spectrum agency test

8/9/2019 Spectrum Agency Test

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Spectrum Agency Test

37 problems

Time: 61 minutes

Questions

(1) You have to take three criminals back to the County Jail: Alexei

Asimov, Carlo Carlucci and Walter Trunch. You have to cross a river

on the way, and the boat only takes two people at a time. The trouble

is that if you leave the criminals together, Asimov will kill Trunch,

and Trunch will kill Carlucci. How can you get them safely across the

river?

(2) You have seven gold bars. However one of them is a counterfeit

and weighs less than the others. You have a set of balance scales but

you may only use them twice. How do you identify the counterfeit gold

bar?

(3) Calculate:

(4) The entrance to enemy HQ is protected by a special lock. To break

in you must arrange the numbers from 1 to 9 in a 3x3 square so thatif you add up the numbers in any row, column or along the two

diagonals the answers are all different.



(5) You are a Spectrum agent in space and you have an important

mission to visit 9 space stations. However after lift-off you

discover a glitch in your rocket boosters. The space craft will only

travel in straight lines and you only have enough energy to fire the

boosters four times, to make four changes of direction. Can youcomplete your mission?

(6) To break into enemy HQ you have to enter a number into the

keypad. You’ve been tipped off that the key is given by the next

number in the following sequence:

1, 11, 21, 1211…

What is the key?

(7) The precious emerald of Copan was first discovered in 25BC but it

went missing 50 years later and has never been since. What year did

the emerald disappear?

(8) You’ve been observing the entrance to an enemy missile launch

site trying to crack the secret to getting in. A scientist turns up

at the gate. The guard asks “Twelve?” and the scientist replies “six”and is let in. A second scientist arrives. This time the guard asks:

“Six?” The second scientist replies “Three” and is let in. You think

you’ve cracked it! So when you approach the gate and the guard asks

“Nine?” why did the guard sound the alarm when you answered “four and

a half”?

(9) There is a meeting for the 9 new agents who have joined Spectrum.

How many handshakes will it take for all the agents to meet each

other?

(10) You are out on a mission and need money to buy supplies. But

when you take out £100 from the Spectrum account you are told thatthe money left in the account has doubled. How much was in the

account before you withdrew the money?



(11) You have discovered a U-shaped detonator. In order to defuse the

bomb you must cut the detonator so that ALL the connections are cut.

But you only have time to make 2 straight cuts before the bomb will

explode. How do you defuse the bomb?

(12) Spectrum has nine cells arranged in a 3x3 square with connecting

windows. You’ve captured three gangs of three criminals: the leader,

second and third in command of the red, yellow and blue gang. You

have to arrange the prisoners so that no one from the same gang can

see each other and also so that no one of the same rank can see each

other. Call the prisoners from the red gang R1, R2, R3, from the

yellow gang Y1, Y2, Y3 and the blue gang B1, B2, B3.

(13) A spectrum agent travels to work on his motorbike at 30mph. Onhis return journey, the roads are clearer so he travels at 45 mph.

What is his average speed?

(14) Spectrum HQ has been surrounded and there is no way to bring in

more food. The trapped agents will have to survive on what they’ve

got inside. 40 agents would have enough food for 20 days. 30 agents

would have enough food for 30 days. How long will the food sustain 25

agents?

(15) Spectrum are holding a knock-out tennis tournament. There are 81

agents who enter. How many matches do you need to organize to find

the champion?



(16) You are out on a mission. You travel 5 km south, then 5 km west,

then 5 km north and find yourself back where you started! On your

mission you saw a bear. What colour was the bear?

(17) Count von Count has concocted an evil plan to take over the

world. Every month each member of his gang must recruit a new member.

So each month the gang doubles in size. How long would it take forthe whole population of the world to be in Count von Count’s gang?

(18) You are guarding Spectrum HQ and your shift begins at 12

midnight and finishes at 12 midnight the following day. You spend a

lot of time looking at your watch. How many times does the minute

hand pass over the hour hand?

(19) You are in the basement of Spectrum HQ. In front of you are

three light switches, all in their OFF position. One of the switches

is connected to a lightbulb in the room at the top of the building

but you don’t know which one. There’s no way you can check, unless

you climb the stairs. You have as much time as you need to play withthe switches in the basement, but you can only go upstairs once to

check on the state of the bulb. How can you tell with 100% certainty

which switch operates the bulb?

(20) You and fellow agent Bob Black have been captured by the enemy.

You are told that you are going to be blindfolded and taken into a

room where red or green hats are put on your heads. The blindfold

will be removed and then you have to write down on a piece of paper

(without talking to each other) the colour of your own hat. If any of

you gets his colour correct he can go free. Can you devise a strategy

with your fellow agent that will guarantee at least one of you goes

free?

(21) You have infiltrated a criminal gang that has stolen 100

diamonds from the state jewels. There are ten member of the gang

including you. Each gang member can propose a way to divide the

diamonds and a vote will be taken whether to accept the proposal. As

you are the newest member of the gang you are asked to go first. The

proposal is accepted if half the members or more vote for your

proposal. (You’re allowed to vote too). Otherwise you will be shot

and it’s the second most junior gang member who goes next. If he

loses the vote, he dies and it moves to Gang member number 3, and so

on until a Gang member wins the vote. What is your best strategy? You

certainly want to survive but you also want to take back as much of

the stolen diamonds as you can. Remember these gang members are veryclever, very greedy and none of them wants to die.

(22) Spectrum have sent you a new credit card but in order to find

out the PIN you have to crack the following mathematical puzzle: the

PIN is the smallest number that can be written as the sum of two cube

numbers in two different ways.

(23) It appears that Agent P might be working for the enemy. But in

order to get into the safe where he keeps his private documents, you

have to enter a string of 8 numbers. You’ve got 7 of them but what’s

the last number that will complete this sequence 13, 17, 31, 37, 71,

73, 79…?



(24) You have been caught by the enemy and trapped in a collection of

room full of doors. To free yourself you have to find a way to get to

the exit by going through all the doors once and once only. If you go

through a door twice the building blows up.

(25) Spectrum agents Bret and Emily and Chuck are all driving to a

Clairvoyant’s concert. They set off an hour before the concert. Bret

takes route A which is twice as long as Emily’s route B but the

average of their two routes is the same as Chuck’s route C. Trouble

is Bret gets lost and goes 10 miles out of his way, meaning he ends

up traveling as much as the combined distance Chuck and Emily travel.

Assuming they all drive at 40 miles an hour, how late is Brett for

the concert?

(26) In the Spectrum canteen today’s special dish of the day has got

a special price: “Cryptic Curry costs £2 plus half its price”. How

much does Cryptic Curry cost?

(27) You are on a mission to the snowy Alps. Your skis are 5 feet

long but the Spectrum jet that is due to take you to the Alps does

not allow any luggage that is over 4 feet by 3 feet so the pilot

refuses to take you. How can you get to the mission on time?

(28) You have to cross a crocodile-infested river. There are 40

stepping stones that you can jump across to get to the other side,

but you notice that there are crocodiles next to every sixth stone.

You can jump up to 10 stones ahead at a time, but you must jump the

same number of stones ahead with each jump. How many stones shouldyou jump each time to get to the other side without being eaten by a

crocodile?

(29) You are trying to break into an enemy agent’s apartment, but to

open the door you must place a hexagon against the entry pad.

However, all you have is a cube. How can you cut a cube with one cut

to reveal a hexagonal face that you can use to break into the

apartment?

(30) An enemy agent has just jumped on board a moving freight train.

The train is one mile long and is travelling at 15 miles an hour. It

is just about to enter a tunnel which is also one mile long. You need

to get to the other end of the tunnel before the whole train has

passed through. How long does it take for the train to passcompletely through the tunnel?



(31) You are on a mission with three Spectrum agents and a sniffer

dog. You reach a river, but the boat to cross it can only take a

maximum of 150 pounds in weight. You and agent X weigh 75 pounds but

agents Y and Z each weigh 150 pounds. How many trips will it take to

get all the agents (and the dog) across the river?

(32) While on a mission in a forest you realise that the enemy haveset fire to the forest and it is spreading rapidly in your direction,

aided by a strong westerly wind. You have no transport and no water

to put the fire out. All you have is box of matches. How can you save

yourself from the approaching fire?

(33) What’s the next symbol in this sequence?



S p e c t r u m A g e n c y T e s t

S o l u t i o n s

( 1 ) S o l u t i o n : F i r s t t a k e T r u n c h a c r o s s t h e r i v e r . A s i m o v a n d C a r l u c c i a r e s a f e

t o g e t h e r . T h e n t a k e A s i m o v a c r o s s b u t s i n c e y o u c a n ’ t l e a v e A s i m o v a n d T r u n c h

t o g e t h e r y o u m u s t b r i n g T r u n c h b a c k . T h e n t a k e C a r l u c c i a c r o s s t h e r i v e r .

F i n a l l y c o m e b a c k f o r T r u n c h . E v e r y o n e i s s a f e l y o n t h e o t h e r s i d e .

( 2 ) S o l u t i o n : P u t t h r e e b a r s o n e a c h s i d e o f t h e s c a l e s . I f t h e y b a l a n c e t h e n

t h e g o l d b a r y o u d i d n ’ t p u t o n t h e s c a l e s i s t h e c o u n t e r f e i t . O t h e r w i s e t a k e

t h e t h r e e b a r s t h a t a r e l i g h t e s t o n t h e s c a l e s . T a k e t w o o f t h e s e b a r s a n d p u t

t h e m o n e i t h e r s i d e o f t h e s c a l e s . I f t h e y b a l a n c e , t h e n t h e b a r y o u d i d n ’ t

p u t o n t h e s c a l e s i s t h e c o u n t e r f e i t . O t h e r w i s e , t h e l i g h t e r o f t h e t w o b a r s

i s t h e c o u n t e r f e i t .

( 3 ) S o l u t i o n : 4 2

( 4 ) S o l u t i o n : T h i s i s t h e o p p o s i t e t o a m a g i c s q u a r e w h e r e a l l t h e r o w s , c o l u m n s a n d d i a g o n a l s a d d u p t o t h e s a m e n u m b e r . T h e r e a r e a c t u a l l y l o t s o f

s o l u t i o n s ( 2 4 9 6 0 t o b e p r e c i s e ) . H e r e ’ s a n i c e o n e w h e r e y o u a r r a n g e t h e o t h e r

n u m b e r s i n i n c r e a s i n g o r d e r i n a s p i r a l s t a r t i n g w i t h 1 i n t h e m i d d l e :



( 5 ) S o l u t i o n :

( 6 ) S o l u t i o n : 1 1 1 2 2 1 . E a c h n u m b e r d e s c r i b e s t h e p r e v i o u s n u m b e r . O n e ; o n e “ o n e ” ;

t w o “ o n e s ” ; o n e “ t w o ” a n d t w o “ o n e s ” .

( 7 ) S o l u t i o n : M o s t p e o p l e ’ s r e s p o n s e i s 2 5 A D b u t t h a t i s i n c o r r e c t ! T h e r e w a s n o

y e a r 0 s o a c t u a l l y t h e e m e r a l d w e n t m i s s i n g i n 2 6 A D .

( 8 ) S o l u t i o n : Y o u s h o u l d h a v e a n s w e r e d “ f o u r ” , t h e n u m b e r o f l e t t e r s i n t h e

q u e s t i o n .

( 9 ) S o l u t i o n : A g e n t 1 s h a k e s 8 a g e n t s ’ h a n d s . A g e n t 2 h a s a l r e a d y s h a k e n h a n d s

w i t h a g e n t 1 s o o n l y h a s t o s h a k e 7 m o r e h a n d s . C o n t i n u i n g l i k e t h i s w e n e e d 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

= ( 8 + 1 ) + ( 7 + 2 ) + ( 6 + 3 ) + ( 5 + 4 )

= 4 x 9

= 3 6 h a n d s h a k e s .

( 1 0 ) S o l u t i o n : t h e a c c o u n t w a s £ 1 0 0 o v e r d r a w n . W h e n y o u w i t h d r e w £ 1 0 0 i t b e c a m e

£ 2 0 0 o v e r d r a w n : ( - 1 0 0 ) x 2 = - 2 0 0 .

( 1 1 ) S o l u t i o n : F i r s t c u t a l o n g l i n e A B . T h e n p u t t h e t h r e e p i e c e s t o g e t h e r s u c h

t h a t l i n e s C D a n d E F l i n e u p a n d y o u c a n c u t a l o n g t h e c o m b i n e d l i n e i n a s i n g l e

c u t .



( 1 2 ) S o l u t i o n : t h i s i s o n e p o s s i b l e w a y t o a r r a n g e t h e p r i s o n e r s :

( 1 3 ) S o l u t i o n : 3 6 m i l e s p e r h o u r . M o s t p e o p l e t h i n k t h e a n s w e r i s

3 7 . 5 m i l e s p e r h o u r – a n a n s w e r o b t a i n e d b y a d d i n g t h e s p e e d s

t o g e t h e r , 3 0 + 4 5 = 7 5 – a n d t h e n d i v i d i n g i n b y t w o , t o o b t a i n a s i m p l e

a v e r a g e . B u t t h a t i s w r o n g .

S p e e d i s a c t u a l l y w o r k e d o u t t h r o u g h a s i m p l e f o r m u l a – d i s t a n c e

d i v i d e d b y t i m e . S o s u p p o s e t h e d i s t a n c e f r o m t h e a g e n t ’ s h o m e t o

S p e c t r u m H Q i s 4 5 m i l e s . T h i s w o u l d t a k e 1 . 5 h o u r s i n t h e m o r n i n g a n d

1 h o u r o n t h e w a y h o m e . T h e a v e r a g e s p e e d w o u l d t h e n b e d i s t a n c e –

4 5 + 4 5 = 9 0 m i l e s – d i v i d e d b y t i m e – 1 + 1 . 5 = 2 . 5 h o u r s . T h i s g i v e s u s t h e

a n s w e r 9 0 / 2 . 5 = 3 6 m i l e s p e r h o u r . Y o u g e t t h e s a m e a n s w e r h o w e v e r f a r

t h e d i s t a n c e i s b e t w e e n S p e c t r u m H Q a n d t h e a g e n t ’ s h o m e .

( 1 4 ) S o l u t i o n : 4 0 d a y s . M a n y p e o p l e t h i n k t h e a n s w e r i s 3 5 , b u t

t h a t ’ s b e c a u s e t h e y a r e a s s u m i n g t h a t t h e r e i s a d i r e c t r e l a t i o n b e t w e e n a g e n t s a n d d a y s . B u t a c t u a l l y i t i s a n i n v e r s e r e l a t i o n . T h e

m o r e a g e n t s y o u p u t i n , t h e l e s s d a y s t h e f o o d s u r v i v e s . T h i s m e a n s

t h a t i f y o u p l o t a g r a p h w i t h n u m b e r o f a g e n t s o n o n e a x i s a n d t h e

i n v e r s e o f t h e d a y s o n t h e o t h e r , y o u w i l l g e t a s t r a i g h t l i n e . ( T h e

i n v e r s e o f a n u m b e r m e a n s y o u c a l c u l a t e 1 d i v i d e d b y t h a t n u m b e r : t h e

i n v e r s e o f 2 0 i s 1 / 2 0 . ) W e c a n m a r k t w o p o i n t s o n t h e g r a p h : t h e

f i r s t p o i n t i s a t 4 0 a g e n t s a n d 1 / 2 0 f o r t h e i n v e r s e o f t h e d a y s ; t h e

s e c o n d p o i n t i s a t 3 0 a g e n t s a n d 1 / 3 0 d a y s . D r a w a s t r a i g h t l i n e

t h r o u g h t h e s e t w o p o i n t s . H o w h i g h i s t h e g r a p h a b o v e 2 5 a g e n t s ? T h e

a n s w e r i s 1 / 4 0 . S o t h a t m e a n s i f t h e r e a r e 2 5 a g e n t s t h e n t h e f o o d

i n s i d e S p e c t r u m H Q w o u l d l a s t f o r 4 0 d a y s .



( 1 5 ) S o l u t i o n : 8 0 m a t c h e s . T h i s i s b e c a u s e e a c h a g e n t l o s e s o n c e –

e x c e p t f o r t h e c h a m p i o n .

( 1 6 ) S o l u t i o n : W h i t e . T h e o n l y p l a c e o n t h e e a r t h w h e r e y o u c a n g o

s o u t h 5 k m t h e n w e s t 5 k m t h e n n o r t h 5 k m a n d e n d u p w h e r e y o u s t a r t e d

i s t h e n o r t h p o l e . W h e n y o u g o s o u t h y o u a r e o n a l i n e o f l o n g i t u d e .

G o i n g w e s t y o u r u n a l o n g a l i n e o f l a t i t u d e . T h e n h e a d i n g n o r t h y o u

a g a i n d r o p d o w n a l i n e o f l o n g i t u d e . T h e o n l y b e a r s a t t h e n o r t h p o l e a r e p o l a r b e a r s . S o t h e b e a r w a s w h i t e .

( 1 7 ) S o l u t i o n : O n l y 3 3 m o n t h s . E a c h m o n t h t h e g a n g d o u b l e s i n s i z e .

S o a f t e r o n e m o n t h t h e r e a r e 2 g a n g m e m b e r s , a f t e r t w o m o n t h s t h e r e

a r e 4 m e m b e r s , a f t e r 3 m o n t h s t h e r e a r e 8 m e m b e r s . I f y o u k e e p o n

d o u b l i n g t h e n a f t e r o n l y 3 3 m o n t h s t h e r e a r e a l r e a d y o v e r 8 b i l l i o n

g a n g m e m b e r s . T h e p o p u l a t i o n o f t h e e a r t h i s a p p r o x i m a t e l y 6 . 7

b i l l i o n . D o u b l i n g m a k e s t h i n g s v e r y b i g v e r y q u i c k l y .

( 1 8 ) S o l u t i o n : 2 1 t i m e s . B e t w e e n 1 2 m i d n i g h t a n d 1 a m t h e h a n d s d o n ’ t

c r o s s . T h e n b e t w e e n 1 a m a n d 2 a m t h e h a n d s c r o s s o n c e , j u s t a f t e r

1 : 0 5 . D u r i n g e a c h h o u r t h e h a n d s c r o s s o n c e u n t i l 1 1 a m . S o t h a t ’ s 1 0

t i m e s . T h e s l i g h t l y u n e x p e c t e d t h i n g i s t h a t b e t w e e n 1 1 o ’ c l o c k a n d 1

o ’ c l o c k t h e m i n u t e h a n d p a s s e s o v e r t h e h o u r h a n d o n l y o n c e – a t m i d d a y . F r o m 1 p m t o 1 1 p m t h e h a n d s a g a i n c r o s s 1 0 t i m e s . T h e n i n t h e

f i n a l h o u r t h e y d o n ’ t c r o s s . S o t h a t ’ s a t o t a l o f 2 1 t i m e s .

( 1 9 ) S o l u t i o n : T u r n s w i t c h n u m b e r 1 a n d 2 O N . A f t e r a f e w m i n u t e s

t u r n O F F s w i t c h n u m b e r 2 . N o w g o u p s t a i r s .

I f t h e b u l b i s O N , i t ’ s s w i t c h n u m b e r 1

I f t h e b u l b i s O F F b u t W A R M , s w i t c h n u m b e r 2 o p e r a t e s i t .

I f t h e b u l b i s O F F a n d C O L D , i t ’ s s w i t c h n u m b e r 3 .

( 2 0 ) S o l u t i o n : Y o u w r i t e d o w n t h e c o l o u r o f A g e n t B o b ’ s h a t . A g e n t

B o b w r i t e s d o w n t h e o p p o s i t e o f y o u r h a t . B o t h o f y o u c a n ’ t b o t h b e



w r o n g . ( Y o u a l s o c a n ’ t b o t h b e r i g h t ) . S o o n e a g e n t e x a c t l y g o e s

f r e e .

( 2 1 ) S o l u t i o n : Y o u j u s t n e e d f o u r g a n g m e m b e r s t o v o t e f o r y o u s i n c e

i n c l u d i n g y o u r v o t e t h a t w i l l b e 5 v o t e s t o 5 a n d t h e p r o p o s a l i s

p a s s e d . S o y o u p r o p o s e t o g i v e G a n g m e m b e r s 3 , 5 , 7 a n d 9 o n e d i a m o n d

e a c h a n d y o u k e e p t h e o t h e r 9 6 d i a m o n d s . W h y d o y o u g e t t h e v o t e o f

G a n g m e m b e r s 3 , 5 , 7 a n d 9 ? B e c a u s e t h e y r e a l i s e t h a t u n l e s s t h e y v o t e f o r y o u , t h e y w i l l e n d u p g e t t i n g n o t h i n g o r b e i n g s h o t . F o r

e x a m p l e , i m a g i n e t h e r e w e r e j u s t t h r e e g a n g m e m b e r s . Y o u o f f e r g a n g

m e m b e r 3 o n e d i a m o n d . H e w i l l v o t e f o r y o u b e c a u s e o t h e r w i s e y o u g e t

s h o t , a n d t h e n G a n g m e m b e r 2 p r o p o s e s t o k e e p t h e l o t , v o t e s f o r

h i m s e l f a n d g i v e s G a n g m e m b e r 3 n o t h i n g .

( 2 2 ) S o l u t i o n : 1 7 2 9 . B e c a u s e 1 7 2 9 = 1 2 3 + 1 3 = 1 0 3 + 9 3 .

( 2 3 ) S o l u t i o n : 9 7 . A g e n t P i s a b i g f a n o f p r i m e n u m b e r s , n u m b e r s

t h a t a r e o n l y d i v i s i b l e b y t h e m s e l v e s a n d 1 . T h e s e q u e n c e o f n u m b e r s

i n h i s s a f e c o d e i s m a d e u p o f t h e r e v e r s i b l e p r i m e s , p r i m e n u m b e r s

t h a t g i v e a n o t h e r p r i m e n u m b e r w h e n y o u r e v e r s e t h e i r d i g i t s .

( 2 4 ) S o l u t i o n :

( 2 5 ) S o l u t i o n : f i f t e e n m i n u t e s .

( 2 6 ) S o l u t i o n : £ 4 . M a n y p e o p l e t h i n k i t ’ s £ 3 b u t t h a t ’ s n o t r i g h t . I f

c u r r y c o s t s C p o u n d s t h e n C = 2 + C / 2 . P u t C = 4 a n d t h e e q u a t i o n i s r i g h t : 2 + 4 / 2 = 2 + 2 = 4 .

( 2 7 ) S o l u t i o n : G e t a 4 f o o t b y 3 f o o t r e c t a n g u l a r b o x a n d p u t t h e 5

f o o t s k i e s d i a g o n a l l y i n s i d e t h e b o x . W h o s a i d P y t h a g o r a s w a s n ’ t

u s e f u l !

( 2 8 ) S o l u t i o n : 7 s t e p s a h e a d . T h e f i r s t n u m b e r d i v i s i b l e b y b o t h 6

a n d 7 i s 4 2 s o y o u w i l l g e t t o t h e o t h e r s i d e w i t h o u t m e e t i n g a

c r o c o d i l e . A l l t h e o t h e r c h o i c e s f a i l . F o r e x a m p l e , i f y o u j u m p 9

s t e p s a h e a d t h e n y o u w i l l m e e t a c r o c o d i l e a t t h e 1 8 t h s t o n e .

( 2 9 ) S o l u t i o n : I m a g i n e h a n g i n g t h e c u b e f r o m o n e o f t h e c o r n e r s . I f

y o u c u t t h e c u b e h o r i z o n t a l l y b e t w e e n t h e p o i n t a t t h e t o p a n d p o i n t



c u t s a l l s i x f a c e s . E a c h f a c e c o n t r i b u t e s a n e d g e t o t h e n e w f a c e .

T h e s h a p e s h o u l d b e s y m m e t r i c a l . H e n c e y o u g e t a h e x a g o n .

( 3 0 ) S o l u t i o n : 8 m i n u t e s . W h e n t h e f r o n t e n d o f t h e t r a i n e n t e r s t h e

t u n n e l , t h e w h o l e l e n g t h o f t h e t r a i n i s s t i l l o u t s i d e t h e t u n n e l .

A f t e r t h e t r a i n t r a v e l s o n e m i l e , t h e f r o n t e n d l e a v e s t h e t u n n e l ,

b u t t h e w h o l e l e n g t h o f t h e t r a i n i s i n s i d e t h e t u n n e l . A f t e r i t

t r a v e l s a s e c o n d m i l e t h e r e a r e n d o f t h e t r a i n l e a v e s t h e t u n n e l . S o

t h e t i m e i t t a k e s t o p a s s t h r o u g h t h e t u n n e l i s t h e t i m e i t t a k e s t o

t r a v e l 2 m i l e s . T h e t r a i n d o e s 1 m i l e i n 4 m i n u t e s s o t h e t o t a l t i m e

t o p a s s t h r o u g h t h e t u n n e l i s 8 m i n u t e s .

( 3 1 ) S o l u t i o n : 1 1 . F i r s t y o u a n d a g e n t X c r o s s . Y o u r e t u r n . A g e n t Y

c r o s s e s . A g e n t X r e t u r n s . T h e n b o t h y o u a n d a g e n t X c r o s s a g a i n . Y o u

r e t u r n . A g e n t Z c r o s s e s . A g e n t X r e t u r n s . B o t h y o u a n d a g e n t X c r o s s

a g a i n . Y o u r e t u r n . Y o u a n d t h e d o g c r o s s .

( 3 2 ) S o l u t i o n : U s e t h e m a t c h e s t o s e t f i r e t o t h e g r o u n d w h e r e y o u

a r e . T h e n w a l k w e s t t o w a r d s t h e m a i n f i r e . T h e w i n d w i l l b l o w y o u r

f i r e f u r t h e r e a s t , t h u s b u r n i n g o u t t h e l a n d t o t h e e a s t o f y o u . T h e n

w a l k b a c k t o t h e b u r n t a r e a o f l a n d a s t h e m a i n f i r e a p p r o a c h e s . I t

i s i m p o s s i b l e f o r t h e f i r e t o c a t c h l i g h t h e r e , a s t h e r e i s n o t h i n g l e f t t o b u r n .

( 3 3 ) S o l u t i o n :

I t ’ s t h e n u m b e r s n e x t t o t h e i r m i r r o r i m a g e s a t t h e b o t t o m y o u h a v e

t w o p i e c e s e a c h w i t h a n e w f a c e . T h e s l i c e

spectrum agency test

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