ROUND 12020

WPF PUZZLE GP 2020INSTRUCTION BOOKLET

Host Country: SerbiaČedomir Milanović, Zoran Tanasić, Nikola Živanović

Special Notes: Point values are not final yet.

1. Product Lines [Nikola Živanović] (10 points)

Points:

1. Product Lines 10

2. Word Search (Count) 11

3. Arithmetic Square 14

4. Heyawake 14

5. Compass 15

6. Minesweeper 17

7. Battleships (Phrase) 17

8. Doppelblock Skyscrapers 22

9. Skyscraper Sums 30

10. Index Sums 16

11. Modes 38

12. Scrabble 39

13. Slitherlink (Out-Liars) 51

14. Fillomino (Off-By-One) 52

15. Yajilin (Regions) 55

16. Tera XX 59

17. Summon 67

18. Nanro 88

19. Hideout Fences 97

20. Japanese Sums 132

TOTAL: 844

Fill in each circle with an integer from 1 to N (N is the number of circles) so that every circle has a different number. The circled numbers connected to each rectangle must have a product equal to the number in that rectangle.

Answer: For each row, enter the contents of the circles, from left to right. Use only the last digit for two-digit numbers; e.g., use ‘0’ for the number 10.

Example Answer: 7380

6

7 3

1

10

5

4

8

2

920 18

16

8

24

18

219a

20 18

16

8

24

18

219a

2020ROUND 1WPF PUZZLE GP

2. Word Search (Count) [Nikola Živanović] (11 points; 6 points if the answer is too low by one)

3. Arithmetic Square [Čedomir Milanović] (14 points)

E E L P M A X E X E X M A L L P A E X A M P L E M E L P M A X E P E X A M P L E L E X A M P L E E E L P M A X E

EXAMPLE

9

EL

E

P L

M P

A M

E X

A

E

EX

E

AX

MA

PM

EL

P

EEXAMPLE E L P M A X E

E X A M P L EE X A M P L E

E X A M P L EE L P M A X E

E L P M A X E

9a

E E L P M A X E X E X M A L L P A E X A M P L E M E L P M A X E P E X A M P L E L E X A M P L E E E L P M A X E

EXAMPLE

+ + > 23

+ − +

× ÷ = 8

× × −

× + = 11

= = = 75 8 9

9 8 7

6 4 3

5 2 1

4a

4a

4a

+ + > 23

+ − +

× ÷ = 8

× × −

× + = 11

= = = 75 8 9

4a

4a

4a

Find the given word in the grid along a straight line in any of the eight standard directions. How many times does the word appear?

Answer: The number of times the word appears in the grid.

Example Answer: 9

Place the numbers from 1 to 9 into the cells (a different single number in each cell) so that the indicated equations/relations are correct. Evaluate from left-to-right and top-to-bottom (ignore the usual precedence of the operators).

It is possible for expressions and partial expressions to be negative or non-integral.

Answer: For each designated row, enter the contents of the cells, in order from left to right.

Example Answer: 987,643,521

4. Heyawake [Zoran Tanasić] (14 points)

Shade some cells black so that all remaining cells are connected orthogonally and no two black cells share an edge. The grid is divided into regions by thick borders; a number in a region indicates exactly how many cells in that region must be shaded black. Every “word” in the grid (a group of unblackened cells connected to each other either only horizontally or only vertically) may not cross more than one thick border.

Answer: For each indicated row, enter its contents from left to right. Use ‘O’ for an unshaded cell and ‘X’ for a black cell. Ignore borders and numbers when entering your answer.

Example Answer: XOOXOO,XOXOOX

2 3

1a

1b

2 3

1a

1b

2020ROUND 1WPF PUZZLE GP

5. Compass [Čedomir Milanović] (15 points)

6. Minesweeper [Nikola Živanović] (17 points)

7. Battleships (Phrase) [Nikola Živanović] (17 points)

Divide the grid along the dotted lines into regions (groups of cells that are connected north-south or east-west, where north is towards the top of the page). Each cell must be in exactly one region, and each region must contain exactly one clue. For each clue, the number in the north part indicates how many cells of that clue’s region are located North of the clue cell (irrespective of their East-West location). Analogously, numbers in the west, east, and south part indicate how many cells of that region are located West, East and South of the clue cell.

The letters in the clue cells are for Answer purposes only.

Answer: For each designated row, enter the letter of the region each cell belongs to.

Example Answer: ACCAB,DEEAE

Place mines into the un-numbered cells in the grid, at most one mine per cell, so that each number in a cell represents the number of mines adjacent to that cell (including diagonally adjacent cells).

The number of mines you must locate is provided.

Answer: For each designated row, enter its contents from left to right. Use ‘O’ for a cell containing a mine and ‘X’ for a cell that does not contain a mine (but may contain a number). You may use any letters or digits, as long are they are distinct.

Example Answer: XXOO,XOXX

Locate the indicated fleet of ships in the grid. Each ship piece occupies a single cell. Ships can be rotated. Ships do not touch each other, not even diagonally (that is, if two ship pieces are in touching cells, they must be part of the same ship).

The letters in the cells containing ship parts should precisely match the given phrase.

The numbers above the grid are for Answer purposes only.

Answer: For each row from top to bottom, enter the number of the first column from the left where a ship piece appears (the number on far top of that column). Use only the last digit for two-digit numbers; e.g., use ‘0’ if the first ship piece appears in column 10. If the row is empty, enter ‘0’.

Example Answer: 514242

A T A E A T L L A S B E A S L T E B E H T E B A E T A B B E B S T E E T

1 2 3 4 5 6

5 1 4 2 4 2

4a

A T A E A T L L A S B E A S L T E B E H T E B A E T A B B E B S T E E T

1 2 3 4 5 6

4a

ALL THE BEST

1a

1b

A 4 0 B 1 2 2 C

D 2 3 3 E

1a

1b

A 4 0 B 1 2 2 C

D 2 3 3 E

0 3

3 4

• • • • • •

(6 mines)

3a

3b

0 3

3 4

(6 mines)

3a

3b

2020ROUND 1WPF PUZZLE GP

8. Doppelblock Skyscrapers [Čedomir Milanović] (22 points)

9. Skyscraper Sums [Zoran Tanasić] (30 points)

Place either a block or a number from 1 to X (integers only) into each cell so that each number appears exactly once in each row and each column. (X is two fewer than the number of cells in each row.) Each row and each column will therefore have exactly two cells with blocks in them.

Each number represents a skyscraper of its respective height. The numbers outside the grid indicate how many skyscrapers between the two blocks can be seen from the first block in the respective row or column from the respective direction; smaller skyscrapers are hidden behind higher ones. (Skyscrapers not between the two blocks are not seen.) Some numbers may already be filled in for you.

Answer: For each designated row, enter its contents from left to right. Use ‘X’ to denote a block. Use only the last digit for two-digit numbers; e.g., use ‘0’ for the number 10. Do not include any given numbers outside the grid.

Example Answer: 3X1X2,13X2X

1 3 4

3 2

2

Skyscraper Clue Examples

Place a number from 1 to X (integers only) into each cell so that each number appears exactly once in each row and column. (X is the number of cells in each row.) Each number represents a skyscraper of its respective height. The numbers outside the grid indicate the sum of the heights of the skyscrapers that can be seen in the respective row or column from the respective direction; smaller skyscrapers are hidden behind higher ones. Some numbers may already be filled in for you.

Answer: For each designated row, enter its contents. Do not include any numbers outside the grid.

Example Answer: 3214,2341

3 1 2 1 3 2 1 2 3 2 1 3 2 3 1

1 1 0

3

2 1

3a

3b

2

1 1 0

3

2 1

3a

3b

1

2

3

4

1 2 3 4

3 6 5 9 4 71a

1b

1

2

3

4

1 2 3 4

3 6 5 9 4 71a

1b

1 4 2 3 3 2 1 4 4 1 3 2 2 3 4 1

4 5 7

9 7

3a

3b

4 5 7

9 7

3a

3b

10. Index Sums [Zoran Tanasić] (16 points)Each cell in the grid has a row number (the small numbers to the right of the grid) and a column number (the small numbers below the grid). Shade in some cells, leaving the other cells empty. Each large number above the grid represents the sums of the column numbers of the shaded cells in that column. Each large number to the left of the grid represents the sums of the row numbers of the shaded cells in that row.

Answer: For each designated row, enter its contents from left to right, using ‘X’ for a shaded cell and ‘O’ for an empty cell. Do not enter numbers that are outside the grid. You may use other letters or digits instead, as long as they are distinct from each other.

Example Answer: XXOX,OXXX

2020ROUND 1WPF PUZZLE GP

11. Modes [Nikola Živanović] (38 points)

12. Scrabble [Čedomir Milanović] (39 points)

13. Slitherlink (Out-Liars) [Čedomir Milanović] (51 points)

Fill in each unblackened cell with a single letter from the designated set so the number of cells containing each letter is equal for each letter. A letter along a row represents the mode of all the letters in that row (that is, the letter or set of letters that appear more than any other letter). Some cells are blackened out and will not contain a letter.

Answer: For each designated row, enter its contents, from left to right. Skip blackened cells.

Example Answer: BAAC,CBC

Put at most one letter into each cell so that the given words can be read either across (left-to-right) or down (top-to-bottom) in consecutive cells in the grid. Every word must appear in the grid exactly once, and no other words may appear in the grid (that is, if two cells are filled and are adjacent, then there must be a word that uses both of them). Every word must have either a blank cell or the edge of the grid before and after it. All letters must be (orthogonally) connected in a single group.

Copies of some letters are already supplied in the grid. All instances of those letters are given.

Answer: For each designated row, enter its contents from left to right, ignoring any blank cells. If all cells in the row are blank, enter a single letter ‘X’.

Example Answer: CYPRUSO,ONMUO,AUR,GA

Draw a single, non-intersecting loop that only consists of line segments between the dots along the dotted lines. A number inside a cell indicates how many of the edges of that cell are part of the loop when it is inside the loop.

All numbers inside the loop are correct, but all numbers outside the loop are incorrect; they are either one more or one less than the correct number for that cell.

Answer: For each designated row, enter its contents from left-to-right. Use ‘O’ for a cell inside the loop and ‘X’ for a cell outside the loop. You may use other letters or digits instead, as long as they are distinct from each other.

Example Answer: OXOX,OOOX

A A B B C C A A A C A C B B B C B C

C B B

A ABC

A AC

A C AB

{A,B,C}

9b

9a

C B B

A ABC

A AC

A C AB

{A,B,C}

9b

9a

M A S L M C Y P R U S O E A X L D I C E L A N D O N M U O N B S V I C R O A T I A A U R G E O R G I A G A

1a

1a

1a

1a

A

A A

A A A A A

A U S T R I A C R O A T I A C Y P R U S G E O R G I A I C E L A N D L U X E M B O U R G M A C E D O N I A M O L D O V A S P A I N

1a

1a

1a

1a

3 0 1 3 1 1 4 2

1b

1a

3 0 1 3 1 1 4 2

1b

1a

2020ROUND 1WPF PUZZLE GP

14. Fillomino (Off-By-One) [Nikola Živanović] (52 points)

15. Yajilin (Regions) [Nikola Živanović] (55 points)

16. Tera XX [Zoran Tanasić] (59 points)

Divide the grid along the dotted lines into regions (called polyominoes) so that no two polyominoes with the same area share an edge. Inside some cells are numbers; each number must equal the area of the polyomino it belongs to. A polyomino may contain zero, one, or more of the given numbers. (It is possible to have a “hidden” polyomino: a polyomino without any of the given numbers. “Hidden” polyominoes may have any area, including a value not present in the starting grid, such as a 6 in a puzzle with only clues numbered 1-5.)

All numbers given are one higher or one lower than the correct number would be for that cell.

The dots in cells are only used for entering your answers.

Answer: Enter the area of the polyomino each dot is in, reading the dots from left to right. (Ignore which row the dots are in.) Use only the last digit for two-digit numbers; e.g., use ‘0’ for a polyomino of size 10.

Example Answer: 3213

Blacken some cells so that you can draw a single closed loop (without intersections or crossings) through all remaining white cells. Loop paths must be orthogonal. Blackened cells cannot share an edge with each other. The grid is divided into regions by thick borders; a number in a region indicates exactly how many cells in that region must be blackened. Numbered cells may be blackened. The number of blackened cells for a region without a number is for you to determine.

The numbers on top of the diagram are for Answer purposes only. Any shading of the regions is purely for decorative purposes.

Answer: For each row from top to bottom, enter the column number of the left-most blackened cell. Use only the last digit for two-digit numbers; e.g., use ‘0’ for column 10. If none of the cells in a row are blackened, enter ‘0’ for that row.

Example Answer: 625324

Place a digit from 0 to 9 into each region so that each region has one digit. Regions with the same digit cannot touch along an edge. All areas where regions would touch diagonally are marked with a small circled 20; the digits in those four regions must sum up to 20. Some digits are already given to you.

Answer: For each designated row, enter the contents of all regions that are in (or partly in) that row, from left to right.

Example Answer: 56486,90579

0 3 2 0 2 4 3 2

3 2 1 316

0 3 2 0 2 4 3 2

16

7 2 8 6 4 5 6 2 4 9 0 7 5 9 2 9 4 2

7 8 6 4 9 59b

20

20 20 20

2020

20 20

20 20

9a

7 8 6 4 9 59b

20

20 20 20

2020

20 20

20 20

9a

1 2 3 4 5 6

6 2 5 3 2 4

2

1

1

2

17

1 2 3 4 5 6

2

1

1

2

17

2020ROUND 1WPF PUZZLE GP

17. Summon [Nikola Živanović] (67 points)

18. Nanro [Nikola Živanović] (88 points)

Place a digit from 1 to X into some cells, at most one digit per cell, so that each digit in the range appears exactly once in each bolded region. (The range of permitted digits will be provided to you above the grid.) The digits in the grid connect with horizontally and vertically adjacent digits to form multi-digit numbers. The numbers outside the grid indicate the sums of the numbers appearing in the respective rows and columns, where empty cells separate numbers.

Answer: For each designated row, enter its contents. Use “X” for empty cells.

Example Answer: 1X12X,X1X3X

Label some cells with numbers such that each bold region contains at least one labeled cell. Each number (including any given numbers) must equal the total count of labeled cells in that region. When two labeled cells from different regions are connected orthogonally, they must contain different numbers. All labeled cells are connected orthogonally. No 2×2 group of cells can be entirely labeled. Some cells may already be labelled for you.

While not required, it may be helpful to shade in the unlabeled cells (as in the displayed solution).

Answer: For each designated row, enter its contents, from left to right. Use ‘X’ for an unlabeled cell. Use only the last digit for two-digit numbers; e.g., use ‘0’ for a cell labeled with 10.

Example Answer: 616X1XX3,12X1XX34

6 6 6 6 1 3 3 6 1 6 1 3 1 1 2 3 2 1 2 1 3 1 2 1 3 4 1 2 1 3 4 2 1 2 3 3 4 1 2 1 2 2 4

6 3

3

3 2

3a

3b

6 3

3

3 2

3a

3b

25

1356

[1−3]

44 21 14 35

[1−3]

1 1 2 2 2 3 1 3 3 1 3 2 2 3 1

1b

1a

25

1356

[1−3]

44 21 14 35

[1−3]

1b

1a

2020ROUND 1WPF PUZZLE GP

19. Hideout Fences [Zoran Tanasić] (97 points)

20. Japanese Sums [Zoran Tanasić] (132 points)

Draw a single, non-intersecting loop that only consists of line segments between the dots along the dotted lines.

A number outside the grid indicates the sum of all numbers directly behind loop edges along that row (or column).

Answer: For each designated row, enter whether each cell (from left to right) is inside or outside the loop. Use ‘O’ for a cell inside the loop and ‘X’ for a cell outside the loop. You may use other letters or digits instead, as long as they are distinct from each other.

Example Answer: OOXO,XOOO

Place a digit from the specified list into some cells so that no digit appears more than once in each row or column. Cells may remain empty. Numbers outside the grid indicate all sums of continuous groups of digits (including “sums” of a single digit) along that row or column. These groups are separated by empty cells. These sums are given in the same order as their corresponding groups of digits.

Answer: For each designated row, enter its contents, using ‘X’ for an empty cell.

Example Answer: 7X1X4,127X5

2 2 1 2 2 3 2 1 2 0 1 0 2 2 2 1

6 2 3 5 3 3 0 3 2

1b

1a 2 2 1 2 2 3 2 1 2 0 1 0 2 2 2 1

6 2 3 5 3 3 0 3 2

1b

1a

3 11 6 13 2 19 1 24 7 8 18 7 1 4 10 5 5 14

3 4 2 6 7 5 4 2 7 1 4 1 2 7 5 5 6 1 7

{1–7}

1a

1b

3 11 6 13 2 19 1 24 7 8 18 7 1 4 10 5 5 14

{1–7}

1a

1b