Puzzles and Teasers for Everyone

Citation preview

PUZZLES & TEASERS For EVERYONE

Compiled by Darryl Francis edited with an introduction by David Pritchard

Puzzles and Teasers for Everyone

In the same series

PUZZLES AND TEASERS FOR THE EASY CHAIR Uniform with this book

PUZZLES AND TEASERS FOR EVERYONE

Compiled by

DARRYL FRANCIS

Edited with an introduction by

DAVID PRITCHARD

GAURAV PUBLISHING HOUSE New Delhi (INDIA).

Published by: VIRINDER K. VERMA

Gaurav Publishing House 9265, Street No. 6. Multanl Dhanda, Pahar Ganj, New Delhi-110055.

Published by arrangement with Elliot Right Way Books

AU rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocoping, recording or any information storage and retrieval system, without permission in writing from the publishers.

PRINTED AT

SHIBA OFFSET PRINTING PRESS LAXMI NACAR. DELHI-110092

CONTENTS Page

Introduction

7

Numbered main Puzzles 1 to 150 (Quickies—also referenced by their quickie numbers—are interspersed in the main puzzles throughout the book)

9

Answers to main Puzzles in random order

107

Answers to Quickies in sequence

155

Index to main Puzzle answers

159

Cartoons in this book are by Artie

INTRODUCTION Puzzles have a fascination that is hard to resist. They are a challenge to our intelligence as their solving is a tonic for our ego; and even where a puzzle fails to arouse our interest, curiosity may still drive us to look up the answer. In this book there is much to challenge and much to arouse the curiosity, and at the same time much to entertain. The whole puzzle gymnasium is brought into use to provide stimulating, but I hope not exhaust­ ing, mental exercise. Here are mathematical puzzles, word puzzles, dis­ sections, exercises in logical deduction, and also a few of what might be called ‘open-ended’ problems, with tentative solutions on which the reader is invited to improve—if he can. The word puzzles calls for special mention. Whereas most words are to be found in most dictionaries, some words and spellings are peculiar to certain ones. Any good dictionary is adequate for all but a few words in the harder puzzles. Our recommendation is Chambers 20th Century Dictionary, which, apart from listing all the words used in this book, has many attractions for the puzzler, not least a clear distinction between proper and improper nouns. The puzzles you are about to attempt have been selected, though many with modification, from those that have appeared in GAMES & PUZZLES maga­ zine and have survived the scrutiny of experts. Even so, it is still possible that a few of the problems could be better expressed and one or two of the solutions 7

improved on. Do not hesitate to write and tell us if you have any constructive suggestions. The puzzles are arranged in ascending order of diffi­ culty irrespective of type, though this grading is neces­ sarily only very approximate as we all have different ideas as to what is easy and what is difficult. A series of short posers—‘Quickies’—have been included, use­ fully to fill odd comers of space and hopefully to fill odd moments of the reader’s time. Quickies have not been graded and some are by no means easy. Solutions to puzzles are given at the end and have been arranged in random order so as to avoid spoiling the reader’s pleasure by permitting an unwanted glimpse of answers to adjacent problems. An index (page 159) follows the solutions. Answers to the Quickies are listed sequentially after the puzzles solutions. I hope very much that you will get pleasure from this book. DAVID PRITCHARD

8

PUZZLES 1

Nothing to it?

Study this paragraph and all things in it. What is vitally wrong with it? Actually, nothing in it is wrong, but you must admit that it is most unusual. Don’t just zip through it quickly, but study it scrupulously. With luck you should spot what is so particular about it and all words found in it. Can you say what it is? Tax your brains and try again. Don’t miss a word or a symbol. It isn’t all that difficult....

2

Cut!

This diagram is supposed to show five loops of string. If you cut one of the loops, the others will all fall apart. Which loop must be cut?

9

3

Xn Airport Problem (c. 2000 A.Dj A young man about to take off in his private super-jet spotted a pretty girl on the concourse. ‘Hi, did you miss your plane?’ he asked. ‘Yes, and now I’m stranded here for a few more days.’ ‘I’d be glad to give you a lift,’ he offered. ‘But,’ she replied, ‘you don’t even know where I’m going!’ ‘It doesn’t matter. I can take you there without going out of my way more than a few miles.’ Naturally, the girl thought this was a fresh young man with a new line, and she refused his offer until he told her where he was headed. She then realised he had been telling the truth and went with him. Given that this sequence of events happened at the airport in Perth, Australia, can you say where the young man was heading? QUICKIE No.

1. What are the next two numbers in this series? 1

4

4

13

28

49

—

—

Magic and Antimagic

Nearly everyone knows what a magic square is. You take an empty grid, such as that shown, and arrange to have a different number in each space such that the totals in the three columns and two diagonals are the same. Given the numbers 1 to 9, they could be arranged as,shown in the second figure, giving totals of 15 in all eight directions. Now, can you place those same numbers in such a way that the total in every direction is different? You could call your resulting square an antimagic one. Now, can you create an antimagic square with the additional restriction that none of the totals is 15? 10

QUICKIE No.

2. What are the next two letters in this series? AEFHIKLM

5

Find the Country (I)

In each of the following sentences is hidden the name of a country. For example, in the sentence *His pains­ taking efforts were much admired.’ ‘Spain’ is hidden in the first two words. (1) Couples wed entirely of their own accord nowa­ days. (2) There’s no catch in any of these sentences. (3) The greenhorn sheriff ran celebrities out of town. (4) His bank withdrawal established a new all-time record. (5) Fighting against the strong wind, I advanced very slowly. (6) They easily scan a day’s order forms in half an hour. (7) The money that I bet you will go to charity if I win. The coal ban I authorized has not been com­ pletely effective. (9) Each advertisement on television is thoroughly vetted before being shown. 11

6

Domino Dots

A set of dominoes usually consists of 28 rectangular tiles. Each tile has two squares, each numbered from 0 to 6. Every combination of two numbers is repre­ sented. The basic rule in playing dominoes, of course, is that, in adding to a chain, you have to match the value of one square of your tile to the value of a square at one end of the chain. If you place all 28 dominoes in a continuous chain, bearing in mind that adjacent ends of tiles must match, so that 5 dots are at one end, how many will be at the other end of the chain? Try solving this mentally before checking with actual dominoes. QUICKIE No.

3. Which are there more of: inches in a mile or Sundays in a thousand years?

7

Voden’s Flag

Perhaps trouble would never have arisen if the com­ plete job of designing a flag for the country of Voden had been given to one firm. But wanting to share the honour around, the government of Voden decreed that one firm should design the flag (shown below) whilst another firm would be responsible for deciding on the colours. When the second firm came to handle the colouring, they noticed a penalty clause in the contract which required them to use the least number of colours pos­ sible. This caused a considerable amount of head scratching, until one of their more brilliant young men showed how it could be done with—how many colours? No adjacent sections of the design may, of course, be of the same colour. 12

QUICKIE No.

4. Which are there more of: seconds in a week or feet in 100 miles? 8

Hey,

Riddle, Riddle!

(1) Why is a crossword puzzle like a quarrel? (2) Why are riddles that cannot be answered like a man disappointed by his visitors? (3) What letter is most useful to a deaf woman? (4) Why is a bad cold like a great humiliation? (5) Why is a schoolboy being flogged like your eye? (6) What time is it when the clock strikes thirteen? (7) What is black and white and red all over? (8) What occurs once in a minute, twice in a moment, but not once in a hundred years? (9) What ship has two mates but no captain? (10) Why is a person reading these puzzles like a mar condemned to undergo a military execution? 13

9

Bob-a-Job

The Scouts had all been out bob-a-jobbing, and three of them met up on their way back to the Scout hut. Naturally, the conversation concerned how much they had each collected. It worked out that if Athelstan were to give 36p to Balthazar, then Balthazar would have twice as much as Athelstan. But if, on the other hand, Balthazar gave 36p to Caleb, then Caleb would have twice as much as Balthazar. And if, instead of all this, Caleb were to give 36p to Athelstan, that would make them both equal. Well, it passed the time away for them, and when they got back to their headquarters, they handed in a grand total of—how much?

10

Lunar Survival

This is a survival problem that originated with the American space organisation NASA. You are captain of a space crew originally scheduled to rendezvous with a mother ship on the lighted sur­ face of the moon. Due to mechanical difficulties, though, your ship was forced to land at a spot some 200 miles from the rendezvous point. During re-entry and landing, much of the equipment aboard your ship was damaged, and since survival depends on reaching the mother ship, the most critical items available must be chosen for the 200-mile trip. Below are listed the fifteen items left intact and undamaged after your landing. Your task is to place them in rank order in terms of their importance to your crew in helping them to reach the rendezvous with the mother ship. Place the fifteen items in descending order of importance, from 1 to 15. Then turn to the answers 14

section and score your decisions against NASA's selection. (a) Box of matches (b) Food concentrate (c) 50 feet of nylon rope (d) Parachute silk (e) A portable heating unit (f) Two .45 calibre pistols with ammunition (g) One case of dried milk (h) Two 100-pound tanks of oxygen (i) A stellar map (j) A liferaft (k) A magnetic compass (l) 5 gallons of water (m) Signal flares (n) A first-aid kit containing injection needles (o) Solar-powered receiver-transmitter

11

More Antimagic

2

3

8

4

6

6

F

1

©nnnnna BHnnoHQoa© 109

Plus and Minus

The fewest number of plus and minus signs for the ascending digits is three: 123-45-67+89=100. The fewest for the descending digits is four:

98 -76+ 54 + 3 + 21 = 100. 116

80

Think!

It is not possible to deduce whether statement E is true or false.

39

A Superior Sum

ELEVEN+TWO=TWELVE+ONE.

24

A Word Square

R 0 S E T T E R

0 V E R

S E Q U

E R U P

R 1 T U N 1 L E V E D E

T R 1 T 1 C A L

117

T E U L N E 1 V C A A T T E E S

R E D E L E S S

89 How Many Triangles? The diagram shows how seven lines can produce eleven nonoverlapping triangles.

141

The Five Couples

Abraham is married to Isabella; Boris is married to Katie; Clarence is married to Gwendolin; Dwight is married to Janice; Ephraim is married to Hermione; Ferdinand is married to Louisa.

2

cmi

Loop number 2.

29

Today's Special

Two sausages would cost lip. Since xy+wy=yw and yw—wy=xy, w must be an even number. And xy must be divisible by 9. Leading to w=2, x=3, y=6, and z=7.

67 The collector has 301 stamps. 118

The Stamp Collector

6

Domino Doti

Five. Each value appears on an even number of squares—eight. Inside the chain the values match in pairs, therefore a 5 at one end of the chain must be matched by a 5 at the other end.

91

The Six Prisoners

Call the prisoners in cells 1, 2, 3, 4, 5 and 6, A, B, C, D; E and F respectively. The gaoler took prisoner B into the unnumbered cell, closed the door, and then, moved the prisoners about as follows, always closing the door. FCDFCEACFDEFCAFEDCB

Obviously, in each case the prisoner is always moved to the only vacant cell.

30

Honeycomb

me)

1. revere 2. retort 3. serene 4. terror 5. relate 6 secret 7. rotate 8. tables ^relent 10. Albert 11. estate 12. trifle 13. rebate 14. retire 119

142

. Games and Puzzles

The number of different ways of spelling out GAMES AND PUZZLES is 3432. The number of different ways of reaching any of the hexagons starting from the letter G is the sum of the number of ways to each of the two hexagons above it, when there are two. Write 1 in each of the top As. There is 1 way to the leftmost M, 1 + 1 to the middle M, and 1 to the right­ most M. The line of Es runs 1, 1 +2, 1 +2, 1. And so on, right down to the final S. The figure in the bottom hexagon will be the number of different ways of spell­ ing out GAMES AND PUZZLES.

3

An Airport Problem (c. 2000 a.d.)

Since the man must have been able to go in any direc­ tion from Perth without going out of his way, he could only have been going to the antipodal point, that is, the point opposite Perth on the globe, which happens to be Bermuda. 120

101

Triangulation

Any one of the four colours may be put in the middle, and the remaining three colours may be put around the outside in only two different ways:

A or A BC CB assuming that the colouring is effective on one side only. That is, the colours do not show through to the other side so that the whole thing can be turned over. The total of different large triangles is 4x2=8. Given five colours it is possible to take these four at a time in five different ways. As above, each of these four will give eight different large triangles. So the total is now 5x8=40.

143

More

Pathfinder

Here is a path which totals 2534 and is probably the maximum obtainable. 9020911992188317921991178918 169*1894189814 99119613 941891 8721882083268817842386288817 2679187830752078307729762774 7234693868346732694067426342 486446 a 48624980438648 SO 4681 8060666889636768836849676843 8* 76088 488468 6060806380 60 TO SO 786430 Msa 3059 39703739 3478 7884 7S3S 287819861290 177837 99108818821786107318 8918 8911

5

Find the Country

(1) Sweden, (2) China, (3) France, (4) Wales, (5) India, (6) Canada, (7) Tibet, (8) Albania, (9) Chad. 121

52

The Right Lines

The 25 points can be connected with a minimum of 8 lines.

83

Beheadments

7. spike, pike 8. grumble, rumble 9. ramble, amble 10. stumble, tumble 11. egad, gad 12. aether, ether

2. flute, lute 3. smelt, melt 4. arise, rise 5. fowl, owl 6. tern, em

105

A Non-Magic Square

I merely cut a piece out of the square as shown and then reinserted it upside down. 4 14

15 10 5 1|11 ' 8

4 14

15 10 1 |8

5 11

7 9

12 13 6 3

7 9

12 6

2 16

16

122

13 3

Missing Animals

The missing animals and the words they complete are: (1) cat (education) (8) cow (scowling) (2) ram (pyramid) (9) ewe (brewery) (3) cur (excursion) (10) pig (spigot) (4) ass (passage) (11) lamb (clamber) (5) lion (billionaire) (12) ape (newspaper) (6) rat (duration) (13) stag (backstage) (7) ox (fox) (14) yak (kayak)

144

Six Sportsmen

The man drinks cola, comes from Belgium, and is the cyclist.

7

Voden’s Flag

No more than three colours are necessary.

53

And the Next, Please (ll)

31, 63 (one less than successive powers of 2) 252, 392 (the sum of successive cubes and squares) 336, 504 (product of n, n+1 and n+2) 18, 30 (two simple series interlocked: 18-22-26 ' and 22-20-18) (5) 40384, 362961 (factorial n plus the square of n, starting with n=3) (6) 36, 57 (differences between terms is 1-3-6-10 etc.) (7) 100,121 (squares of consecutive integers to base 7)

(1) (2) (3) (4)

9

Bob-a-lob

Assume that Athelstan, Balthazar and Caleb have respectively collected A, B and C pence. Then: 2x(A—36)=B+36 2x(B—36)=C+36 A+36=C—36 which can be manipulated to give: A=132, B=156, and C=204. So, they handed in a grand total of 492 pence, or £4.92. 123

112

Domino Rectangles

The smallest number of dominoes is 15, forming a 5-by-6 rectangle. Here is one of several solutions:

41

Division

840. This has 32 divisors. They are, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420 and 840.

106

Five Triangles

Each of the triangles has angles of 30, 30 and 120 degrees. Thus:

122

Cryptograms

1. The distinctive features of the vocal group style were in the vocal harmonies and in the tone of the lead singer. 2. Slang may be desbribed as the common man’s heaven-sent opportunity of being, for a moment, Shakespeare Or Mark Twain. 124

3. You can make your own lazy susan, or you cart buy one that is manufactured especially for use with Scrabble. 4. Influenza is an acute infectious, epidemic disease marked by depression, distressing fever, acute catarrhal inflammation of the nose, larynx, and bronchi, neuralgic and muscular pains, gastrointestinal disorder and nervous disturbances.

The first of the four codes is generated by writing down the alphabet in order, from A to Z. The word UNHOSPITABLE is written under the first 12 letters, followed by all the letters of the alphabet, in order, which do not appear in-that word. Thus: ABCDEFGHIJKLMNOPQRSTUVWXYZ

UNHOSPITABLECDFGJKMQRVWXYZ

Each letter in the original message is encoded by looking up the letter in the top row and coding it as the corresponding letter in the bottom row. The second, third and fourth codes are generated similarly, using respectively the words polysemantic, atmosphering and bulky together, and candleWRIGHT.

81

A Positioning Problem

The digits 1 to 8 should be placed in the circles as shown below. In the series 1, 2, 3, 4, 5, 6, 7, 8 each digit has two neighbours except for the end numbers 1 and 8. Circle C in the diagram is connected to every circle except H. So if circle C contains any of 2, 3,4, 5, 6 and 7, only circle H is left to both the neigh­ bours of whatever goes into circle C. As this is impos­ sible, it is clear that circle C must contain either 1 or 8. Exactly the same argument applies to circle F. Be­ cause of the symmetry of the pattern, it doesn’t matter 125

whether 1 is placed in circle C or circle F, So let us put it in C. Now circle H is the only available circle for 2. Similarly, with 8 in circle F, only circle A can contain 7. The remaining numbers, 3, 4, 5 and 6, can be quickly placed in the remaining circles.

42

Hard Boiled

15 minutes! Start both the timers. Pop the eggs into the boiling water and at time 7, when the small timer runs out, restart it. At time 11, when the big timer runs out, the small timer has been running for four minutes. Invert it, and it will run for another four minutes, run­ ning out at time 15. The eggs will then be hard-boiled to perfection.

17

Crack the Code

Encoding each abbreviation consists simply in subiB^Uting the terminal letter of each word for the initial. Thi* RSVP is encoded as ZLST. 126

120

The Five Hats

The man’s reply ran: ‘I began by calling my two rivals A and B. Since I saw two white hats, I reasoned as fol­ lows : 1.1 could be wearing a black hat or a white hat. 2. Assume it is black. 3. Each of my rivals will there­ fore see a black hat and a white hat. 4. The quicker thinker of the two (say B) might deduce from this that his own hat could not possibly be black because if it were, the man wearing the white hat (A) would see two black hats and would easily infer that his own was white. And then say so. But since A makes no move, B must reason that A does not see two black hats, and as I see one black hat (B continues to reason), the hat I am wearing cannot be black. Therefore, B must be wearing a white hat. 5. But B does not make this claim, and after the lapse of a few minutes one of the two other men would surely arrive at this conclusion if my assumption (number 2) was correct. 6. It seems fair to judge from B’s inactivity that the assumption is invalid, therefore my hat must be white.’

64

Tangrams

The E and the parallelogram can be constructed as shown here.

127

84

Give Us a Word

(1) (2) (3) (4) (5) (6)

Rotisseries Rerehearsals Entrepreneur Redispersed Restructures Shanghaiing

(7) (8) (9) (10) (11) (12)

Offendednesses Embarrasses Intelligent Trustbusters Coincidence Perpetrated

99

The Red Faced Dice

a. 8 b. 12 c. 6 d. 1 Hands up all those who used this information to work out the probability ! There is a much simpler way. All the cubes in the bag together have 27x6 faces. But there are only 9x6 red faces. So, the prob­ ability is clearly: 9x6

27x6 Or one in three.

145

Another Clueless Crossword

Across: 1. tapir 5. overt 8. idiom 9. green 10. essay 11. glean 12. ratio 15. sided 18. agate 19. never 20. gears 24. state 27. patio 28. orate 29. radio 30. exist 31. plead 32. surge Down: 1. tiger 2. pleat 3. Ringo 4. timer 5. omens 6. eased 7. toyed 13. angle 14. inter 16. inert 17. exert 20, group 21. abate 22. speed 23 staid 24. sorts 25. adder 26. elope

108

A Magic Product

The square with the smallest magic product known to us in this one, with the product equal to 216. 128

can cud rann 33

Esther v. Marcie

While the northbound and southbound trains arrive equally often—at five-minute intervals—it happens that their timetables are such that the Edgware train always comes to the platform one minute after the Morden train. Thus the Edgware train will be the first to arrive at Leicester Square station only if the young man arrives during this one-minute interval. If he arrives at the platform at any other time (that is. during the four-minute interval), the Morden train will arrive first. Since the young man’s arrival at the plat­ form is random, the odds are four to one in Martie’s favour.

63

More Animalgrams

1. Racoon 2. Bearcat (also cat-bear) 3. Leopard 4. Terrier 5. Lioness 6. Samoyed 7. Echidna 8. Centaur 9. Spaniel 10. House rat 11. Carthorse 12. African lion

78

Cryptarithmetic

We know that abc*=abca. a=l can be rejected because lb= 1 and ti=c. This means that aV, where a= 1, would become just c. And since c cannot equal abca, we must try further values of a. 129

a=2 gives 2hc*=2bc2. To investigate 2”, write down the first nine powers of 2 (call this list A). To investigate c*. write down the squares of the first nine numbers (call this list B). The product of a number from list A and a number from list B must be of the form 2bc2 if a=2 is to be correct. There is one number in list A and one number in list B which have this property: 2s in list A and 9* in list B give 2592 when multiplied together. Thus 2*9*—2592. a=3 and higher values can be dismissed after setting up similar lists to A and B above and verifying that there are no other answers at all.

111

4 Word Diamond

B M U M A R B U R G

c 0 R R

W A L 1 E D S S E 8

1 V E S T C 0 A T 1 0 N S V A S E T _S_

E C T

w A 1 S L E S D E S

26

C 0 R R E

Across ike Board

48,639. Each square may be approached from one of three possible squares, so we can progressively insert the number of ways of reaching any squire by adding the number* of ways of reaching die three preceding squares. Continuing from one comer of the chessboard to the other, the required answer will appear in the opposite comer. 130

The numbers in the squares in the bottom left-hand corner look like this: 1 7 1 5 13 13 5 7 11111 8

Hey,

Riddle, Riddle!

1. Because one word leads to another. 2. Because there is a host put out and not one guessed. 3. The letter A, because it makes her hear. 4. Because it brings the proudest man to his sneeze. 5. Because he is a pupil under the lash. 6. Time to have the clock repaired. 7. An embarrassed zebra (not a newspaper, that’s ‘read’ all over!). 8. The letter M. 9. Courtship. 10. Because he is pretty sure to be riddled to death.

13Z Channel Choosers Let x be the number who watched all three channels. So (17—x) watched only BBC1 and ITV, (13—x) watched only BBC1 and BBC2, and another (13—x) watched only BBC2 and ITV. So (14+x) watched only BBC1, (2+x) watched only BBC2, and (13+x) watched only ITV. So, the sum of the viewers who watched one, two, and three channels, and non-viewers, should be 100. That is: (17-x) + (13-x)+(13-x)+(14+x) 4-(2+x) +(13+x)+23 = 100. Solving this gives: x=5. That is, five people watched all three channels on the night concerned. 131

113

A Cover Job

0.5882 to 1. The main thing to establish is the radius of the large circle. It is possible to write down two expres­ sions involving this radius and the horizontal distance between the centre of the small circle and the centre of the large circle. Call the big circle’s radius R, and the horizontal separation of the centres h. Then: R=7/2—h • is ■ ; . . and R=7/4+h.(squarerootof 2) Eliminating h and simplifying leads to R equalling 2.776 indies. It is then simple to calculate the total tancoloured area and the total red-coloured area (14.58 and 24.79 square inches), arriving at a tan-to-red ratio of 0.5882 to 1.

95

More Twelvers

Cardsharping (grip, dash, cran); dodecahedron (hand, code, Oder); Freightliner (gilt, heir, fem); headmistress (mass, herd, site); Peeblesshire (beep, Hess, lire); xylophonists (onyx, host, slip).

50

The Rubber Duck

Three miles per hour. In the frame of reference of the Chester River, which is moving, the rower rowed away from the duck and then back to it. At a constant row­ ing rate, it took ten minutes to leave and thus ten minutes to return. Since in these twenty minutes the duck went one mile, the river must flow at 3 m.p.h.

16

A Birthday Poser

Uncle George was bom in 1911. Let his age at death=x. Therefore he was bom in the year of 39x. Therefore 39x+x=40x=year of death. The only year since the Second World War divisible by 40 was I960, making x=49. Therefore Uncle George was bom in i 911. 132

121

A Challenge

Here are two different solutions, both yielding 26 single spaces :

55

Missing Girls

1. Liz 2. Ada 3. Eve 4. Amy 5. Ena 6. Ella 7. Sue 8. Rita 9. Anne 10. Ruth 11. Una 12. Iris 13. Clara 14. Rose 15. Sonia 16. Ida 17. Nonna 18. Vera 19. Marie 20. Dora

115

Clueless Crossword

Across: 1. wed 3. strip 6. sis 8 Eli 9. elk 10. ebb 12. Roger 15. icy 17. Cos 19. refer 21. spy 23. psi 24. out 25. cue 26 aga 27. awe 28 orb 29. air 31. rover 34. set 36. dye 38. radar 41. imp 43. emu 44. ait 45. oil 46. green 47. sob Down; 1. wee 2. deb 3. sir 4. rig 5. per 6. ski 7. sty 11. boo 13. ore 14. ewe 16. cop 17. cocoa 18. spear 19. river 20. rotor 21. stabs 22. yeast 30. ivy 32. ova 33. era 35. elm 36. duo 37. eel 38. rug 39. doe 40. ran 41. its 42. pub 133

23

A Strange Ending

Eight cigarettes. After the seventh is smoked there will be seven ends left—just enough to make one more cigarette.

65

A Bridge Four

Mr. North is the architect, sitting west. Mr. South is the doctor, sitting north. Mr. East is the chartered accountant, sitting south. Mr. West is the banker, sitting east.

130

Three Men (and Three Women) in a Boat

1. A and his wife cross the river. 2. A returns. 3. B’s wife and C’s wife cross the river. 4. A’s wife returns. 5. B and C cross the river. 6. B and his wife return. 7. A and B cross the river. 8. C’s wife returns. 9. A’s wife and B’s wife cross the river. 10. C returns. 11. C and his wife cross the river.

27

The Old Gold Chain

Three. The traveller cut the fifth, 14th and 31st links, leaving him with three single links, one four-link section, one eight-link section, one 16-link section, and a 32-link section. For the first three days he paid the landlord with the single links. On the fourth day he proffered the four-link section, and got the first three links as change. On the fifth, sixth and seventh days, he used the single links again. Then on the eighth day he handed over the eight-link section, and got his seven previous links back. He was able to continue in this manner for all of the 63 days. 134

140

Pathfinder

This line totals 2,840 points and is probably the maxi­ mum obtainable. 505446654566445347 59416040594159 47574649624653475341594060415941 56425451485447535367485449574659 48505254565857474849484746535251 5056 504849 5061 »42 60 39 62 38 63 38 50 604050506050604055465545 56445644 6045463756504339605356396058 3949 26 56 54 3a4MMMW 54 60 4MMV 46 46 28 45 35 6**343432 UMMMU 24 * 34 50 40 5060*45564647 35 36 39 27 38*51 52 29 38 47 *48 37 5058 37 46 5060 9MD 50 50 47 48 49 * 5MM06MU47 43 47 B 46 3032 59 4747 M 3446 24 35 45 B 8M6 54 53 46 36 45 29 46 46 B 23 32 4046 Mt B 20 53 5O66OMP43 43 S 34 35 64 30 50 40 4M9 5212 17 50