The 125 Best Brain Teasers of All Time
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Copyright © 2018 by Marcel Danesi
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ISBN: Print 978-1-64152-008-9 | eBook 978-1-64152-009-6
I dedicate this book to my three grandchildren, Alexander, Sarah, and Charlotte. They have solved my own puzzle of existence simply by being born and being so beautiful.
CONTENTS
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THE TIME-HONORED FUN OF BRAIN TEASERS
LEVEL
1 SMARTYPANTS
1: Change-a-Letter: Saliva
2: Anagram: Admirers
3: Coins, Coins
4: Dudeney’s Relations
5: Jobs, Jobs
6: Compound Words
7: Racing: Three Runners
8: Odd-One-Out: Materials
9: Lateral Thinking: Seven Letters
10: Coffee Math
11: Matching Colors: 20 Balls
12: Matching Colors: 30 Balls
13: A Common Word
14: Fibonacci’s Legacy
15: A Trickier Fibonacci
16: Palindrome: Vessel
17: Palindrome: Round and Round
18: Fishy Size
19: Doublet: Cold to Warm
20: Alcuin’s Masterpiece
21: Word Chains
22: Count Carefully
23: Trainspotting
24: Rebus: Popular Expression
25: The Riddle of the Sphinx
2 PRODIGY
26: Anagram: Dormitory
27: Odd-One-Out: Shapes
28: Portia’s Dilemma
29: Weighing Conundrum
30: Don’t Smoke
31: Iron to Lead
32: Racing: Four Runners
33: Lateral Thinking: Frank’s Children
34: Missing Number
35: Alphametic: Three Letters
36: Alphametic: Four Letters
37: A Classic Nursery Rhyme
38: Voltaire’s Riddle
39: Jumble: A Proverb
40: Jumble: Alexander Pope
41: Most Frequent Number?
42: Containers
43: The Beverley Family
44: Reversals
45: Counting Pets
46: Counting Coins
47: Rebus: Book Title
48: Phillips’s Liar Puzzle
49: What Did He Say?
50: Nabokov’s Word Golf
3 BRAINIAC
51: Gardner’s Matching Shoes
52: The Snail’s Journey
53: Anagram: Princess Diana
54: Racing: Five Runners
55: Anagram: Credible
56: Anagram: Space Traveler
57: Lateral Thinking: Truck Stuck
58: Word Combinations
59: How Many Socks?
60: Caliban’s Truth-Teller or Liar?
61: Sequence: Seven Letters
62: Sequence: Eleven Letters
63: Sequence: Six Letters
64: Code Logic
65: How Much Does It Weigh?
66: Change-a-Letter: Perspicuity
67: A Bigger Fibonacci
68: Which Colors Make a Couple?
69: Sequence: Four Words
70: Lies, Lies
71: Signs, Signs
72: Math Signs
73: Change-a-Letter: Paramour
74: Change-a-Letter: Caring
75: Musicians
4 MASTERMIND
76: Zeno’s Conundrum
77: Ladder Rungs
78: Racing: Six Runners
79: Number Riddle: A Warm-Up
80: Number Riddle: Prime
81: Matching Colors: 30 More Balls
82: Matching Colors: 25 Balls
83: Number Riddle: Three Digits
84: Number Riddle: A Second Prime
85: Number Riddle: Single Digit
86: Relations: Sister’s Nephew
87: Relations: Mother’s Grandson
88: Relations: Mother’s Niece
89: Doublet: Four to Five
90: Carroll’s Bag of Marbles
91: Doublet: Wheat to Bread
92: Codes and Ciphers
93: Sarah’s Climbing Escapade
94: Anagram: Shred
95: Anagram: Incentive
96: Anagram: Fatherly
97: Gardner’s Sock Puzzle
98: An Ace or a King
99: Dudeney’s Kinship Masterpiece
100: Time Logic
5 GENIUS
101: Ancient Math
102: A Polybius Cipher
103: Trainspotting, Logically Speaking
104: Which Offer?
105: Duma or Ruma?
106: What Day Is It?
107: Racing: Five International Runners
108: Throwing a 6 or 7
109: Horace Walpole’s Riddle
110: Alcuin Revisited
111: Doublet: Flour to Bread
112: Doublet: Black to White
113: Doublet: River to Shore
114: Roman Numerals
115: House Numbers
116: Missing Letters
117: Doublet: Winter to Summer
118: Relations: Daughter’s Mother
119: Number Relations
120: Anagram: Opposition
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121: Anagram: Marked Down
122: Number Formation
123: Digit Addition
124: Gangster Talk
125: A Take on Phillips’s Masterpiece
BONUS PUZZLE
CLUES
ANSWERS
FURTHER READING
ABOUT THE AUTHOR
The Time-Honored Fun of
BRAIN TEASERS
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SINCE THE DAWN OF CIVILIZATION, we have been fascinated by conundrums, rebuses, riddles, and enigmas of all kinds. The historical record has made this quite obvious, demonstrating our innate propensity for puzzles and games that has no parallel in any other species. The oldest known cipher—a message laid out in secret code—is a Sumerian text written in cuneiform (wedge-shaped markings carved in soft clay tablets), which dates back to around 2500 BCE. This text is one of the first examples of cryptography, now a popular genre of puzzles. Similar kinds of puzzles and games from the Old Babylonian period (1800–1600 BCE), Egypt (1700–1650 BCE), and the ancient civilizations of the Orient and the Americas have also been discovered by archaeologists. Even more ancient discoveries include game sticks in Africa going back ten thousand years.
One of the oldest puzzles known is the so-called Riddle of the Sphinx. In Greek mythology, the Sphinx was a monster with the head and breasts of a woman, the body of a lion, and the wings of a bird. Lying crouched on a rock, it stopped all those about to enter the city of Thebes by asking them a riddle. (You will find that riddle here in this book as puzzle 25.) Those who failed to answer the riddle correctly were killed on the spot. On the other hand, the Sphinx vowed to destroy itself if anyone managed to come up with the correct answer. When the hero Oedipus solved the riddle, the Sphinx killed itself as forewarned. For ridding them of this terrible monster, the Thebans crowned Oedipus their king.
Throughout history, puzzles have captivated the fancy of many famous personages. Riddle contests were organized by the biblical kings Solomon and Hiram. Charlemagne (742–814), the founder of the Holy Roman Empire, hired a scholar to create puzzles for various reasons. Edgar Allan Poe (1809–1849), the great American writer, and Lewis Carroll (1832–1898), best known for his two great children’s novels, Alice’s Adventures in Wonderland (1865) and Through the Looking-Glass (1872), made ingenious puzzles. The love of puzzles is ancient and shared by everyone, as witnessed today by the widespread popularity of puzzle magazines, “brain challenging” sections in newspapers, riddle books for children, TV quiz shows, websites, social media sites, and game tournaments. Millions of people the world over simply enjoy solving puzzles for their own sake. As the great British puzzlist Henry E. Dudeney (1857–1930) aptly put it, “A good puzzle, like virtue, is its own reward.”
15 FASCINATING FACTS
1.There is no culture on earth without puzzle and game traditions. This strongly suggests that puzzles are hardwired in the brain and may serve some basic function in our species.
2.Many puzzles are associated with myth and legend. For example, arranging the first nine integers in a square pattern so that the sum of the numbers in each row, column, and diagonal is the same is called Lo Shu in China. (In English, it’s Magic Square.) Lo Shu was invented 4,000 years ago, and the Chinese have always believed it possesses mystical properties. To this day, it is thought to protect against the evil eye when placed over the entrance to a dwelling or room. I have one on the door to my office, and I carry another in my wallet, just in case!
3.Author Mark Twain (1835–1910) had this take on riddles (both of the puzzling and the philosophical variety): “Let us consider that we are all partially insane. It will explain us to each other; it will unriddle many riddles; it will make clear and simple many things which are involved in haunting and harassing difficulties and obscurities now.”
4.The Alzheimer’s Association in the United States has endorsed sudoku as a preventive therapy against the disease. Their recommendation is based on published studies. Other puzzle genres such as crosswords and jigsaw puzzles are also recommended. In other words, puzzles may indeed be therapy for the aging brain.
5.The number of possible sudoku puzzles that can be made with the first nine digits is calculated to be 6,670,903,752,021,072,936,960! It would take a computer over 211 billion years to solve them all.
6.The late puzzlist James Fixx (1932–1984) wrote, “Puzzles not only bring us pleasure, but also help us to work and learn more effectively.” Consider that to be a general principle.
7.Cryptograms greatly appeal to our sense of mystery, as evidenced by their frequent use today in mystery and adventure movies, from Sneakers (1992) to The Da Vinci Code (2006) and The Imitation Game (2014).
8.Little is known of the Greek mathematician Metrodorus, who may have lived in the sixth century. His collection of puzzles, which he called “epigrams” in his book the Greek Anthology, is still a challenging one, and rather contemporary in its style and content.
9.Archimedes (287–212 BCE) invented a game called the loculus, which was essentially a type of geometrical jigsaw puzzle. The objective was to combine the pieces in such a way that they fit seamlessly together.
10.Perhaps more than any other puzzle, the riddle genre has appeared in countless movies, including those as divergent as Die Hard with a Vengeance (1995) and The Hobbit: An Unexpected Journey (2012). The reason may well be that a riddle is effective for achieving multiple purposes, from keeping audiences in suspense to making indirect commentary on the plot.
11.Lateral-thinking puzzles truly sharpen the brain. Here’s a classic one: How can it be that someone can fall from the window of a 50-story building and still survive? The answer: He or she fell from the ground-floor window.
12.The word “puzzle” was first documented in a book titled The Voyage of Robert Dudley to the West Indies, 1594–1595 (1899) by Sir George F. Warner (1845–1936). It marked the first time the word was used to describe a type of game.
13.One of longest-running shows on TV is Wheel of Fortune, attesting to the popularity of word puzzles across generations.
14.Chess is an important element in Blade Runner (1982), suggesting that the game is a gauge of human creativity and intelligence. It begs the question: If an advanced robot can play chess, does that make it intelligent?
15.Perhaps the most famous use of chess in film is Ingmar Bergman’s classic from 1957, The Seventh Seal. The scene in which a medieval knight challenges Death to a chess game to save his own life is one of the most memorable in the history of cinema.
HOW TO USE THIS BOOK
I love puzzles. I love researching what goes on in the mind as we solve them. The best brain teasers of all time are—as you might imagine—those that have withstood the test of time. In this book, you will find a number of “classic nuts,” as they are called, in many cases paraphrased for convenience. Having written so many puzzles and taught on the subject, I believe that the classic ones I’ve selected here are among the best of all time. Many have their origins in distant centuries and far-flung cultures, but they are all united by being at once fun and challenging to solve. Although I have organized them from easy to challenging, the sequencing is bound to be subjective. One principle has guided me throughout—all puzzles should be “doable.” Some may take more patience to crack, but they too should be understandable and eventually lead to a clear solution.
This book is designed to provide hours of entertainment and mental challenge. It contains 125 puzzles spread out over five levels of difficulty. The puzzles are numbered consecutively across the levels. Unless you are already an experienced puzzle-solver, you should go through them in order; otherwise skip a tough nut, and come back to it later. Clues are provided to help you for all puzzles—if you need them, of course.
Answers as well as step-by-step solutions for all the puzzles are given at the back. But you should not read these until you have attempted to solve the puzzles on your own first, no matter how frustrated you may be with any particular puzzle. After a while, you
will get the knack of how to go about attacking the different genres of puzzles. If you discover the answer using a different line of attack than the one suggested in the book, you should still study the given solution, simply to get a different perspective on the puzzle-solving process itself. This, too, will enhance your puzzle-solving skills. Incidentally, these skills are not correlated with quickness of thought or IQ. A slow thinker can solve a puzzle just as successfully as a fast one can.
Puzzles can be both pleasurable and frustrating—they are fun if you solve them easily with an aha moment; they can be frustrating if you do not. Hopefully, you will achieve more of the former with this book. It offers intriguing and complex brain teasers (not cheap “gotcha” questions) from around the world and throughout history. It also provides puzzles in a variety of different types (math, logic, and wordplay), organized from easy questions to harder ones, turning the book into a progressively more challenging journey. It is designed to delight you by presenting mental challenges that are “doable” while making no assumptions.
If you are an inveterate puzzle-solver, you will recognize some of the classic ones here, paraphrased in specific ways. But there is ample material to keep you entertained, as well. If you only dabble in puzzles, consider this both a collection of classic puzzles with historical anecdotes and a set of original puzzles derived from them.
No specialized knowledge or intellectual tools are necessary to solve any of the brain teasers. To help you pace yourself, the difficulty level within each section is, more or less, uniform. But this can be hard to maintain or even determine, since puzzle-solving is, by its nature, very subjective. You may find solving Carroll’s doublet puzzles or their derivatives easy but even a simple math puzzle very challenging.
So, there is really no single, “right” way to move through this book, although I suggest that you do start at the beginning if you are a beginner. Of course, you can always decide to skip around or plow straight through. The only requirement is that you challenge yourself (and your friends) and have a little fun.
10 PUZZLE-SOLVING TIPS
1.Before attempting to solve any specific puzzle, ask yourself the following questions: What does it ask me to do? What linguistic, logical, or mathematical feature is applicable? You have to grasp the basis of the puzzle first, before attempting to solve it.