50

Math, Logic and Word

Puzzles

Volume 1

By Flemming Bermann

Black Cone Publishing

50 Math, Logic and Word Puzzles

Volume 1

Published by Black Cone Publishing

ISBN 978-0-9576484-0-1

Publishing History

KDP edition published 2013

Copyright © 2013 Flemming Bermann

Puzzle illustrations Copyright © 2013 Flemming Bermann

Cover design by Black Cone Publishing

The right of Flemming Bermann to be

identified as the author of this work

has been asserted in accordance

with the Copyright, Designs

and Patents Act 1988

Introduction

Have fun with the 1st volume of the ‘50 Puzzles’ series. In this brand-new Kindle book you will find 50 puzzles never published before in different categories: math, logical, word, geometry, code cracking, sticks and many others.

All puzzles are created by the author and are exclusive to the Kindle platform. The majority of images are in black-and-white and optimized for e-readers. This provides crisp, clear images, which loads fast and is enjoyable to look at.

Whatever your puzzle solving level, you will be sure to find puzzles to match your ability. The puzzles are ranked as follows:

!:Very easy; !!:Easy; !!!:Okay;  !!!!:Hard;  !!!!!:Very hard

Remember that puzzle solving is an excellent recreational activity. Anyone can have a go, whatever their age, alone or together with others. But perhaps best of all, solving puzzles helps keep the brain mentally fit and active.

Happy, fun puzzling, and never give up!

How to use

Each puzzle has an interactive link to a ‘hint’ page, which provides a little help with the answer. Another interactive link takes the reader directly to the ‘solution’ page for the puzzle, where the correct answer is explained in detail.

When on the ‘hint’ page be careful not to go to the ‘next page’, as this will instantly reveal the solution to a puzzle.

If the font size is set to three (3) on Kindle Fire each puzzle fits neatly onto a single screen, which is also the case with most puzzles on older models of the Kindle platform.

Also by Flemming Bermann

Global Warming for Young Minds

(ISBN 978-1-60911-4688)

Evolution for Young Minds

(ISBN 978-1-61897-0046)

Author website

www.globalwarmingforyoungminds.com

Table of Contents

Introduction. 3

How to use. 4

Puzzle 1 – Elementary Dr Watson-! 11

Puzzle 2 – The making of one-!! 12

Puzzle 3 – The cost of tea-!!! 13

Puzzle 4 – Five little words-!! 14

Puzzle 5 – The length of a date-!!! 15

Puzzle 6 – Cutting a piece of wood-!! 16

Puzzle 7 – A super sequence-!!! 17

Puzzle 8 – Age old puzzle-!!!!! 18

Puzzle 9 – A verse to poor Jack-! 19

Puzzle 10 – A wordy sequence-!! 20

Puzzle 11 – Muddled sticks-!! 21

Puzzle 12 – Square problem-!! 22

Puzzle 13 – I spy with my little eye-!!!! 23

Puzzle 14 – Mathematical sticks-! 24

Puzzle 15 – Strange circles-!! 25

Puzzle 16 – Missing something-!!! 26

Puzzle 17 – The spinning cube-!!!!! 27

Puzzle 18 – Winning four in a row-! 28

Puzzle 19 – Picking silver-! 29

Puzzle 20 – Target shooting-!!! 30

Puzzle 21 – Best pick ever-!!! 31

Puzzle 22 – Repetitive pattern-!!!! 32

Puzzle 23 – A strange operator-!!!! 33

Puzzle 24 – A question of age-!!!!! 34

Puzzle 25 – Being a good spy-!!!! 35

Puzzle 26 – Road trip-!! 36

Puzzle 27 – Replacement sequence-!!! 37

Puzzle 28 – Cutting more wood-! 38

Puzzle 29 – The monkey problem-!!!! 39

Puzzle 30 – You are a winner-!!! 40

Puzzle 31 – The wrong entry-!!!!! 41

Puzzle 32 – Logical math problem-!!! 42

Puzzle 33 – A square problem-!!! 43

Puzzle 34 – The green lawn-!!!! 44

Puzzle 35 – Sticking together-!!! 45

Puzzle 36 – Bletchley Park-!!!!! 46

Puzzle 37 – A binary sequence-!!! 47

Puzzle 38 – Powerful connection-!!! 48

Puzzle 39 – A sweet question-!!! 49

Puzzle 40 – The black brick road-!! 50

Puzzle 41 – The hidden arrow-!!!! 51

Puzzle 42 – Not enough equations-!!! 52

Puzzle 43 – Four bits of time-!! 53

Puzzle 44 – World famous city-! 54

Puzzle 45 – Odd name out-!! 55

Puzzle 46 – Naturally connected-!! 56

Puzzle 47 – Triangular math-!! 57

Puzzle 48 – The thin red line-!!!! 58

Puzzle 49 – A very big jump-!!!! 59

Puzzle 50 – Odd clocks-! 60

Hints and solutions. 61

Puzzle 1 - Hint 62

Puzzle 1 - Solution. 63

Puzzle 2 – Hint 64

Puzzle 2 – Solution. 65

Puzzle 3 – Hint 66

Puzzle 3 - Solution. 67

Puzzle 4 – Hint 68

Puzzle 4 – Solution. 69

Puzzle 5 – Hint 70

Puzzle 5 - Solution. 71

Puzzle 6 – Hint 72

Puzzle 6 – Solution. 73

Puzzle 7 – Hint 74

Puzzle 7 – Solution. 75

Puzzle 8 – Hint 76

Puzzle 8 – Solution. 77

Puzzle 9 - Hint 78

Puzzle 9 - Solution. 79

Puzzle 10 - Hint 80

Puzzle 10 - Solution. 81

Puzzle 11 - Hint 82

Puzzle 11 - Solution. 83

Puzzle 12 - Hint 84

Puzzle 12 – Solution. 85

Puzzle 13 - Hint 86

Puzzle 13 - Solution. 87

Puzzle 14 – Hint 88

Puzzle 14 - Solution. 89

Puzzle 15 - Hint 90

Puzzle 15 - Solution. 91

Puzzle 16 - Hint 92

Puzzle 16 – Solution. 93

Puzzle 17 – Hint 94

Puzzle 17 - Solution. 95

Puzzle 18 - Hint 96

Puzzle 18 – Solution. 97

Puzzle 19 - Hint 98

Puzzle 19 - Solution. 99

Puzzle 20 - Hint 100

Puzzle 20 – Solution. 101

Puzzle 21 – Hint 102

Puzzle 21 - Solution. 103

Puzzle 22 – Hint 104

Puzzle 22 – Solution. 105

Puzzle 23 – Hint 106

Puzzle 23 - Solution. 107

Puzzle 24 – Hint 108

Puzzle 24 – Solution. 109

Puzzle 25 – Hint 110

Puzzle 25 – Solution. 111

Puzzle 26 - Hint 112

Puzzle 26 – Solution. 113

Puzzle 27 – Hint 114

Puzzle 27 – Solution. 115

Puzzle 28 – Hint 116

Puzzle 28 – Solution. 117

Puzzle 29 – Hint 118

Puzzle 29 – Solution. 119

Puzzle 30 – Hint 120

Puzzle 30 – Solution. 121

Puzzle 31 – Hint 122

Puzzle 31 – Solution. 123

Puzzle 32 – Hint 124

Puzzle 32 – Solution. 125

Puzzle 33 – Hint 126

Puzzle 33 – Solution. 127

Puzzle 34 – Hint 128

Puzzle 34 - Solution. 129

Puzzle 35 – Hint 130

Puzzle 35 – Solution. 131

Puzzle 36 – Hint 132

Puzzle 36 – Solution. 133

Puzzle 37 – Hint 134

Puzzle 37 - Solution. 135

Puzzle 38 - Hint 136

Puzzle 38 – Solution. 137

Puzzle 39 – Hint 138

Puzzle 39 – Solution. 139

Puzzle 40 – Hint 140

Puzzle 40 – Solution. 141

Puzzle 41 – Hint 142

Puzzle 41 – Solution. 143

Puzzle 42 – Hint 144

Puzzle 42 – Solution. 145

Puzzle 43 – Hint 146

Puzzle 43 – Solution. 147

Puzzle 44 – Hint 148

Puzzle 44 – Solution. 149

Puzzle 45 – Hint 150

Puzzle 45 – Solution. 151

Puzzle 46 – Hint 152

Puzzle 46 – Solution. 153

Puzzle 47 – Hint 154

Puzzle 47 – Solution. 155

Puzzle 48 – Hint 156

Puzzle 48 – Solution. 157

Puzzle 49 - Hint 158

Puzzle 49 – Solution. 159

Puzzle 50 – Hint 160

Puzzle 50 - Solution. 161

Puzzle 1 – Elementary Dr Watson-!

5 reverse is to Stephenson as

20 reverse is to Elgar as

20 reverse is to Faraday as

50 obverse is to…?

What name completes the logical sequence?

Hint  Solution

Puzzle 2 – The making of one-!!

By moving just one of the four letters, make up a mathematical expression equal to 1.

Hint  Solution

Puzzle 3 – The cost of tea-!!!

If

P + E + A = £22

P + E + A + T = £42

How much is T + E + A?

Hint  Solution

Puzzle 4 – Five little words-!!

Shape

Disturb  

Shake  

Upshot  

Alter

Which word is the odd one out?

Hint  Solution

Puzzle 5 – The length of a date-!!!

On planet Earth, for how many hours did the 21st July 2011 exist?

Hint  Solution

Puzzle 6 – Cutting a piece of wood-!!

Cut the strange looking piece of wood in two places and create a 6 x 4 rectangle. When cut, the wood pieces can be rotated, but there is no need to flip them.

Hint  Solution

Puzzle 7 – A super sequence-!!!

Which figure continues the sequence?

Hint  Solution

Puzzle 8 – Age old puzzle-!!!!!

Dan says to Lisa: "Did you know that the difference between you and Peter is the exact number of years it was since Rani was my age?"

Lisa says to Dan: "Yes, I knew that. But do you know that if you add all our ages together you get a cube number?

Rani says: "Here we go again! As usual the twins are trying to outsmart each other."

Peter says: "In two years Dan will be as old and clever as me."

How old are the four teenagers?

Hint  Solution

Puzzle 9 – A verse to poor Jack-!

There was this lad named Jack,

White and pale he looked.

Eating too much and sleeping too little,

New puzzles had him completely hooked.

Tragic as it may sound,

You already know how this tale will end.

One day Jack came across this puzzle,

Nothing could stop him, not even a friend.

Endlessly he tried, but died, leaving it unsolved.

How old was poor Jack when he died?

Hint  Solution

Puzzle 10 – A wordy sequence-!!

Artwork

Fourier    

Sixteen    

Heights    

?

A: Tenacity    B: Canine

C: Baronet    D: Length

Which word continues the sequence?

Hint  Solution

Puzzle 11 – Muddled sticks-!!

Before the horizontal sticks slid down, and mixed up the three letters, the sticks spelled out the title of a famous book.

Can you put the horizontal sticks back and discover the title of the famous book?

Hint  Solution

Puzzle 12 – Square problem-!!

A small cube with six identical sides is shown from above.

How many visible, whole diamonds are there in total on a 2 x 2 x 2 cube made up of the smaller cube, if placed on a non-transparent surface?

Hint  Solution

Puzzle 13 – I spy with my little eye-!!!!

Lauran is standing in front of picture of a lion.

Her brother Jack walks up behind her and puts a hand over her left eye.

"What can you see?" asks Jack.

"The same as before," says Lauran.

Jack removes his hand before covering her right eye.

"What can you see?" asks Jack.

"The same as before," says Lauran.

Jack then covers both Laura's eyes.

"What can you see?" asks Jack.

"The same as before," says Lauran.

If Lauran is not lying, how can her last statement be true?

Hint  Solution

Puzzle 14 – Mathematical sticks-!

By moving just one match on the left side of the equation it is possible to make the expression true. No matches can touch each other, and the total number of matches on each side of the equal sign must remain the same.

How can the expression be made true?

Hint  Solution

Puzzle 15 – Strange circles-!!

Find the name of a creature living on Earth?

Hint  Solution

Puzzle 16 – Missing something-!!!

Combine the two letter words on the right with those on the left.

What hidden letter goes in the circle?

Hint  Solution

Puzzle 17 – The spinning cube-!!!!!

As a blank cube is spun, four markers, a white, black and grey, are placed in turn onto an empty side of the cube. The marker placement is indicated by the white arrow.

Holding the F cube up against a mirror, so the three hidden sides are visible, what colour marker in shown in position A, B and C?

Hint  Solution

Puzzle 18 – Winning four in a row-!

Black and white is playing four in a row. It is white's turn to play.

What is the minimum number of moves needed by white to win the game?

Hint  Solution

Puzzle 19 – Picking silver-!

A large black bag contains 10 silver spoons and 20 silver forks.

Without looking and picking just one item from the bag at a time, what is the probability of picking the following combination: Spoon – Fork – Spoon?

Hint  Solution

Puzzle 20 – Target shooting-!!!

Jack (o) and Peter (*) is target shooting. The one with the best score must pay the other $1500 dollars. It is Jack's turn to take his final shot.

What must Jack shoot next to avoid losing the $1500 dollars?

Hint  Solution

Puzzle 21 – Best pick ever-!!!

Two sealed cylinders, each containing a total of 19 physically identical balls.

One cylinder contains balls marked '£10' with a total value of £100, the other cylinder contains balls marked '£5' worth just £95.

Mixed in with the money balls are worthless black balls.

Picking one ball at a time from either cylinder and without looking, how many balls will you have to pick before you are able to identify the cylinder worth £100?

Hint  Solution

Puzzle 22 – Repetitive pattern-!!!!

Position X shows when the sequence repeats for the first time. What is X?

Hint  Solution

Puzzle 23 – A strange operator-!!!!

A strange new operator leads to some surprising results.

What is the result of this operation?

Hint  Solution

Puzzle 24 – A question of age-!!!!!

One upon a time there was three children, Bob, Ben and Tom.

If you add together the age of Bob and Ben you get Tom's age.

If you add together the age of Bob and Ben, after having raised both to the power of the children involved in this puzzle, then you still get Tom's age squared.

If you add together the age of Bob and Ben, after having squared Bob's age and raise Ben's age to the power of the children involved in this puzzle, then you still get Tom's age squared.

How old are the three children?

Hint  Solution

Puzzle 25 – Being a good spy-!!!!

“DTTZ  DT  QZ  ZVH  XFRTK  ZIT  VIOZT WKORUT”

A secret message has been typed on a reconfigured QWERTY keyboard.

What does the message read?

Hint  Solution

Puzzle 26 – Road trip-!!

Three cars take off from the same spot.

The first car sets off at 2 miles per hour.

Half an hour later the second car sets off at 1.5 miles per hour.

Half an hour later the third car sets off at 1 mile per hour.

After 7 hours, what is the common distance completed by all three cars?

Hint  Solution

Puzzle 27 – Replacement sequence-!!!

0-2-0-4-0-0-0-8-0-10-?-?-?

Identify what numbers have been replaced by zero (0), and find the next three numbers in the sequence?

Hint  Solution

Puzzle 28 – Cutting more wood-!

Cut the strange looking piece of wood in one place and create a 6 x 4 rectangle without flipping or rotating the wood pieces.

Hint  Solution

Puzzle 29 – The monkey problem-!!!!

Four houses next to each other, somewhere in suburbia.

Dave lives in number 3.

The red house is in between the white and yellow houses.

Ian does not live at the end.

House number 9 is not blue and doesn’t belong to Nick.

Eric’s neighbour has an unusual pet.

Ian lives in the yellow house with his pet giraffe.

Nick and Dave are not neighbours.

At what number does the monkey live?

Hint  Solution

Puzzle 30 – You are a winner-!!!

Black and white is playing four in a row. It is white's turn to play.

If you are playing white, what is the best move you can make?

Hint  Solution

Puzzle 31 – The wrong entry-!!!!!

When professor G. Inius checked the work of a student he could not believe his own eyes. The student had made a wrong entry, which the professor was kind enough to correct.

Can you find the students mistake and correct it?

Hint  Solution

Puzzle 32 – Logical math problem-!!!

Two symbolic equations are shown below. Use the logical relationship between the symbols to complete both equations, replacing all questions marks (?) with the correct symbol.

Hint  Solution

Puzzle 33 – A square problem-!!!

Which square continues the sequence?

Hint  Solution

Puzzle 34 – The green lawn-!!!!

A garden is laid out as a triangle with equal sides. Inside the garden are two types of flower beds – one for white and one for yellow flowers, and in the centre a green lawn.

 One side of the garden is 14.142 meters long.

The area covered by all As is 16 sq. meters.

The area covered by all Bs is 9 sq. meters.

The area covered by a single C is 1.75 sq. meters.

The area covered by all the white flower beds is 12 sq. meters.

The old gardener is 100% sure that the lawn is less than 5 sq. meters.

Given the above proportions, how big is the area of the green lawn?

Hint  Solution

Puzzle 35 – Sticking together-!!!

The horizontal sticks have slid down, and mixed up a five letter word.

Can you put the horizontal sticks back and discover the word?

Hint  Solution

Puzzle 36 – Bletchley Park-!!!!!

Can you crack the secret code?

Hint  Solution

Puzzle 37 – A binary sequence-!!!

1   101   01   0101   101    ?

a) 10101    b) 1010101    c) 111   

d) 010101    e) 1010100

Which pattern continues the sequence?

Hint  Solution

Puzzle 38 – Powerful connection-!!!

S_ _ _ _LE

WOOD_ _ _ _

D_ _ _ _ LE

_ _ _ _UP

RE_ _ _ _

 _ _ _ _BURN

What four letter word completes the above words?

Hint  Solution

Puzzle 39 – A sweet question-!!!

Sanjev and Susan eat the rest of Jack's sweets, after he had enjoyed 3/8 of them.

Susan eats 200% more than Sanjev, who only had 15 sweets.

How many sweets did Jack eat?

Hint  Solution

Puzzle 40 – The black brick road-!!

Dave wants to pave his driveway with 10 x 30 cm black bricks.

The driveway is 1 x 9 meters long.

To make the driveway extra strong, Dave decides to add 1 cm of cement in between and around the edges of the bricks.

Without breaking any bricks, how many black bricks will Dave need to cover his driveway, if he uses the pattern shown above?

Hint  Solution

Puzzle 41 – The hidden arrow-!!!!

Find a white arrow hidden in the picture.

Hint  Solutions

Puzzle 42 – Not enough equations-!!!

Four equations, but five hidden numbers!

Find the sum of:

Hint  Solution

Puzzle 43 – Four bits of time-!!

Two-yearly

Semi-annual

Twice-yearly

Six-monthly

Which word is the odd one out?

Hint  Solution

Puzzle 44 – World famous city-!

What famous world city is hidden in the pictures?

Hint  Solution

Puzzle 45 – Odd name out-!!

Which name is the odd one out?

Hint  Solution

Puzzle 46 – Naturally connected-!!

BAT_ _ _ _

BOAR_ _ _ _

TIGER_ _ _ _

TOAD_ _ _ _

WOLF_ _ _ _

What word can be added to the end of each word and create five new words.

Hint  Solution

Puzzle 47 – Triangular math-!!

Using the relationship between the numbers in the first triangle, what value should be assigned to ‘a’ and ‘b’ in the second triangle?

Hint  Solution

Puzzle 48 – The thin red line-!!!!

A ball-pen contains enough ink to draw a 25 metre line.

When Mr Doodle used a new red, ball-pen to draw a line from A to B, his ball-pen runs out 2.85 metres from B.

Why didn’t Mr Doodle’s red line reach B?

Hint  Solution

Puzzle 49 – A very big jump-!!!!

A pair of super twins, Sally and Sarah is standing next to each other on equator. Sally jumps straight up in the air with super force, while Sarah remains standing on the ground.

At the time Sally lands on the ground again, on equator, her twin sister has rotated far away, and the distance between them is π/6 * r, where r is Earth’s radius.

If Sally was jumping up and falling down at a constant speed of 1 mile per hour, how high was Sally’s jump?

Hint  Solution

Puzzle 50 – Odd clocks-!

Which clock is the odd one out?

Hint  Solution

Hints and solutions

This section contains hints and solutions for all 50 puzzles. Each puzzle has a ‘hint’ page, which is immediately followed by the puzzle’s ‘solution’ page.

Puzzle 1 - Hint

English bank notes.

Back

Puzzle 1 - Solution

Solution is ‘Windsor’.

On an English £5 pound note, on the reverse side, there is a picture of George Stephenson.

Edward Elgar and Michael Faraday have both featured on the ‘reverse’ side of a £20 note.

Queen Elizabeth II can be found on the ‘obverse’ side of all bank notes, including a £50 note.

Only the person’s surname is displayed in the puzzle.

The Queen’s surname is Windsor, which is the solution to the puzzle.

Back  Next puzzle

Puzzle 2 – Hint

Interpret the letters as mathematical symbols and numbers.

Back

Puzzle 2 – Solution

Move letter V next to letter T to create ‘square root of one’.

Square root of one times one = 1

Back  Next puzzle

Puzzle 3 – Hint

Latin alphabet.

Back

Puzzle 3 - Solution

Solution is £26.

Use the two small equations to find that T = 20.

This result suggests that each letter from A to Z in the Latin alphabet have given a number from 1 to 26.

Hence, A = 1, E = 5 and T = 20, which means that T + E + A = £26

Back  Next puzzle

Puzzle 4 – Hint

Influence or change.

Back

Puzzle 4 – Solution

The odd word out is: ‘Upshot’.

All the other words mean to influence or change something, while ‘Upshot’ means result.

Back  Next puzzle

Puzzle 5 – Hint

A day is 24 hours, but a date is not a day.

Back

Puzzle 5 - Solution

On planet Earth the 21st June 2011 or any other day for that matter exists for 48 hours.

Start at the International Date Line and follow an imaginary line as it sweeps westwards across the world, starting a new day, the 21st June, as it progresses.

When back at the date line, the 21st June has already existed for 24 hours. Now jump off just before the date line. Here the 21st June has just started, and you have to wait another 24 hours before it is the 22nd June 2011.

In total the date, not the day, has existed for a total of 48 hours.

Back  Next puzzle

Puzzle 6 – Hint

Cut in two places close to hole.

Back

Puzzle 6 – Solution

Back  Next puzzle

Puzzle 7 – Hint

Link between inside shapes and outside shape.

Back

Puzzle 7 – Solution

Figure C continues the sequence.

Of the four inside shapes, the top left determines the outside shape. The inside shapes square, triangle and plus rotate one shape anti-clockwise each time. The circle is never rotated.

Back  Next Puzzle

Puzzle 8 – Hint

A lot of easy math to complete and two sets of twins.

Back

Puzzle 8 – Solution

Solution: Dan (D) is 15; Lisa (L) is 15; Rani (R) is 17; Peter (P) is 17.

From the clues we get the following equations:

|L – P| = R – D (1)

We don’t know if L or P is oldest, so use absolute value, but we do know that R is older than D. Note (1a) |L – P| = |P – L|

D + R + P + L = ‘Cube No’ (2)

L = D (3)

They are twins and therefore have the same age

P – D = 2 (4) or D = P – 2 (4a)

Difference between P and D, and P is the oldest

From (1) and (1a) we have |P –L| = R – D (5)

From (5) and (3) we get: |P – D| = R – D => |P| = R =>  P = R (6)  i.e. two sets of twins.

Using (3) and (4) we get: P – L = 2 => L = P – 2 (7)

Using (2) with (4a), (6) and (7) we have: (P – 2) + P + P + (P – 2) = ‘Cube No’

Reducing we get: 4P – 4 = ‘Cube No’ (8)

There are three ‘sensible’ cube numbers, which gives whole number ages when solving (8). These are 8, 64 and 216. However, only 64 give teenage ages, which was the last piece of information in the puzzle.

Hence, using 64 with (8) we have 4P – 4 = 64 => P = 17

Using the above equations, we find that R = 17, L = 15 and D = 15

Back  Next puzzle

Puzzle 9 - Hint

Read the verse very carefully, paying attention to each line.

Back

Puzzle 9 - Solution

First letter from each line spells: ‘Twenty one’.

Back  Next Puzzle

Puzzle 10 - Hint

Words within.

Back

Puzzle 10 - Solution

The next word is: ‘Tenacity’.

Each word contains a number in a sequence: Artwork; Fourier; Sixteen; Heights.

The next word must contain 'ten', which is 'Tenacity'.

Back  Next puzzle

Puzzle 11 - Hint

A famous school book.

Back

Puzzle 11 - Solution

Before being disturbed, the sticks spelled: ‘ABC’.

Back  Next Puzzle

Puzzle 12 - Hint

Focus on one side of the cube at a time, and don’t worry about the bottom.

Back

Puzzle 12 – Solution

There are 56 whole, visible diamonds on the outside of the 2 x 2 x 2 cube.

Though the diamonds ‘wrap’ around a corner, it is still a whole diamond, and so are diamonds made up of two cubes placed next to each other.

Each side, there are four sides, contains 11 whole diamonds. Two half make a whole diamond except against the non-transparent bottom.

This means that the two half diamonds at the bottom of the cube should not be counted and therefore not shown in above picture.

There are one top, which contains 12 whole diamonds.

Total diamonds = (4 x 11) + 12 = 56.

Back  Next Puzzle

Puzzle 13 - Hint

Try it on a friend, and the answer will come to you.

Back

Puzzle 13 - Solution

Lauran is standing with both her eyes closed.

Each time Jack asks her, she can see the same as before - nothing.

Back  Next puzzle

Puzzle 14 – Hint

Look for a way to turn -2 into +1.

Back

Puzzle 14 - Solution

Mathematically we have: - - 1 = 1 or 1=1, which is always true.

Back  Next Puzzle

Puzzle 15 - Hint

Look for three letters.

Back

Puzzle 15 - Solution

The circles spell out the word: 'man'.

Each large circle contains a single letter, which is mirrored.

Use a piece of paper to cover the lower half of each circle, and the letters will appear.

Back  Next puzzle

Puzzle 16 - Hint

Think vowel.

Back

Puzzle 16 – Solution

The letter 'o' goes in the middle.

The words are: ‘Cross’, ‘Float’, ‘Abort’, ‘Glove’, ‘Proof’ and ‘Looks’.

Back  Next puzzle

Puzzle 17 – Hint

Get a dice or make a cube, and try to follow the instructions.

Back

Puzzle 17 - Solution

At position F, the hidden sides of the cube are showing:

Hence, A = Black; B = White; C = Grey marker.

Back  Next puzzle

Puzzle 18 - Hint

Like in chess, try to force the issue.

Back

Puzzle 18 – Solution

Solution: White can win in one move.

White will always win the game, as long as the next white piece is placed on either F3 or F6. No matter where black’s next piece is placed, white will win along the f-file.

Back  Next puzzle

Puzzle 19 - Hint

Get an old bag, some forks and spoons, and then try it out.

Back

Puzzle 19 - Solution

As it is easy to feel the physical difference between a spoon and a fork, you should be able to pick a spoon followed by a fork followed by a spoon without making a mistake.

Hence, the probability of picking the right combination is 1 or 100%.

Back  Next puzzle

Puzzle 20 - Hint

Think outside the box.

Back

Puzzle 20 – Solution

Jack would have to shoot himself or Peter, as Jack has no chance of winning the game fair and square and therefore avoid losing the $1500 dollars.

Back  Next puzzle

Puzzle 21 – Hint

Get a couple of bowls, some sweet and salted popcorn, and try it out.

Back

Puzzle 21 - Solution

You will need to pick just one ball.

The cylinder worth £95 holds exactly 19 balls worth £5 each. It does not contain any black balls. The other cylinder contains black balls and 10 balls worth £10 each.

Picking just one ball from either cylinder will therefore immediately tell you the value of the cylinder's content.

Back  Next puzzle

Puzzle 22 – Hint

Get a pen and paper and write out the different combinations. The sequence repeats after less than 20 elements.

Back

Puzzle 22 – Solution

Solution: X = 13.

The sequence is made up of the small square moving anti-clockwise around the big square, one position at a time.

Back  Next puzzle

Puzzle 23 – Hint

The strange operator means ‘combine’.

Back

Puzzle 23 - Solution

The strange operator means “take one number and place it on top of the other.”

The combination of the two numbers leads to a new number, which is the result.

Back  Next puzzle

Puzzle 24 – Hint

Each clue provides an equation. Here is one of the equations:  BoB3 + Ben3 = Tom².

Back

Puzzle 24 – Solution

Bob is 1, Ben is 2 and Tom is 3.

Each clue provides an equation:

Bob + Ben = Tom (1)

Bob3 + Ben3 = Tom² (2)

Bob2 + Ben3 = Tom² (3)

From (2) and (3) we find Bob = 1 (4)

Using (1) with (4) we have Tom = Ben + 1 (5)

Inserting (5) and (4) in (2), we get:

1 + Ben3 = (Ben + 1) 2

1 + Ben3 = Ben² + 2Ben + 1

Ben3 = Ben² + 2Ben

Ben² - Ben – 2 = 0 (6) Standard quadratic function in Ben

Solving (6) we find Ben = (-(-1) + 3) / 2; Ben = 2 (7)

Inserting (4) and (7) into (1), we find Tom = 3 (8)

Back  Next puzzle

Puzzle 25 – Hint

Consider what would be the simplest way of turning a QWERTY keyboard into a code writing keyboard.

Back

Puzzle 25 – Solution

The message reads: 'MEET ME AT TWO UNDER THE WHITE BRIDGE!

On a QUERTY keyboard, imagine the Q key reading A, W reading B,..., A reading K and so on. Hence, when pressing A the letter Q will be printed and so on for the other renamed keys.

Back  Next puzzle

Puzzle 26 - Hint

What car determines the minimum distance driven?

Back

Puzzle 26 – Solution

The same minimum distance driven by all three cars is 6 miles.

The question can be reduced to asking: how far does the slowest car, which is C, travelled in 6 hours?

Car A and B may be able to travel faster and longer in 7 and 6.5 hours respectively, but if all cars are to complete the same minimum distance, then it is the slowest car that determines the minimum distance.

Car C waits on hour and then travels 1 mile per hour for 6 hours, which is 6 miles.

Back  Next puzzle

Puzzle 27 – Hint

Try to find two sequences, which are connected to the 0 numbers.

Back

Puzzle 27 – Solution

Solution: 0, 0 and 0.

All prime numbers and numbers that can be divided with 3 have been replaced with a '0'. The next three numbers in the sequence are therefore: 0, 0 and 0.

Back  Next puzzle

Puzzle 28 – Hint

One cut is required.

Back

Puzzle 28 – Solution

Back  Next puzzle

Puzzle 29 – Hint

Draw five houses numbered 3, 5, 7 and 9. Ian lives in number 5.

Back

Puzzle 29 – Solution

The monkey lives in number 7.

Dave lives in number 3

Ian lives in number 5 in the yellow house with his pet pig

Nick lives in number 7 in the red house with the monkey

Eric lives in number 9 in the white house

Back  Next puzzle

Puzzle 30 – Hint

Find a way to force black’s next move.

Back

Puzzle 30 – Solution

White must place next piece on D4.

To avoid losing, Black is forced to place piece on C4. But this allows White to place a piece on B4, winning the game along the diagonal B4 – E7.

Back  Next puzzle

Puzzle 31 – Hint

Look for a duplicate entry, and where it is located.

Back

Puzzle 31 – Solution

The missing entry is: 'DCAB', which should be located top right, where the duplicate ‘ABCD’ entry can be found.

There are two 'ABCD' entries.

The entry near the top right hand corner is the incorrect entry, as the entry ending in 'D' is located within the L-shaped area containing entries ending in 'B'.

Back  Next puzzle

Puzzle 32 – Hint

Symbols can be made up of other symbols. What known symbols makes a +?

Back

Puzzle 32 – Solution

The first logic calculation shows in what order the symbols are place on top of each other and that the circles are not transparent. It also shows that symbols can be combined to make new symbols.

The circles in the second calculation confirm that symbols can be swapped around.

The + symbol can logically be made up of a – and I line, creating a new # symbol. Placing all symbols under the circles gives the final result.

Back  Next puzzle

Puzzle 33 – Hint

Inside the square is a line, which is flexible in the middle.

Back

Puzzle 33 – Solution

The next square in the sequence is B.

Outside the square is a line, which moves anti-clockwise one side at a time.

Inside the square is a line, which moves first one end anti-clockwise 90 degrees, then moves the other end anti-clockwise 90 degrees and so on.

Back  Next puzzle

Puzzle 34 – Hint

What shape does that lawn in the middle really have?

Back

Puzzle 34 - Solution

The lawn is 4.9 sq. meters.

All As (There are 4) totals 16 sq. meters. One A equals 4 sq. meters

All Bs (There are 10) totals 9 sq. meters. One B equals 0.9 sq. meters.

The lawn is A + B and therefore equals 4.9 sq. meters.

Back  Next puzzle

Puzzle 35 – Hint

The last letter in the word is ‘n’.

Back

Puzzle 35 – Solution

The word is ‘woman’.

Back  Next puzzle

Puzzle 36 – Hint

Try to identify four groups of six letters as 'Y' and 'Z' are not used in code.

Second last word is ‘THE’.

Back

Puzzle 36 – Solution

The message reads: 'TOP SECRET AGENT X ARRIVES IN THE MORNING'

There are four groups of six letters, as 'Y' and 'Z' is not used in code.

Group 1:

Start of the other groups:

Back  Next puzzle

Puzzle 37 – Hint

Sequence combines two rules. One rule involves removing a digit.

Back

Puzzle 37 - Solution

Solution is B.

Sequence combines two rules.

In every second step every '1' is replaced by '101' i.e. ’1’ turns into ‘101’.

In every other second step, the first digit is removed i.e. ‘101’ turns into ‘01’.

Sequence starts with a replacement.

Final step is a replacement step i.e. 101 turns into 101 0 101 or 1010101.

Back  Next puzzle

Puzzle 38 - Hint

Hold onto your hat or it might blow off!

Back

Puzzle 38 – Solution

The word is ‘wind’.

Back  Next puzzle

Puzzle 39 – Hint

Susan eats 45 sweets.

Back

Puzzle 39 – Solution

Jack eats 36 sweets.

Sanjev eats 15 and Susan eats 200% more, which is 45.

Together Sanjev and Susan eat 60 sweets, which is equal to 5/8 of the total.

1/8 of the total equals 12 sweets, and hence, the 3/8 Jack eats equal 36 sweets.

Back  Next puzzle

Puzzle 40 – Hint

Combine the brick and cement in the calculation.

Back

Puzzle 40 – Solution

The 1 x 9 meter driveway can be covered by 9 x 29 = 261 bricks and 1 cm cement - without breaking any of the bricks.

A brick + cement is 1 + 10 = 11 cm. Dividing the 11 cm into the 100 cm driveway gives 9 bricks with exactly 1 cm to spare for the cement on the other side.

A similar calculation can be made with the other dimension of the brick and driveway – dividing 31 cm into 900 cm driveway gives 29 bricks with 1 cm to spare.

Back  Next puzzle

Puzzle 41 – Hint

Think of a famous US logistics company.

Back

Puzzle 41 – Solution

The FedEx logo has an arrow ‘hidden’ between the ‘E’ and ‘X’.

Back  Next puzzle

Puzzle 42 – Hint

Calculate a value for  * + %.

Back

Puzzle 42 – Solution

The solution is: * + ! + % = 14.

If * + 2£ + % = 19 then * + 2£ + % + 1 = 20 (1)

Combining the two first equations, we have: * + 2£ + % + 1 = % + $ + £ + *

Reducing we find: £ + 1 = $ (2)

Inserting (2) into 3$ + 2£ = 18 we get: 3£ + 3 + 2£ = 18 => £ = 3 (3)

Inserting (3) into 3$ + 2£ = 18 we get: 3$ + 6 = 18 => $ = 4 (4)

Inserting (3) into * + 2£ + % = 19 we get: * + % + 6 = 19 => * + % = 13 (5)

Rewriting 2% + 2* - 9! = 17 we get 2(* + %) – 9! = 17 (6)

Inserting (5) into (6) we get: 2(13) – 9! = 17 => ! = 1 (7)

Using (5) and (7) we find: * + % + ! = 14 (8)

Back  Next puzzle

Puzzle 43 – Hint

The passing of time is important.

Back

Puzzle 43 – Solution

The solution is: ‘Two-yearly’.

‘Two-yearly’ means every two years, while the other words mean twice a year.

Back  Next puzzle

Puzzle 44 – Hint

Say out loud what you see on the pictures.

Back

Puzzle 44 – Solution

The famous city is:

Budapest (Buddha + Pest)

Back  Next puzzle

Puzzle 45 – Hint

Something odd about those names?.

Back

Puzzle 45 – Solution

Based on Oxford’s English Dictionary, ‘Carl’ is the only name which does not have a secondary meaning.

Back  Next puzzle

Puzzle 46 – Hint

Think of an animal.

Back

Puzzle 46 – Solution

The word is ‘Fish’.

Back  Next puzzle

Puzzle 47 – Hint

Combine 2, 4 and 8 to get 20.

Back

Puzzle 47 – Solution

The values are: a = 2.5 and b = 5.

The three numbers at the bottom of the triangle is combined to get the number at the top of the triangle. (2 * 8) + 4 = 20 (1)

There is also another relationship between the bottom numbers. Starting from 2, the next two numbers are found by doubling each time. We have 2 * 2 = 4 and 2 * 4 = 8.

Hence, working our way backwards from 10, we must have b = 5 and a = 2.5, which gives the expected 30. Using (1) with new numbers we have (2.5 * 10) + 5 = 30

Back  Next puzzle

Puzzle 48 – Hint

Think 3D.

Back

Puzzle 48 – Solution

Seen from the side, Mr. Doodle is drawing on a shape made up of two flat surfaces and a sphere inserted between the two surfaces.

The length of the line is: 10 m + half the circumference of the circle + 7.15 m.

Half the circumference of the circle: ½ * 2 *Pi * 2.5 (radius) = 7.85 meters

Length of line: 10 + 7.85 + 7.15 = 25 meters or 2.85 meters from B.

Back  Next puzzle

Puzzle 49 - Hint

Calculate how long time it took Sarah to rotate a distance of π/6 * r.

Back

Puzzle 49 – Solution

Sally jumped 1 mile up in the air.

If Sarah had rotated for 24 hours, she would have returned to her starting point, and she would have rotated 2πr, which is the circumference the Earth. However, she only rotated π/6 * r.

The ratio π/6 * r versus 2πr (note how π and r are irrelevant) gives 1/12 of 24 hours. In other words, Sarah rotated π/6 * r  in 2 hours.

In those 2 hours Sally jumped up and down. Jumping up and down at a constant speed, she spent the same amount of time jumping up as falling down. In other words Sally spent 1 hour jumping up and 1 hour falling down.

Sally’s highest point was therefore after 1 hour, at which point she was 1 mile above the Earth, as she jumped at a speed of 1 mile per hour.

Back  Next puzzle

Puzzle 50 – Hint

What time is it?

Back

Puzzle 50 - Solution

Solution is D.

Clock D is the odd one out because it is showing an actual time. The other clocks are showing a time, which is not possible to encounter.

Back