A List of the Puzzles and a Note on Their Sources

The references below include the texts from where I have taken, or adapted, the puzzles in this book. Often these texts are not the original sources. In some of the cases, the titles are my own. An asterisk (*) denotes that I have used the original wording of the puzzle (or a translation of the original) in the question.

Every attempt has been made to contact copyright holders. All queries should be addressed to the publisher.

In addition to the books mentioned below I am indebted to the following wonderful resources: David Singmaster’s Sources in Recreational Mathematics, which although unpublished is easily available online; Alexander Bogomolny’s site www.cut-the-knot.org; and St. Andrews University’s MacTutor History of Mathematics Archive.

Introduction

Number Tree: Nobuyuki Yoshigahara. Puzzles 101, A K Peters/CRC Press (2003).

Canals on Mars: Sam Loyd. Martin Gardner (ed.), Mathematical Puzzles of Sam Loyd, Dover Publications Inc. (2000).

Ten tasty teasers
Are you smarter than an 11-year-old?

All problems © United Kingdom Mathematics Trust.

Cabbages, Cheating Husbands, and a Zebra
LOGIC PROBLEMS

1 Wolf, Goat, and Cabbages (puzzle p. 14; solution pp. 14–16): Alcuin, Propositiones ad Acuendos Juvenes (9th century).

2 Three Friends and Their Sisters: Alcuin, Propositiones ad Acuendos Juvenes (9th century).

3 Crossing the Bridge: William Poundstone, How Would You Move Mount Fuji?, Little Brown and Co. (2003).

4 * The Double Date: Alcuin, Propositiones ad Acuendos Juvenes (9th century).

5 * The Dinner Party: Lewis Carroll, A Tangled Tale, Macmillan and Co. (1885).

6 Liars, Liars: Lewis Carroll in Martin Gardner, The Universe in a Handkerchief, Copernicus (1996).

7 Smith, Jones, and Robinson: Henry Ernest Dudeney, Strand Magazine (April 1930).

8 * St. Dunderhead’s: Hubert Phillips, S. T. Shovelton, G. Struan Marshall, Caliban’s Problem Book, T. De La Rue (1933).

9 * A Case of Kinship: Hubert Phillips, S. T. Shovelton, G. Struan Marshall, Caliban’s Problem Book, T. De La Rue (1933).

10 The Zebra Puzzle: Life International (December 17, 1962).

11 * Caliban’s Will: Hubert Phillips, S. T. Shovelton, G. Struan Marshall, Caliban’s Problem Book, T. De La Rue (1933).

12 Triangular Gunfight: Hubert Phillips, Question Time, J. M. Dent (1937).

13 Apples and Oranges: William Poundstone, How Would You Move Mount Fuji?, Little Brown and Co. (2003).

14 Salt, Pepper, and Relish: Adapted from Martin Gardner, My Best Mathematical and Logic Puzzles, Dover Publications (1994).

15 Rock, Paper, Scissors: Yoshinao Katagiri in Nobuyuki Yoshigahara, Puzzles 101, A K Peters/CRC Press (2003).

16 Mud Club (puzzle p. 33; solution pp. 33–35): Hubert Phillips, Week-End, taken from Hans van Ditmarsch, Barteld Kooi, One Hundred Prisoners and a Light Bulb, Springer (2015).

17 Soot’s You: George Gamow, Marvin Stern, Puzzle-Math, Viking Books (1957).

18 Forty Unfaithful Husbands: George Gamow, Marvin Stern, Puzzle-Math, Viking Books (1957).

19 Box of Hats: Kobon Fujimura, The Tokyo Puzzles, Biddles Ltd (1978).

20 Consecutive Numbers: Hans van Ditmarsch, Barteld Kooi, One Hundred Prisoners and a Light Bulb, Springer (2015), based on J. E. Littlewood, A Mathematician’s Miscellany, Methuen and Co. Ltd (1953).

21 Cheryl’s Birthday: Joseph Yeo Boon Wooi, Singapore and Asian Schools Math Olympiad.

22 Denise’s Birthday: Joseph Yeo Boon Wooi, theguardian.com.

23 The Ages of the Children: Author unknown.

24 * Wizards on a Bus: John Hhorton Conway, Tanya Khovanova, “Conway’s Wizards,” The Mathematical Intelligencer, vol. 35 (2013).

25 Vowel Play: Peter Wason, “Wason selection task,” Wikipedia.

Ten tasty teasers
Are you a wizard at wordplay?

Questions 1, 3, 5, 7, and 9 are examples of the game of HIPE, invented by Peter Winkler and featured in his book Mathematical Mind-Benders, AK Peters/CRC Press (2007).

Questions 2 and 4 I have seen in many places, but I first read them in Nobuyuki Yoshigahara, Puzzles 101, AK Peters/CRC Press (2003).

Question 6: David Singmaster, Puzzles for Metagrobologists, World Scientific (2006).

Questions 8 and 10: Author unknown.

A Man Walks Round an Atom
GEOMETRY PROBLEMS

26 The Lone Ruler: The Grabarchuk Family, The Big, Big, Big Book of Brainteasers, Puzzlewright (2011).

27 Rope Around the Earth: Author unknown.

28 Bunting for the Street Party: Based on a conversation with Colin Wright.

29 On Yer Bike, Sherlock!: Joseph D. E. Konhauser, Dan Velleman, Stan Wagon, Which Way Did the Bicycle Go?, The Mathematical Association of America (1997).

30 Fuzzy Math: Based on an idea in Joseph D. E. Konhauser, Dan Velleman, Stan Wagon, Which Way Did the Bicycle Go?, The Mathematical Association of America (1997).

31 Round in Circles: New York Times (May 25, 1982).

32 Eight Neat Sheets: Kobon Fujimura, The Tokyo Puzzles, Biddles Ltd (1978).

33 A Square of Two Halves: Kobon Fujimura, The Tokyo Puzzles, Biddles Ltd (1978).

34 The Wing and the Lens: Kobon Fujimura, The Tokyo Puzzles, Biddles Ltd (1978).

35 Sangaku Circles: H. Fukagawa, A. Rothman, Sacred Mathematics: Japanese Temple Geometry, Princeton University Press (2008).

36 Sangaku Triangle: H. Fukagawa, A. Rothman, Sacred Mathematics: Japanese Temple Geometry, Princeton University Press (2008).

37 Treading on the Tatami: Kobon Fujimura, The Tokyo Puzzles, Biddles Ltd (1978).

38 Fifteen Tatami Mats: Donald Knuth, The Art of Computer Programming, Addison-Wesley (1968).

39 Nob’s Mats: Nobuyuki Yoshigahara, Puzzles 101, A K Peters/CRC Press (2003).

40 Around the Staircases: Based on the Mutilated Chessboard Problem, author unknown, Wikipedia.

41 Random Staircases: Adapted from the Mutilated Chessboard Problem, author unknown, Wikipedia.

42 Woodblock Puzzle: Suggested by Joseph Yeo Boon Wooi.

43 Picture on the Wall: Peter Winkler, Mathematical Mind-Benders, A K Peters/CRC Press (2007).

44 A Notable Napkin Ring: Martin Gardner, My Best Mathematical and Logic Puzzles, Dover Publications (1994).

45 Area Maze: © Naoki Inaba.

46 Shikaku: © Nikoli.

47 Slitherlink: © Nikoli.

48 Herugolf: © Nikoli.

49 Akari: © Nikoli.

50 The Dark Room: Joseph D. E. Konhauser, Dan Velleman, Stan Wagon, Which Way Did the Bicycle Go?, The Mathematical Association of America (1997).

Ten tasty teasers
Are you smarter than a 12-year-old?

All problems © United Kingdom Mathematics Trust.

Mathematics Most Fowl
PRACTICAL PROBLEMS

51 One Hundred Fowls: David Singmaster, Sources in Recreational Mathematics.

52 One Hundred Birds: Abu Kamil, Book of Birds (n.d.).

53 The 7-Eleven: Author unknown.

54 The Three Jugs: Abbott Albert, Annales Stadenses (13th century).

55 The Two Buckets: Adaptation of the Three Jugs puzzle.

56 The White Coffee Problem: Author unknown.

57 Water and Wine: Martin Gardner, My Best Mathematical and Logic Puzzles, Dover Publications (1994).

58 Famous for 15 Minutes: Yuri B. Chernyak, Robert M. Rose, The Chicken from Minsk, Basic Books (1995).

59 A Fuse to Confuse: (i) Author unknown. (ii) “Time to Burn,” Varsity Math week 25, Wall Street Journal; and MoMath.org.

60 The Biased Coin: Attributed to John von Neumann.

61 Divide the Flour: Adapted from Boris A. Kordemsky, The Moscow Puzzles, Dover Publications (1955).

62 Bachet’s Weight Problem: Claude-Gaspard Bachet, Problèmes Plaisants & Délectables Qui Se Font Par Les Nombres, 5th ed., A. Blanchard (1993).

63 The Counterfeit Coin: Boris A. Kordemsky, The Moscow Puzzles, Dover Publications (1955).

64 The Fake Stack: Martin Gardner, My Best Mathematical and Logic Puzzles, Dover Publications (1994).

65 From Le Havre to New York: Charles-Ange Laisant, Initiation mathématique, Hachette (1915).

66 The Round Trip: William Poundstone, Are You Smart Enough to Work at Google?, Little, Brown and Co. (2012).

67 The Mileage Problem: Harry Nelson in Scott Kim, The Little Book of Big Mind Benders, Workman Publishing (2014).

68 The Overtake: Dick Hess, Mental Gymnastics, Dover Publications (2011).

69 The Running Styles: Joseph D. E. Konhauser, Dan Velleman, Stan Wagon, Which Way Did the Bicycle Go?, The Mathematical Association of America (1997).

70 The Shriveled Spuds: Author unknown.

71 The Wage Wager: W. W. Rouse Ball, Mathematical Recreations and Essays, Project Gutenberg (1892).

72 A Sticky Problem: Frederick Mosteller, Fifty Challenging Problems in Probability, Dover Publications (1965).

73 The Handshakes: Author unknown.

74 The Handshakes and the Kisses: The Grabarchuk Family, The Big, Big, Big Book of Brainteasers, Puzzlewright (2011).

75 The Lost Ticket: Peter Winkler, Mathematical Puzzles, A K Peters/CRC Press (2003).

Ten tasty teasers
Are you a genius at geography?

The idea of having geography questions in a book of mathematical puzzles is borrowed from Peter Winkler, who did the same in Mathematical Puzzles, A K Peters/CRC Press (2003). Some of my questions are inspired by his, and they all involve some kind of mathematical thinking.

Your Aid I Want, Nine Trees to Plant
PROBLEMS WITH PROPS

Four Coins: H. E. Dudeney, 536 Puzzles & Curious Problems, Scribner Book Co. (1983).

76 The Six Coins: H. E. Dudeney, 536 Puzzles & Curious Problems, Scribner Book Co. (1983).

77 Triangle to Line: Erik Demaine, Martin Demaine, “Sliding Coin Puzzles” in Tribute to a Mathemagician, A K Peters/CRC Press (2004).

78 The Water Puzzle: Nobuyuki Yoshigahara, Puzzles 101, A K Peters/CRC Press (2003), and Erik Demaine and Martin Demaine, “Sliding Coin Puzzles” in Tribute to a Mathemagician, A K Peters/CRC Press (2004).

79* The Five Pennies: H. E. Dudeney, Amusements in Mathematics, Project Gutenberg (1958), and Kobon Fujimura, The Tokyo Puzzles, Biddles Ltd (1978).

80 Planting Ten Trees: H. E. Dudeney, Amusements in Mathematics, Project Gutenberg (1958).

81 The Space Race: H. E. Dudeney, Amusements in Mathematics, Project Gutenberg (1958).

82 Tait’s Teaser: P. G. Tait, Introductory Address to the Edinburgh Mathematical Society, Nov 9, 1883, found in Philosophical Magazine (January 1884). Extra puzzle: Martin Gardner, My Best Mathematical and Logic Puzzles, Dover Publications (1994).

83 The Four Stacks: Édouard Lucas, Recreations Mathematiques.

84 Frogs and Toads: Édouard Lucas, Recreations Mathematiques.

85 Triangle Solitaire: Martin Gardner, Mathematical Carnival, Alfred A. Knopf (1975).

86 Coins in the Dark: Author unknown.

87 The One Hundred Coins: Gyula Horváth, International Olympiad in Informatics 1996, in Peter Winkler, Mathematical Puzzles, A K Peters/CRC Press (2003).

88 Free the Coin: Jack Botermans, Matchstick Puzzles, Sterling (2007).

89 Pruning Triangles: H. E. Dudeney, 536 Puzzles & Curious Problems, Scribner Book Co. (1983).

90 Triangle, and Triangle Again: Kobon Fujimura, The Tokyo Puzzles, Biddles Ltd (1978).

91 Growing Triangles: (i) The Grabarchuk Family, The Big, Big, Big Book of Brainteasers, Puzzlewright (2011). (ii) Author unknown.

92 A Touching Problem: Martin Gardner, My Best Mathematical and Logic Puzzles, Dover Publications (1994).

93 Point to Point: Joseph D. E. Konhauser, Dan Velleman, Stan Wagon, Which Way Did the Bicycle Go?, The Mathematical Association of America (1997).

94 The Two Enclosures: H. E. Dudeney, 536 Puzzles & Curious Problems, Scribner Book Co. (1983).

95 Folding Stamps: H. E. Dudeney, 536 Puzzles & Curious Problems, Scribner Book Co. (1983).

96 The Four Stamps: H. E. Dudeney, Amusements in Mathematics, Project Gutenberg (1958).

97 The Broken Chessboard: H. E. Dudeney, The Canterbury Puzzles, E. P. Dutton and Co. (1908).

98 Folding a Cube: Nobuyuki Yoshigahara, Puzzles 101, A K Peters/CRC Press (2003).

99 The Impossible Braid: Author unknown.

100 Tangloids: Martin Gardner, New Mathematical Diversions, The Mathematical Association of America (1996).

Ten tasty teasers
Are you smarter than a 13-year-old?

All problems © United Kingdom Mathematics Trust.

The Number Games
PROBLEMS FOR PURISTS

101 Mirror, Mirror: Boris A. Kordemsky, The Moscow Puzzles, Dover Publications (1955).

102 Nous Like Gauss: Derrick Niederman, Math Puzzles for the Clever Mind, Sterling (2001).

103 That’s Sum Table: Anany Levitin, Maria Levitin, Algorithmic Puzzles, Oxford University Press (2011).

104 The Square Digits: Kobon Fujimura, The Tokyo Puzzles, Biddles Ltd (1978).

105 The Ghost Equations: Nobuyuki Yoshigahara, Puzzles 101, A K Peters/CRC Press (2003).

106 Ring My Number: Nobuyuki Yoshigahara, Puzzles 101, A K Peters/CRC Press (2003).

107 The Four Fours: Solutions thanks to http://mathforum.org/ruth/four4s.puzzle.html.

108 Our Columbus Problem: Sam Loyd in Martin Gardner (ed.), More Mathematical Puzzles of Sam Loyd, Dover Publications (1960).

109 Threes and Eights: Author unknown.

110 Child’s Play: Author unknown.

111 Follow the Arrow 1: Nobuyuki Yoshigahara, Puzzles 101, A K Peters/CRC Press (2003).

112 Follow the Arrow 2: Nobuyuki Yoshigahara, Puzzles 101, A K Peters/CRC Press (2003).

113 Follow the Arrow 3: William Poundstone, Are You Smart Enough to Work at Google?, Little, Brown and Co. (2012).

114 Dictionary Corner: Dick Hess, Mental Gymnastics, Dover Publications (2011).

115 The Three Witches: Mike Keith, http://www.cadaeic.net/alphas.htm.

116 Odds and Evens: Martin Gardner, The Unexpected Hanging and Other Mathematical Diversions, University of Chicago Press (1963).

117 The Crossword That Counts Itself: Lee Sallows in Joseph D. E. Konhauser, Dan Velleman, Stan Wagon, Which Way Did the Bicycle Go?, The Mathematical Association of America (1997).

118 An Autobiography in Ten Digits: Martin Gardner, Mathematical Circus, Vintage Books (1968).

119 Pandigital Pandemonium: Ivan Moscovich, The Big Book of Brain Games, Workman Publishing (2006).

120 Pandigital and Pandivisible?: Author unknown.

121 1089 and All That: Joseph D. E. Konhauser, Dan Velleman, Stan Wagon, Which Way Did the Bicycle Go?, The Mathematical Association of America (1997).

122 Back to Front: New York Times online (April 6, 2009).

123 The Ninth Power: Derrick Niederman, Math Puzzles for the Clever Mind, Sterling (2001).

124 When I’m Sixty-Four: William Poundstone, Are You Smart Enough to Work at Google?, Little, Brown and Co. (2012).

125 A Lot of Nothing: William Poundstone, Are You Smart Enough to Work at Google?, Little, Brown and Co. (2012).