 = g3D2 = gnx9,39 = grG21 =gtx8,33 = glx7,40 = gmx7,34 = nrQ2 = r2D2 = vx9,51

(001) h21x16,95 = h1h3x16,77 = h2x17,93 = gx14,67 = d1P

3h25 = e1x14,42 =

qx12,48 = yx12,44 = x8,32Q1

19 (1) Px15,78

20 (10) h2x19,86

(01) d20x12,55 = e0Px12,60 = Pd0x12,64 = Pe0x12,60 = x′B23 =

Q1 x10,27 = Q1 x10,28 = B221

continued



20x12,55 = h0e0Px12,60 = h0Pd0x12,64 = h0Pe0x12,60 =

h0x′B23 = h0Q1 x10,27 = h0Q1 x10,28 = h0B

221 = h2d0Px12,60 =

h2Pd0x12,60 = h2Pe0x12,55 = h2x′x10,27 = h2x

′x10,28 =h2Q1 B21 = h5Px16,35 = h6d0P

3e0 = h6e0P3d0 = h6Pd0P

2e0 =h6Pe0P

2d0 = d0Ph2x12,60 = d0B2Q1 = e0Ph2x12,55 = e0B2x′

22 (100) gx18,60 = rx16,48 = mx15,41

(010) e0x18,63

(001) h1x21,84 = Ph1x17,79

(011) d0x18,68

Stem 1199 (1) x9,117

10 (10) x10,118

(01) h0x9,117 = h1x9,115 = h4x9,97

11 (1000) x11,109

(0010) h1h3x9,107 = h23x9,99 = h6gt = gx7,83 = g2x7,53

(0110) h6Q1

(0001) h1x10,116

12 (100) D2A

(010) h0x11,109

(001) h0h6Q1 = h2h6x′

(111) H1Q2 = D2A′

13 (10000) gx9,86

(00011) h20x11,109

(01000) h4x12,80

(00100) h1x12,100

(00001) h20h6Q1 = h0h2h6x

′

(01001) d0x9,99

(00010) h0D2A = h21x11,103 = h2D

22

14 (10) x14,108

(01) h30h6Q1 = h3

0x11,109 = h20h2h6x

′ = h0d0x9,99 = h31h6x

′ =h1h6Ph1B1 = h1c0x10,102 = h1d0x9,97 = h3x13,91 = h6d0v

15 (100) x15,103

(010) h1Px10,102 = Ph1x10,102

(001) h0x14,108 = h3x14,91 = D2X1 = Q2x8,32

17 (1) h2x16,95 = h23x15,68 = Q2x10,27

18 (01) h0h2x16,95 = h0h23x15,68 = h0Q2x10,27 = pP 3h2

5 = yx12,45

(11) Pd0x10,76

19 (100) ix12,64 = jx12,60 = kx12,55 = B4B21

(010) h4x18,68

(001) h0Pd0x10,76 = h21Px13,87 = h1h5x17,50 = h1h6P

2u = h1c0x15,78 =h1Ph1x13,87 = h2Px14,82 = h3x18,83 = h6Ph1Q = h6Ph1Pu =h6P

2h1u = Ph2x14,82 = Pc0x12,78

(101) d20x11,61 = e0x15,65

(111) d0x15,68

continued



20x11,61 = h0e0x15,65 = h0ix12,64 = h0jx12,60 = h0kx12,55 =

h0B4B21 = h2d0x15,65 = h2ix12,60 = h2jx12,55 = h2Pe0x11,61 =h2B4Q1 = e0Ph2x11,61 = f0Px12,60 = B2x13,35 = x′B5

(1000) x20,91

(0100) h1Px15,78 = Ph1x15,78

(0010) h0d0x15,68 = h6d0P2j = h6e0P

2i = h6iP2e0 = h6jP

2d0 =h6Pd0Pj = Ph2x15,74 = x′PD2 = R1B23

(0001) h0h4x18,68 = h22x18,85 = h2h4x18,63 = h2gx15,58 = B2x13,34

21 (100) g2x13,42 = nx16,48 = tx15,41 = mx14,46

(010) x21,87

(001) h20d

20x11,61 = h2

0d0x15,68 = h20e0x15,65 = h2

0ix12,64 = h20jx12,60 =

h20kx12,55 = h2

0B4B21 = h0h2d0x15,65 = h0h2ix12,60 =h0h2jx12,55 = h0h2Pe0x11,61 = h0h2B4Q1 = h0h6d0P

2j =h0h6e0P

2i = h0h6iP2e0 = h0h6jP

2d0 = h0h6Pd0Pj =h0e0Ph2x11,61 = h0f0Px12,60 = h0Ph2x15,74 = h0B2x13,35 =h0x

′B5 = h0x′PD2 = h0R1B23 = h1d

20x12,55 = h1e0Px12,60 =

h1Pd0x12,64 = h1Pe0x12,60 = h1x′B23 = h1Q1 x10,27 =

h1Q1 x10,28 = h1B221 = h2

2ix12,55 = h22Pd0x11,61 = h2

2B4x′ =

h2h6d0P2i = h2h6iP

2d0 = h2d0Ph2x11,61 = h2Ph2x15,68 =h2B2P

2D1 = h2R1x10,27 = h2R1x10,28 = h5iR2 = h6d0iP2h2 =

h6f0P3d0 = h6Ph2iPd0 = h6kP 3h2 = d0Ph1x12,64 = d0B1B21 =

e0Ph1x12,60 = e0B1Q1 = e0B2R1 = f0Ph2x12,55 = f0B2x′ =

gPh1x12,55 = gB1x′ = Ph2B2B4 = iB2

2


Stem 1208 (1) h6Q2

9 (1) x9,118

10 (100) x10,120

(001) h0x9,118

(011) h1x9,117 = h4x9,99

11 (100) x11,113

(010) h0x10,120 = h2x10,114

(001) h20x9,118 = h2x10,113

12 (10000) x12,106

(00011) h20x10,120 = h0h2x10,114 = h1h6Q1 = h1x11,109 = h2h6R1

(01000) x12,107

(00100) h0x11,113

(00001) h30x9,118 = h0h2x10,113 = h2

1x10,116

13 (1) h0x12,106

14 (10) x14,110

(01) h20x12,106 = h2

1x12,100 = h3x13,93

16 (10) h23x14,79 = D2x10,27

(11) h4x15,68

17 (100) P 2x9,97

(110) ix10,76

(001) h0h23x14,79 = h0h4x15,68 = h0D2x10,27 = h2

2x15,90 = gx13,73 =x7,40R1

18 (100) rx12,55 = B24

(110) d0x14,79

(001) h0ix10,76 = h0P2x9,97

(101) kx11,61

19 (100) h0rx12,55 = h0B24 = h3P

2x10,76 = x9,40x′

(110) h0d0x14,79

(001) h20ix10,76 = h2

0P2x9,97

(101) h0kx11,61 = h1Pd0x10,76 = h2jx11,61 = h5x18,50 = h6iP j =c0Px12,80 = d0Ph1x10,76 = f0x15,65 = Pc0x12,80

(011) h2Px14,84 = Ph2x14,84

20 (100) P 2x12,80

(001) h30ix10,76 = h3

0P2x9,97 = h2

0rx12,55 = h20B

24 = h0h3P

2x10,76 =h0x9,40x

′ = h3ix12,55 = h3B4x′ = g2x16,32 = xx15,41

(011) h20d0x14,79 = h0h2Px14,84 = h0Ph2x14,84 = h1h4x18,68 =

h1d0x15,68 = h22x18,87 = h2

2Px14,79 = h2Ph2x14,79 = g2x12,44 =d1x16,48 = Ph1x15,81 = Ph1x15,82 = tx14,46 = R1B5 = Q1 x10,32


Stem 1217 (10) x7,101

(01) h6D2

8 (1) h0h6D2 = h0x7,101

9 (10) x9,119

(01) h20h6D2 = h2

0x7,101 = h1h6Q2

10 (1) h0x9,119 = h1x9,118 = h2x9,116

11 (1) x11,116

12 (10) h1x11,113

(01) h0x11,116

13 (1) h20x11,116 = h1x12,106 = h2x12,100 = h3x12,93

14 (1) Px10,109

15 (10) h4x14,79

(01) h1x14,110

16 (100) d0x12,85 = e0x12,80

(010) x16,109

(001) h0h4x14,79

17 (1011) rx11,61

(0010) h0x16,109

(0001) h20h4x14,79 = h1h4x15,68 = Q2x10,32

(0101) P 2x9,99

18 (100) g3A′ = g3A = gmx7,40 = r2A′ = r2A = wx9,51

(010) h0P2x9,99 = h1P

2x9,97 = h5x17,52 = h6P2v = Ph1x13,91 =

P 2h1x9,97

(001) h20x16,109

(011) h0rx11,61 = G21 x′ = B4X1

19 (1) h30x16,109 = h2

0rx11,61 = h0G21 x′ = h0B4X1 = h3ix11,61 =h3x18,87 = x9,40R1


Stem 1228 (1) h1x7,101 = D2

3

11 (10) h6B21

(01) x11,118

12 (100) A2

(010) h0h6B21 = h2h6Q1

(001) h0x11,118 = D2A′′

(101) A′2 = A′A

(011) h2x11,109

(111) h5x11,61

13 (100) x13,113

(010) h21x11,113 = h4x12,85 = D3X1 = x6,53B1

(001) h20h6B21 = h0h2h6Q1 = h0h2x11,109 = h0h5x11,61 = h2

2h6x′ =

h6Ph2B2 = e0x9,99

14 (1) h0x13,113 = h3D2Q2

15 (10) x15,108

(01) x15,109

16 (100) nx11,61 = rx10,65

(010) x16,112

(001) h0x15,109 = h21x14,110

17 (10) g3H1 = gtx7,40 = nrA′ = nrA = H1r2 = mx10,60 = Q2B23 =

Nx9,51 = x8,33B4 = x8,57w

(01) h0x16,112

18 (100) Pe0x10,76

(010) h1P2x9,99 = Ph1Px9,99 = qx12,55 = PD3x

′ = P 2h1x9,99

(110) d0x14,82

(001) h20x16,112 = h3x17,94 = xx13,46 = rx12,58 = G21 R1

(011) X21


Stem 1238 (1) x8,113

9 (10) x9,121

(01) h0x8,113

10 (100) x10,124

(110) h6B4

(001) h0x9,121 = h2x9,118

11 (10000) x11,119

(01000) x11,120

(00001) h20x9,121 = h0h2x9,118

(01100) h5x10,65 = H1A′ = H1A

(00010) h0h6B4 = h2x10,120

12 (100) x12,116

(010) h0x11,119

(001) h20h6B4 = h0h2x10,120 = h1h6B21 = h2

2x10,114 = h2x11,113 =h6d0B1 = Ph2x7,97

13 (100) x13,116

(010) x13,117

(001) h20x11,119 = h2x12,106 = h3D

22 = h5x12,58 = r1Q2

14 (100) Q2x7,40

(001) h30x11,119 = h0h2x12,106 = h0h3D

22 = h0h5x12,58 = h0r1Q2 =

h1x13,113 = h23x12,86 = h3x13,97 = px10,63 = D3x10,27 = H1X1 =

qx8,75 = Ax8,32

(101) rx8,78 = A′x8,33 = Ax8,33

(011) h0x13,116 = h0x13,117

15 (100) x15,110

(010) h4x14,82 = d1x11,61 = nx10,65 = Q3Q1

(001) h20x13,116 = h2

0x13,117

16 (010) h0x15,110

(110) h1x15,109 = h4x15,74 = c0x13,95 = d0x12,86

(001) h30x13,116 = h3

0x13,117 = h3x15,96

(011) h23y14,83 = A′x10,27

17 (1101) h3x16,95

(0011) h0h23y14,83 = h0A

′x10,27 = h1x16,112 = e1x13,46 = g2x13,42 =nx12,58 = xx12,48 = qx11,61 = Q2B5 = Q2PD2 = x8,32X1

(0100) d0x13,87

(0010) h20x15,110

(0001) h40x13,116 = h4

0x13,117 = h0h3x15,96 = ix10,82

(0101) jx10,76


Stem 1246 (1) x6,94

7 (100) x7,103

(010) h6A

(001) h0x6,94

(011) h6A′

8 (1) x8,114

9 (100) x9,123

(010) x9,124

(001) h0x8,114

10 (00110) H21

(10000) x10,127

(01000) x10,128

(00100) h1x9,121

(00001) h20x8,114

(00010) h0x9,123 = h2x9,119

(00101) h6X1

11 (10000) x11,124

(00011) h3x10,113

(01000) x11,125

(00100) x11,126

(00001) h30x8,114 = h0h6X1 = h3x10,114

(00010) h0x10,127

12 (00110) h0x11,125

(10000) h1x11,120

(01000) h0x11,124

(00011) h0h3x10,113

(00100) h0x11,126 = h2x11,116 = px8,75 = n1Q2 = D2r1

(00001) h40x8,114 = h2

0h6X1 = h0h3x10,114 = h3h6R1

(10100) Q3Q2

(00010) h20x10,127 = h1x11,119 = h3x11,103

13 (1000) h5x12,60 = e0x9,102 = gx9,97 = nx8,78 = H1x8,33 = D2x7,40 =A′x7,34 = Ax7,34

(1100) h4x12,86

(1111) H1x8,32

(0001) h50x8,114 = h3

0h6X1 = h20h3x10,113 = h2

0h3x10,114 = h20x11,124 =

h0h3h6R1 = h3x12,96

continued


Stem 124 continued14 (10000) x14,117

(00011) h1x13,116

(01000) x14,118

(00001) h1x13,117 = h4x13,87 = d0x10,102

(10100) rx8,80

(00010) d1x10,65

15 (0011) h0x14,118

(1000) x15,113

(0100) x15,114

(0110) h4x14,84

(0001) h0x14,117

(0101) h23x13,88 = h4y14,83 = H1x10,27

16 (00110) h0x15,113

(10000) x16,117

(00011) h20x14,118 = h0h4x14,84 = h2h4x14,79 = D2PD2

(01000) h1x15,110 = h3x15,98 = d1x12,58 = e1x12,48 = g2x12,44 = qx10,65 =x2

8,32

(10011) e0x12,85 = gx12,80

(00001) h20x14,117 = h0x15,114


Stem 1255 (1) x5,77

6 (10) h6H1

(01) h0x5,77

7 (1) h20x5,77 = h1x6,94

8 (10) x8,115

(01) x8,116

9 (01101) h6x8,32

(10000) x9,126

(01000) h5x8,80

(00001) h0x8,116

(00010) x9,129

(00101) h6x8,33

10 (10000) x10,132

(01000) x10,133

(00001) h20x8,116

(00111) h0x9,126

(00010) h0x9,129 = h3x9,116

11 (01101) h1x10,127

(00011) h0x10,132

(11000) h6x10,27 = h6x10,28

(01011) Q3D2

(00001) h30x8,116 = h2

0x9,126 = h0x10,133

(00010) h20x9,129 = h0h3x9,116

(01111) h3x10,116

(00101) h1x10,128 = h4x10,102

12 (10000) x12,124

(00011) h30x9,129 = h2

0h3x9,116 = h0h3x10,116

(01000) x12,125

(00100) h0h6x10,27 = h0h6x10,28 = h2h6B21 = h6d0B2

(00001) h40x8,116 = h3

0x9,126 = h20x10,133

(00010) h20x10,132 = h0Q3D2 = h2x11,118 = AA′′

continued



0x9,129 = h30h3x9,116 = h2

0h3x10,116 = h22x11,109 = h2h5x11,61 =

gx9,99

(00100) h0x12,124

(00001) h50x8,116 = h4

0x9,126 = h30x10,133 = h2

0h6x10,27 = h20h6x10,28 =

h0h2h6B21 = h0h6d0B2 = h22h6Q1 = c0x10,114 = d0x9,109

(01001) nx8,80

(00010) h30x10,132 = h2

0Q3D2 = h0h2x11,118 = h0AA′′ = h0x12,125 =

h21x11,120 = h1Q3Q2 = h2D2A

′′ = h2A′2 = h2A

′A = f0x9,102 =rx7,79

(11001) h3x12,100

14 (001) h20x12,124 = h0h3x12,100 = h3A

′Q2 = px10,65

(011) h1h4x12,86 = c0x11,103 = D3x10,32

(111) Px10,113

15 (00110) h1x14,118

(10000) x15,117

(11000) Q2G21

(00100) x15,119

(00001) h30x12,124 = h2

0h3x12,100 = h0h3A′Q2 = h0px10,65 = h2

1x13,116 =h1d1x10,65 = h3x14,104 = D2x9,40 = A′′X1 = x7,33x8,32

(00010) h0Px10,113


Stem 1262 (1) h2

6

3 (1) h0h26

4 (10) D31

(01) h20h

26

5 (1) h30h

26

6 (10) x6,97

(01) h40h

26

7 (01) h50h

26

(11) h1h6H1

8 (100000) x8,117

(010000) x8,118

(001000) x8,119

(001110) h6x7,34

(000100) x8,120

(000001) h60h

26

9 (100000) x9,131

(010000) h1x8,115

(000011) h0x8,118

(001000) h1x8,116

(010011) h2x8,113

(000100) h0x8,117

(000001) h70h

26

10 (10000) x10,137

(00011) h20x8,118 = h0h2x8,113 = h1x9,126 = h1x9,129 = d2D2

(00001) h80h

26

(01001) h0x9,131

(00101) h20x8,117 = h1h5x8,80 = h1h6x8,32 = h3x9,117

(01010) h2x9,121

11 (100000) x11,134

(000011) h20x9,131 = h0h2x9,121 = h2

2x9,118

(001000) h1x10,133

(011000) h1x10,132 = h3x10,118

(000100) h0x10,137 = h2h6B4 = d0x7,97

(000001) h90h

26

continued


Stem 126 continued12 (00110) h0x11,134 = h2

1x10,127 = h21x10,128 = h1h3x10,116 = h1h4x10,102 =

h2h5x10,65 = h2H1A′ = h2H1A = c0x9,115 = c1x9,102 = nx7,79

(00011) h20x10,137 = h0h2h6B4 = h0d0x7,97 = h1h6x10,27 = h1h6x10,28 =

h22x10,120 = h2x11,119 = h6e0B1 = c0x9,116 = d0x8,105

(10011) d1x8,80

(01011) h3x11,109

(00001) h100 h2

6

13 (100) h1x12,125

(010) h0h3x11,109 = h3H1Q2 = h3D2A′

(110) h1x12,124

(001) h110 h2

6

14 (0100) x14,126

(0010) h1h3x12,100 = h2x13,116 = qx8,80

(1010) D2G21

(0001) h120 h2

6


Stem 1271 (1) h7

2 (1) h0h7

3 (10) h1h26

(01) h20h7

4 (1) h30h7

5 (1) h40h7

6 (10) x6,99

(01) h50h7

7 (00110) h2x6,94

(10000) x7,109

(01000) x7,110

(00100) h1x6,97

(00001) h60h7

(00010) h0x6,99 = h6A′′

8 (0011010) h2h6A′

(0011000) h2h6A

(0001100) h0x7,109

(0100000) x8,124

(0000100) h0x7,110

(0000001) h70h7

(1001000) h2x7,103 = h4x7,97

(0000010) h20x6,99 = h0h2x6,94 = h0h6A

′′

9 (10000) h1x8,118 = h1x8,120

(00100) h0x8,124

(00001) h80h7

(11100) h1x8,119

(00010) h20x7,109 = h1x8,117

(10010) h3h6Q2 = h5x8,83

(01010) h2x8,114

10 (010000) x10,143

(000010) h20x8,124 = h0h2x8,114 = h1x9,131

(101000) h2x9,123

(001110) h3x9,118

(000100) h21x8,116

(000001) h90h7

continued


Stem 127 continued11 (0100) h0x10,143

(0010) h0h3x9,118

(1010) h0h2x9,123 = h1x10,137 = h22x9,119 = h2H

21 = h2x10,127 =

h4x10,107 = d1x7,79 = D3x7,40

(0001) h100 h7

12 (100) h1x11,134 = h24x10,76 = c0x9,117 = Q3B3

(010) h20x10,143 = h2x11,124 = px8,80 = A′r1

(110) h3x11,113

(001) h110 h7

13 (00110) gx9,102

(10110) h3x12,106

(01000) x13,132

(00100) h5x12,64 = A′x7,40 = Ax7,40

(00001) h120 h7

(00010) h30x10,143 = h0h2x11,124 = h0h3x11,113 = h0px8,80 = h0A

′r1 =h1d1x8,80 = nx8,83 = rx7,81


Stem 1282 (1) h1h7

4 (1) h21h

26

5 (1) x5,80

6 (1000) x6,101

(0100) x6,102

(0010) h2x5,77

(0001) h0x5,80

7 (010) h0x6,101

(110) h2h6H1

(001) h20x5,80 = h0h2x5,77 = h0x6,102 = h1x6,99

8 (1) h3h6D2 = h3x7,101 = h5x7,81

9 (100) h2x8,115

(010) h1x8,124 = D3Q3

(001) h0h3h6D2 = h0h3x7,101 = h0h5x7,81

10 (0011) h2h6x8,33 = h2x9,126

(1000) x10,148

(0100) x10,149

(0010) h2h6x8,32 = h4x9,111

(0001) h20h3h6D2 = h2

0h3x7,101 = h20h5x7,81 = h2

1x8,118 = h21x8,119 =

h21x8,120 = h1h3h6Q2 = h1h5x8,83 = h2h5x8,80

11 (100) h5x10,76 = h6B23

(010) h0x10,148 = h2x10,132 = px7,79 = H1r1 = n1A′ = Q3A

′

(001) h0x10,149 = h1x10,143

(011) h4x10,109 = Q3A

12 (10000) x12,137

(00100) h3x11,116

(00001) h0h5x10,76 = h0h6B23 = h2h6x10,27 = h2h6x10,28 = h6e0B2 =c0x9,118

(11001) H1x7,40

(00010) x12,140


Stem 1293 (10) h2h

26

(01) h21h7

4 (1) h0h2h26

5 (100) H11

(010) h2D31

(001) h20h2h

26 = h3

1h26

7 (1) h2x6,97

8 (10) h6x7,40

(01) x8,132

9 (0011) h0h6x7,40 = h2h6x7,34 = h2x8,119

(1000) x9,145

(0100) x9,146

(0001) h0x8,132 = h2x8,118

10 (100) x10,152

(010) h0x9,146 = h2x9,131

(001) h20x8,132 = h0h2x8,118 = h2

1x8,124 = h1D3Q3 = h22x8,113 =

h4x9,112 = c0x7,101 = d2A

11 (100000) x11,147

(010000) x11,148

(000011) h0x10,152 = h2x10,137 = e0x7,97

(001000) h6B5 = h6PD2

(000100) h1x10,149

(000001) h20x9,146 = h0h2x9,131 = h2

2x9,121

Stem 1302 (1) h2h7

3 (1) h0h2h7

4 (1) h20h2h7 = h3

1h7

6 (1) h6n1

7 (1) x7,118

8 (10) x8,133

(01) h2x7,109

9 (100) h3x8,113

(010) h1h6x7,40 = h22h6A

′ = h22h6A

(001) h0x8,133 = h2x8,124

10 (10000) x10,155

(00100) h3x9,121

(00001) h20x8,133 = h0h2x8,124 = h1x9,146 = h2

2x8,114

(01100) h5x9,86 = h6x9,39

(00010) h0h3x8,113


Stem 1317 (10) h2x6,101

(01) h3x6,94

8 (0011) h0h2x6,101 = h1x7,118 = h3x7,103 = D3p1

(1000) h22h6H1 = h3h6A

(0100) x8,136

(0001) h0h3x6,94

(1001) h3h6A′

9 (00011) h1x8,133

(00100) x9,154

(00001) h0x8,136

(01001) h6G21

(10010) h3x8,114

Stem 1324 (1) h2

2h26

6 (100) h3x5,77

(010) x6,107

(001) h2H11

7 (010) h0h3x5,77

(001) h0x6,107

(101) h3h6H1

8 (10000) x8,139

(01000) x8,140

(00100) h22x6,97

(00001) h20x6,107

(00010) h20h3x5,77 = h1h3x6,94 = h5x7,88

Stem 1333 (10) h3h

26

(01) h22h7

4 (1) h0h3h26

5 (01) h20h3h

26

(11) h3D31

6 (1) h30h3h

26

7 (100) x7,124

(110) h3x6,97

(001) h1x6,107

Stem 1342 (1) h3h7

3 (1) h0h3h7

4 (10) h1h3h26

(01) h20h3h7

5 (10) h26c0

(01) h30h3h7

6 (1) x6,110


Stem 1353 (1) h1h3h7

4 (1) h7c0

5 (1) h21h3h

26 = h3

2h26

Stem 1364 (1) h2

1h3h7 = h32h7

Stem 137

Stem 138

Stem 139

Stem 140

References

1. Robert R. Bruner, “Calculation of large Ext modules”, Computers in Geometry and

Topology (M. C. Tangora, ed.), Marcel Dekker, New York, 1989, 79-104.2. R.R.Bruner, “Ext in the nineties”, pp. 71-90 in Algebraic Topology, Oaxtepec 1991,

Contemp. Math. 146, Amer. Math. Soc., Providence, 1993.3. Robert R. Bruner, “Root invariants and Sq0’s in ExtA’, preprint, April 1997.

Mathematics Department, Wayne State University, Detroit, Michigan, 48202

E-mail address: [email protected]

the cohomology of the mod 2 steenrod algebra: a computer ...the cohomology of the mod 2 steenrod...

Documents