the big brain workout

THE BIG BRAIN
WORKOUT
Improve your memory and
strengthen your mind
PART 1
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From Arabic and beekeeping, to yoga and Zulu whatever you
want to learn, Teach Yourself has the answer.
Introduction
Contents
Welcome to part one of The Big Brain Workout, The
Telegraph’s guide to keeping your brain healthy. In
this booklet, you’ll find more than 50 puzzles to test
your IQ, numeracy, visual awareness and logic. All are
designed to enhance your mental agility and improve
your memory.
Introduction
3
Diet, exercise and
lifestyle4
The workouts
IQ workout
Numerical thinking Logical thinking
Visual thinking
Cryptic crossword
There are useful tips throughout the booklet to help
sharpen your skills and prepare you for psychometric
tests used by some employers, plus a cryptic
Telegraph crossword to challenge your deductive
language skills. There’s even a diet and lifestyle
section that gives advice on how nutrition and
hydration affect your cognitive capacity.
6
12
16
20
24
Answers
IQ workout
26
Numerical thinking
28
Crossword28
Logical thinking
29
Visual thinking
30
If you get stuck, there are tip boxes throughout and
you can always look up the answers at the back of
the booklet.
Don’t miss part two of The Telegraph’s Big Brain
Workout in tomorrow’s newspaper. It contains more
creative, verbal and memory puzzles to test your
reasoning (and patience), plus seven Sudoku grids
to help improve your numerical, visual and criticalthinking skills.
Good luck!
P.S. Visit telegraph.co.uk/brainworkout for
additional lifestyle tips, offers and more.
DON’T MISS THE SECOND PART
OF THE BIG BRAIN WORKOUT
The second brain-training booklet in
tomorrow’s newspaper contains more
than 50 IQ, creative and numerical
puzzles, as well as a Toughie Telegraph
crossword. There are also more diet and
lifestyle tips to help keep your brain
functioning at capacity.
The Big Brain Workout
Over
50
questions
3
diet, exercise & lifestyle
Your brain responds to what you eat and drink, and it can adapt its structure
depending on how often you exercise, drink alcohol or smoke. B vitamins, for
example, help form new neurotransmitters. They can be found in berries, spinach,
green cabbage, broccoli and watercress.
Fish, eggs and other sources of protein make a good breakfast, although you
should avoid breads and cereals unless they are wholegrain. Drink fruit juice for
the vitamins and water to stay hydrated.
For lunch, try oily fish like mackerel and salmon with salad or raw vegetables. If you
must have dessert, fresh fruit is preferable to biscuits and pastries.
Eat pasta and wholemeal breads or cereal in the evening to provide energy for
the following day. Simple sugars increase the serotonin in the brain and may
help you sleep.
Avoid saturated transfats as they are difficult for the body to break down, deprive
the brain of oxygen and inhibit the uptake of essential unsaturated fatty acids.
Boost cognitive function and improve your memory with folic acid and selenium
in dark leafy vegetables, seafood and wholegrain breads.
Boron, iron and zinc can also improve mental capacity. Boron can be found in
pears, peaches and grapes; zinc in fish, meats, cereal and whole grains; and the iron
in meat and fish is more readily absorbed by the vitamin C in citrus fruits and salad.
4
The Big Brain Workout
The amount of sleep people need varies, but it’s usually from five to eight hours.
Quality rather than quantity is more important for brain health, although this can
be affected by babies, stress or snoring. Try to remove televisions and radios from
the bedroom (or turn them off completely) and use breathing exercises to relax.
Alcohol reduces the body’s stores of vitamin B1, which affects our ability to
think. It also leads to overconfidence, distraction and error-proneness, results in
dehydration and contributes to short-term memory loss.
Smokers seem convinced that a cigarette keeps them mentally alert but smoking
reduces the oxygen-carrying capacity of the blood, limiting the amount of oxygen
that reaches the brain. In the long-term, lung damage severely restricts the amount
of oxygen the blood can absorb.
Anaerobic exercise produces serotonin, which relaxes you and helps you sleep.
Exercises that involve controlling your breathing – like holding yoga positions –
typically produce elongated brainwaves with higher peaks.
The Big Brain Workout
5
IQ WORKOUT
Introduction
There are several kinds of intelligence, most of which continue to develop during our
lifetimes. Unfortunately, many employers still use traditional verbal, numerical and spatial
IQ tests to assess an applicant’s suitablity for a role, which, while they may be important
when discussing overall intelligence, ignore creativity, memory, the ability to predict
behaviour and general knowledge. These skills improve as you age, and life satisfaction has
been found to be more closely linked with emotional intelligence than high IQ scores.
The following puzzles will test your mental agility and reasoning.
Q1. Boxes and coins
Q2. The spider and the fly
Each label is incorrect. You need to relabel each box correctly after removing
a single coin from one box without
looking inside.
What is the shortest distance the spider
can walk to reach the fly (the room is
30m × 12m × 12m)? The spider is 1m from
the floor. The fly is 1m from the ceiling.
All copper coins
12m
Copper and
silver coins
30m
All silver coins
12m
6
The Big Brain Workout
Q3. Getting to the root of the problem
A garden has 12 trees in a row. How could they be uprooted and replanted to make
six rows with four trees in each row?
Q4. Give me one honest person
The man in the road needs to find one honest person. He knows that one side of the
road is Truth Land where everyone always tells the truth, and the other side is False
Land where everyone always lies. He asks Mr A to ask Mrs B which side of the road she
lives on. Mr A returns saying that Mrs B says she is from Truth Land. Is Mr A honest?
B
Truth Land
False Land
A
The Big Brain Workout
7
Q5. Cash
You are a cashier and one customer has shaved 1g of gold off each of the gold coins in
one of their 10 bags. All the bags contain the same number of coins. How can you find
the bag with the shaved coins in one weighing?
Q6. Eight small rectangles
Remove four lines to leave eight small rectangles.
Is it wise to eat sage?
Apparently, if you rip sage leaves into small pieces and add a teaspoon of the ripped
leaves to a cup of boiling water, you will feel the benefit if you sip the drink during
examinations, tests or presentations. Sage inhibits the breakdown of acetylcholine,
which the brain uses when it’s working.
8
The Big Brain Workout
IQ WORKOUT
Q7. What time is it, Mr Wolf?
Which clock, A, B, C or D, completes the series?
Series
A
B
C
D
Q8. Stacking pyramids
Move three lines only to make five triangles.
The Big Brain Workout
9
Q9. Where next?
Where should the next • go (given that the
first • was placed in the top triangle)?
Q10. Topsy-turvy words
When you insert the missing letters you will discover a way of thinking that makes
you more intelligent.
N
T
I
E
L
Y
I
E
N
K
Y O W A
E N O T
R
E
A
P
I
P
Q11. The one-match trick
Move one match to balance the equation.
10
The Big Brain Workout
C O A
E T Y
IQ WORKOUT
Q12. Half full and half empty
How can you change this line of seven glasses so that they alternate full and empty?
You may only touch one glass.
Q13. Water bottles
Three Bedouins travelling together in the desert decided to go their separate ways.
Between them they had seven full, seven half full and seven empty water bottles. The
bottles each held five litres. They decided to divide their water and the 21 bottles
equally between them. How did they do it?
Can you boost your IQ?
Learning different skills helps build new
neuron connections, and practising old
skills leads to thicker myelin insulation
on each pathway. What you learn will
increase your general knowledge and
capacity for creative thinking.
Q15. Refusing to pay for bad service
A restaurant’s royal customer waited
43 minutes for the waiter to take her
order. Finally, she got up and left, so
the manager asked if she had paid her
bill. She shook her head and wrote this
explanation:
10004180204
Q14. What day is it?
In summer, water lilies double their area
every 24 hours, so that on day 30 the
pond is covered. The first lily appeared
on the first day of the month and the
pond is now half covered. What day
of the month is it?
The Big Brain Workout
What did she mean?
11
Numerical
THINKING
Introduction
If you work in business, it seems self-explanatory that you will need to be numerate as
you will be analysing profits, losses, balances, returns and cash. It may be less obvious
why those working in the public service or charity sectors need numeracy skills, but basic
maths is essential for quality control, project management and service planning.
While the ability to make meaningful estimates lies at the heart of maths, accurate mental
arithmetic is more important as engineers, accountants, architects and scientists all work
from precise figures, while fund managers, bankers and analysts need to make forecasts
relating to the economy.
Practising your times tables, plus basic addition, subtraction and division, can help
revitalise dormant neural connections within the brain, increasing intelligence, memory
and cognitive capacity. The questions on these pages will test numeracy and reasoning.
Q1. The Tutonton pyramid
This is a sketch of the profile through
the centre of a pyramid. It has
a square base with an area of 81
square metres. Each block weighs
approximately 1,212 kg.
How tall is the pyramid? How broad
is the pyramid? How many metrecube blocks were needed to build
the Tutonton pyramid? And how
much does it weigh?
Q2. Balancing act
How many triangles will balance scale C (distance from fulcrum is not a factor)?
A
12
B
C
The Big Brain Workout
Q3. A distance too far
Q4. Cracking the code
How far away is London?
Fill in the blank circles.
3
York 50km
1
3
6
5
1
4
5
8
Oslo 60km
Paris 70km
Madrid 80km
Q5. Clocking on
If A = 3 o’clock, what time will clock F show?
A
B
C
E
F
The Big Brain Workout
D
13
Q6. Roll out the barrel
Q7. Sands of time
You only have a torch to determine
whether a wooden barrel is more than
or less than half full. How will you do it?
You need to measure a quarter of an
hour and you have two sand glasses.
One takes 11 minutes to empty, the
other seven minutes. How can you use
them to measure your quarter hour?
Q8. Seeing spots
This is the top die on a single stack of
10 dice. How many dots are visible on
the stack?
Q9. The magic shrinking flute
A musician doesn’t want to check his precious 48cm flute in as hold luggage, but an
officious security officer is limiting the length of hand luggage to 40cm. How can the
musician legally carry his flute on board as hand luggage?
Sleep
Most people have a natural sleep time that varies between five and eight hours. If
you sleep for less than this natural time, your performance in IQ tests is likely to fall.
If this pattern continues for a few nights, your IQ can fall by up to 15 points. This can
impair your ability to learn important information, as well as adversely affecting your
ability to drive or react to unusual circumstances. A study at Southampton University
found that maintaining a sleeping routine was beneficial for cognitive function,
while the University of Perth has backed up the claim that afternoon power naps
can improve performance.
14
The Big Brain Workout
NUMERICAL THINKING
Making number skills count
Numeracy can be improved by playing games like backgammon, cards, darts and
dominoes, as well as by comparing prices by weight in supermarkets or by splitting
the bill in a restaurant. The skills involved in games like backgammon help the brain
recognise numerical patterns, and learning the scoring system in darts helps us to add,
subtract and multiply large numbers with confidence. Mastering basic maths can help
us compute, estimate and quantify. These are the skills that develop the parts of the
brain dealing with memory and logic.
Q10. All the threes
Put a 2 in the centre of the grid below and then select from only three other numbers,
other than 2 and 3, to make each row, column and diagonal add up to 10. Which three
numbers will work?
3
3
3
3
3
3
3
3
3
3
The Big Brain Workout
15
LOGICAL
THINKING
Introduction
The foundation of logic is based on the three I’s, which shows the way we move from
Information via Inferences to Implied action. Applied thinking involves using critical,
creative and reflective reasoning to assess whether the information we receive is true. We
can then process this information, turning it into knowledge on which we can act. We can
use critical thinking to assess whether inferences are reasonable, but we must use caution
to verify the accuracy and relevance of information before forming an opinion.
In deductive logic, reasonableness = a justified belief + a valid conclusion.
In inductive logic, reasonableness = a justified belief + a probable conclusion.
Q1. Brazil for the cup?
Q2. English football fans abroad
Consider the following, which was
overheard on the street: “Brazil have a
better chance of winning than Germany
or France, or even Argentina. Therefore,
they will probably win the World Cup.”
English fans will probably cause trouble
at the World Cup so England could be
expelled, maybe not from the World
Cup itself but certainly from the next
European Championships. Therefore, it
is unlikely that England will be playing in
the next European Championships.
A.Is this statement deductively valid?
B.Is this statement inductively
reasonable?
C.What useful change could you make
to the statement?
A.Is this deductively valid?
B. Is this inductively reasonable?
C.How could you write it as an
inductively reasonable argument?
D.How would you need to write it as
a deductively reasonable argument?
Q3. Theatrical confusion
When you say “go nurse”, which medic stirs?
Q4. Moon starer
Q5. Hearing
At certain times of the month he (or she)
may be a moon starer.
Can you hear four vowels and a D,
if not ‘goodbye’?
16
The Big Brain Workout
Q6. Letter puzzle
These letters ZAYXWBCDEFGVUTSRQHIPJONMK scream Christmas.
Q7. Can you throw any light on this?
Which switch controls which light? The switches are outside the room and you can only
enter the room once. How will you find out?
Becoming a critical friend
You should try to develop your creative, critical and reflective thinking. Critical
thinking is not as destructive as it sounds. The aim is to question the information you
receive, and the person delivering it, so that you can use the knowledge to reach more
accurate conclusions.
The Big Brain Workout
17
Q8. Is this fair?
If he were to give her £300 of what he earns per month, they would earn the same, but
if she were to give him £300 of what she earns, he would earn five times what she earns?
What do they each earn?
Q9. Will you blow it?
The bridge will be blown up at midnight. It is now 22.50. You can only cross with a
torch. There is only one torch and only two people can share it at any time. You are fit
and it only takes you four minutes to cross the bridge. Your colleagues are slow: B takes
eight minutes, C 30 minutes and D 40 minutes. How can you get everyone safely across
the bridge before midnight?
Q10. Board meeting
How many queens can you place on a chess board without one threatening another?
(Queens can move horizontally and on the diagonal.)
Q1 1. And the last shall be… Last
Q1 2. Who’s lying?
Runner 4 is faster than runner 1. Runner
2 is faster than runner 3. Runner 3 is
slower than runner 1. Who will be last?
Larry always lies. Tommy always tells the
truth. Which one of them said of the
other, “He claims he’s Larry.”?
Q13. Have room for a DB5 Volante
A collector of vintage cars wants to expand his collection so he increases the size of
his air-conditioned garage by 50 per cent. Each car on average is 15ft (4.5m) long and 6ft
(2m) wide. During the auction season, the collector acquires four more cars and fills the
garage. How many cars does the collector have now?
More likely than not
Applied thinking is the kind of thinking that allows you to turn information into
knowledge on which you can act. In the practical world, inductive logic is more useful
than deductive logic.
18
The Big Brain Workout
LOGICAL THINKING
Past, present and future
Applied thinking allows you to make decisions that other people see as intelligent. It
helps you to learn new skills, solve problems, assess risk and make practical plans for
the future. These plans are based on your reading of situations to form valid opinions.
You can improve your ability to think by questioning the accuracy of information. This
involves uncovering assumptions, questioning the validity and motivation of sources,
and checking your perceptions against those made by others.
Through creative and reflective thinking, you can list insights, interpretations,
principles, lessons, ideas and conclusions. You can then test your hypotheses using
deductive and inductive logic. If your plans are affordable, ethical and likely to be
effective, they can then be implemented.
Q14. Lord of the ring cycle
When Richard Wagner enrolled for a course, he was asked a question, to which he
replied “9-W”. What was the question?
Q15. The brain train
The brain trains run from A to B, one a minute, 24 hours a day. The return journey at the
same speed takes one hour. How many trains do you pass on the journey from A to B?
Q16. The Monty Hall problem
You reach the final stage of a gameshow and the host shows you three doors. Behind
one is a car, behind the other two, nothing. The host asks you to pick a door to try to
win the car. You choose door A. The host then opens door B to reveal nothing. The
host now offers you the chance to stick with your original choice (A) or switch to door
C. He knows what is behind each door but he’s acting in good faith and is not trying to
influence your decision. What should you do?
The Big Brain Workout
19
VISUAL
THINKING
Introduction
Visual processing is one of the brain’s most important functions. Research shows that even
those who are visually impaired can maintain visual brain health by imagining images.
Visualisation also plays an important role in improving memory, creative thinking, ethical
thinking and empathy.
Reflective thinking relies on you perceiving what you saw, heard and felt to be real. It helps
you turn those experiences into lessons and ideas that you believe to be true, and which
allow you to formulate the actions that guide how you behave in the future. Predictive
thinking draws on many skills, the most important of which is visual thinking.
Problems and puzzles involving visualisation and prediction are the bread and butter
of serious brain-trainers. Those in this section aim to test how visual thinking helps
prediction and reflection.
Q1. Which kite will fly?
Which of these box kites will fly?
O
R
E
O
View A
20
X
X
X
O
View B
E
E
E
R
X
View C
X
R
X
View D
The Big Brain Workout
O
View E
X
Q2. Pack it in
Without using a calculator, how many boxes of size 3 × 3 × 6 can you pack into these
containers?
3
3
3
6
300
C
30
65
3
65
B
30
A
300
600
Visual and spatial IQ
Q3. Which way?
Employment applications usually involve
psychometric tests that assess your
visual and spatial aptitude. Visual IQ is
considered an important predictor of
overall intelligence. You can improve
your visual aptitude by practising
questions like those listed here.
What is the shortest route from A to B?
B
A
Q4. Square things up
Arrange these pieces into a square with no spaces.
1
1
2
2
3
3
4
1
The Big Brain Workout
21
Q5. Gone dotty
Q6. Drawing on experience
How many dots would you see
altogether as you walked around this
stack of giant dice? What is the total
of the concealed faces?
Mr B has four socks tucked away at the
back of his drawer. He only owns black
or grey socks. The chance of him pulling
out two black ones is 50:50. What are his
chances of pulling out two grey socks?
Q7. Bottoms up
Would the flat pack below make the
cube? If so, what symbol would be on
the bottom?
X
Children’s IQ
Recent research shows that the
numerical and verbal IQs of school
children have been falling, most likely
due to changes in the curriculum and
having more screen-based technology
at home. For the same reason, our
children’s visual IQ has been rising.
22
The Big Brain Workout
VISUAL THINKING
Creative visualisation
When you laugh, scream or cry while watching a film, the images may not be real but
your emotions are. You can use visual thinking to create or recall images to help you
feel the way you want to feel. These images can help you feel excited or calm, creative
or comfortable, or they can alleviate the vague despondency that often overcomes
people for no apparent reason. Imagining positive situations vicariously can help boost
your visual IQ, while recalling details about particular events can help embed longterm memories.
Q8. Learner drivers
These L drivers have a mind of their own. They have driven from A to B to C. Where
will they go next?
?
A
B
C
Q9. Sealed with a loving kiss
Where will the next seal go?
Q10. A shocking solution
Ten lively rams need to be separated temporarily. You have one long loop and three
short loops of electric fencing with plenty of stakes. How can you stake out four
circular (more or less) pens that will keep the 10 rams apart?
The Big Brain Workout
23
CROSSWORD
Telegraph CRYPTIC
Introduction
If you’re new to cryptic crosswords, this could be the place to start. Most cryptic clues
consist of a definition (the answer) and wordplay (clues that together make up the answer).
Look out for a word telling you to manoeuvre the letters of the following or preceding
word to make an anagram, or double definitions where two words offer different meanings
of the answer. You might also find abbreviations like C for ‘caught’ (on a cricket scorecard),
H for ‘hearts’ (bridge), B for ‘bishop’ (chess), P for ‘parking’, and T for ‘time’. These may be
inserted or added to another word so keep an eye out for ‘in’, ‘by’ and ‘under’.
Across
5At present time, ad’s on way, being
redesigned (8)
8Living quarters round a royal residence
(6)
10Rank: duke, for example, touching end
of scale (6)
11Contribution made by party leading
country (8)
12Spectators at the match will
understand what is happening (4,3,5)
15 Room and board for guard (4)
17 Apportion a return of tax (5)
18 Diamonds shown by crude sketch (4)
19Teenage stats prepared for brokers
(6,6)
22Fail to hear one about our state (8)
24At home and abroad, to some extent
Down
1 Navy’s first missile, limited in scope (6)
2 To be compassionate, take a card (4,1,5)
3 Trip includes Sweden leg (4)
4 Fish from lake kept by fool (8)
6Ring article in newspaper about new
evergreen shrub (8)
7 Comical team breaking up (4‑9)
9 About to argue and boast (4)
13Abroad, long-suffering person who
might be attending hospital (10)
14Fury surrounding traditional fashion
industry (3,5)
16Friendly, poor farmer, about 50 (8)
20Apprentice finally failing to pass (6)
21Splendid penalty (4)
23Disentangle a French implement (4)
(2,1,3)
25Alcoholic drink in hamper, no doubt (6)
26 Someone telling jokes about the end
of Robin Hood? (8)
24
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5
2
6
3
7
10
4
8
9
11
12
13
14
15
16
17
18
19
20
21
22
23
25
24
26
Solution on page 28
The Big Brain Workout
25
ANSWERS
IQ Workout
Q1. Take one coin from the ‘copper
and silver’ box. If it’s copper, the box
is all copper and the last two labels
must then be swapped.
Q6. 4
2
6
1
8
3
7
5
Q2. 40m.
12m
30m
Q7. B. (Hour hand moving 15
minutes clockwise, minute hand
moving 15 minutes anticlockwise.)
Q8. 12m
24m
40m
32m
Q3. Invert one triangle on another.
Plant one tree at each apex plus one
at each intersection.
Q9. Count each triangle from left to
right, starting with the first • in the
top triangle. Count 2 for the next •,
then 3, then 4, and so on.
Q4. Yes.
Q5. Take one coin from bag 1, two
coins from bag 2, three from bag 3
and so on. Weigh the coins you have
removed together. The number of
grams short is the number of the
bag with the shaved coins.
26
The Big Brain Workout
Q10. Applied thinking.
A
N
T
P
I
E
P
L
Y
L
I
E
I
N
K
E
Y
E
D
O
N
T
W
O
H
A
T
I
R
E
N
A
P
K
I
P
I
C
E
N
O
T
G
A
Y
Q11. Move one match from the
equals sign and place it parallel with
the minus sign.
Q14. The 29th day. The lilies will double
their area overnight to cover the pond
completely on the 30th day.
Q12. Tip the contents of glass three into
Q15. One owes nothing for one ate
glass six.
nothing to owe for.
Q13. Pour two half bottles into two
other half bottles to make nine full
bottles, three half full and nine empty.
The Big Brain Workout
27
ANSWERS
Numerical THINKING
Q1. 5 metres; 9 metres; 165 blocks (81 +
49 + 25 + 9 + 1 = 165). As 165 = 2 × 100 ×
1,000kg ÷ 1,212, the mass is 200 tonnes.
Q7. Start both sand glasses. Your time
starts when the seven-minute glass is
empty. Turn the 11-minute glass again
when it is empty: 4 + 11 = 15 minutes.
Q2. Four triangles.
London = 80km.
Q8. 146. (Opposite sides of dice always
add up to seven, so four sides always
add up to 14. Ten dice = 140 plus the six
you can see on top.)
Q4. Add 222 to 514 and place the first
number of the answer on top of the
last two.
Q9. Wrap it as a rectangular package
30cm × 40cm and lay the flute along the
diagonal, which will be 50cm.
Q3. Vowel = 20km, consonant = 10km.
Q10. 0, 1 and 4.
7
3
6
Q5. 6.35. The clock advances by 2hrs
5mins, then 4hrs 10mins and so on until
32hrs and 80mins. The hands are not
independent so the 80mins moves the
hour hand on an extra hour.
Q6. Tilt the barrel towards you so
that the liquid just comes to the edge
without spilling. Shine the torch into
the barrel. If you can see the bottom of
the barrel, it is less than half full.
28
TELEGRAPH CRYPTIC
CROSSWORD Solution
N O
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D E
A
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D
K E
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M I
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P E
N
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W A D A Y
R
V
G R E E
O
A
OW T H E
E
E P
A L
L
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E S T A
A
S S O U R
A
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R N O D
T
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F
P A L A
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O N A T I
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C O R E
U
A
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D R
P
E A G E N
T
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I N A W
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A N G S T
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The Big Brain Workout
C E
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O N
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Logical THINKING
Q1. A. No.
B. No, Brazil could have a better chance
Q7. Switch one on for a minute and
then switch it off; switch the second
one on and enter to find one light on,
one off and one warm.
C. They are therefore more likely than
Germany, France and Argentina to win.
Q8. £600 and £1,200.
Q2. A. No. B. No.
Q9. Take B and send B back with the
torch. Call for C and D, then take
the torch back yourself to collect B
with two minutes to spare.
than the others without that chance
being greater than the 50:50 necessary
to justify ‘probably win’.
C. We need a justifiably believable
premise, plus a more than 50:50 chance
of the outcome. How about: ‘English fans
will probably cause trouble at the World
Cup, because they usually do in matches
against foreign teams. And English
fans have been warned that trouble at
the World Cup will lead to expulsion
from the European Championships. So
England will probably be banned from
playing in the next Euros.’ This seems
like an inductively reasonable argument.
Q10. 8. (Hint: 4, 6, 5, 2, 7, 1, 3, 8.)
Q11. Runner 3.
Q12. Larry.
Q13. 12.
D. We need a justifiably reasonable
premise plus an inescapable conclusion
for an argument to be deductively
reasonable. So, ‘Some English fans are
bound to cause trouble at the next
World Cup because English fans cause
trouble at every non-friendly away
match. If English fans cause trouble
at the next World Cup, then England
will automatically be banned from the
European Championships. Therefore
England will not play in the next Euros.’
Q3. Surgeon.
Q5. Audio, Adieu.
Q4. Astronomer.
Q6. Noel (no L).
The Big Brain Workout
Q14. “Do you spell your name with a V?”
Q15. 59 brain trains.
Q16. Switch. You have a 50:50 choice
but not a 50:50 chance. You initially
have a 1-in-3 chance of picking the door
hiding the car. If you stick, your chance
of winning remains the same. Two times
out of three your initial choice (A) is
wrong and the remaining door (C) hides
the car. Try it with three cards.
29
ANSWERS
VISUAL THINKING
Q1. D.
Q2. A = 10; B = 1,050; C = 1,000,000.
Q3. There is no single shortest route
because the diagram is symmetrical
about the AB axis. (Hint: it is often easier
than using geometric or trigonometric
calculations to lay a piece of thread
along the routes or to mark the routes
off on the edge of a piece of paper.)
Q4. One of many
possible solutions.
2
3
2
If Mr B is to have any chance of a black
pair, we can eliminate A and B straight
away. In case C, his chances would be
1/2 × 1/3 = 1/6. In case E his chances
are 100 per cent, so a 50:50 chance of
picking two black socks must be case D,
in which case there is no chance of
a grey pair.
Q7. Yes. A triangle.
Q8. Small L always
rotates clockwise by
90°. Middle L never
moves. Big L flips.
3
1 1
4
Q5. 47; 16 (The opposite faces on a die
add up to seven, so 3 x 14 = 42, then add
the five. For the hidden faces 2 × 7 = 14,
then add the two opposite the five at
the top.)
Q9. Each time the
seal is put on the
back of the envelope,
it moves an extra
number of quadrants
clockwise.
Q6. Zero. We have to draw out the
possible scenarios that would give Mr B
a 50:50 chance of picking one black sock
and then another black sock. Visualize
the possible combinations of black and
grey socks:
A. 4 grey
B. 3 grey; 1 black
C. 2 grey; 2 black
D. 1 grey; 3 black
E. 4 black
30
Q10. One of
many possible
solutions.
1
2
5
6
8
7
10
9
The Big Brain Workout
4
3
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