The 125 Best Brain Teasers of All Time Page 2
2.If a puzzle seems particularly difficult or complicated, ask yourself: Can the puzzle be reduced to, or compared to, a simpler version that I have solved before?
3.Another way to approach a challenging puzzle is to ask yourself: What systematic approach (diagram, chart) can I employ, or what resources can I consult (dictionary, previous solutions)?
4.It is always useful to jot down the facts of the puzzle in a systematic and orderly fashion to get a solid grasp of all the essential elements.
5.To increase your chances of solving a tough puzzle, paraphrase it in your own words, inspecting and comparing the original to your version very carefully. You might get the relevant insight from this.
6.If you get frustrated over a puzzle, put it aside for a while, and come back to it at a later time. The unconscious mind will continue to work on it, even as you occupy yourself with something else. The solution may then come to you by a flash of insight.
7.Don’t underestimate the usefulness of trial and error. If one approach works, end of story. If it does not, examine it to find out why it was fruitless. On that basis, try out a new hunch.
8.Always check your answer against the puzzle statement to verify its consistency with the original text.
9.If you do not get the correct solution to a puzzle, read the answer at the back of the book, which generally explains the reasoning behind the solution (unless it is a straightforward riddle, anagram, or the like). You might be able to extract general principles from it, which you can then apply to other puzzles.
10.Above all else, enjoy the simple pleasure of delving into a puzzle, even if it does not lead to a solution. Puzzles are miniature works of intellectual art and can be enjoyed as such. Lewis Carroll, who is probably the greatest puzzle-maker of all time, wrote puzzles in such a way that they can be read for their own sake.
1
Change-a-Letter: Saliva
WORDPLAY
The number of word games, many of them dating back to antiquity, is truly mind-boggling—riddles, anagrams, acrostics, and so on. So, let’s start off with a classic type of word puzzle that involves letter changing, an offshoot of several forms of wordplay. For example, by changing one letter in a five-letter word meaning “frighten,” you will get a word meaning “gaze” or “gape.” One arrives at the solution by changing the c in scare (“frighten”) to t to produce the word stare (“gaze” or “gape”). That’s all there is to it.
Change one letter in a four-letter word that refers to stain to get a colloquial word for saliva.
As you might expect, crosswords are among the most loved of all word puzzles. The inventor of the crossword puzzle was the British-born inventor Arthur Wynne (1871–1945). He created the first puzzle for the “Fun” section of the December 21, 1913, edition of the New York World and titled it “Word-Cross.” However, due to a typesetting error, it appeared in print as “Cross-Word.” That erroneous name stuck, and Wynne’s puzzle has been known as crossword ever since.
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2
Anagram: Admirers
WORDPLAY
Anagrams are words or phrases created by rearranging the letters of other words or phrases. Their origin goes right back to the dawn of recorded history. In antiquity, however, these word games were hardly perceived as mere entertainment; rather, they were believed to harbor secrets or prophetic messages. Below is a classic nut in this genre, meant for enjoyment, not divination!
If you rearrange the letters of the word admirer you will get a word referring to two people in a legal union. What word is that?
Anagrams have been a favorite pastime of many rulers and aristocrats of the past. For example, Louis XIII (1601–1643), the king of France during the early 17th century, hired a royal anagrammatist for a handsome salary. It was his job both to entertain the king and to create and send secret messages to the king’s friends, either to stump them or provide mental recreation.
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3
Coins, Coins
MATH
Puzzles and games based on the use of coins reach back considerably in time. The ancient Japanese called one of their most popular coin games Hiroimono, or “things picked up,” because it is played by picking up and moving items one at a time. Our puzzle involves the value of coins, rather than moving them around in some way.
What three current US coins add up to 45 cents if one of the coins is not a nickel?
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4
Dudeney’s Relations
LOGIC
The following puzzle is based on a genre invented by one of the greatest puzzle-makers of all time, the Englishman Henry E. Dudeney. You will have an opportunity to solve his original puzzle—considerably more difficult than the version presented here—later on in this book.
A young girl answers her cell and asks, “Who is this?” A man’s voice responds, “Figure it out. Your mom’s mother is my mother-in-law.” What’s the man’s relation to the girl?
Physicist Albert Einstein (1879–1955) once said, rather appropriately, that “Logic will get you from A to B. Imagination will take you everywhere.”
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5
Jobs, Jobs
LOGIC
Here is another of Dudeney’s inventions paraphrased for convenience. If this is your first exposure to this kind of puzzle, you are in for a treat in logical thinking. By the way, here is what Dudeney had to say about puzzles: “The fact is that our lives are largely spent in solving puzzles; for what is a puzzle but a perplexing question? And from our childhood upwards we are perpetually asking questions or trying to answer them.” Quite true, isn’t it?
In a certain company, the positions of director, engineer, and accountant are held by Bob, Janet, and Shirley, but not necessarily in that order. The accountant, who is an only child, earns the least. Shirley, who is married to Bob’s brother, earns more than the engineer. What position does each person fill?
As this puzzle demonstrates, logic and language are intertwined—indeed, the hidden logic is enshrouded in the implications of the words chosen. The famous Swiss psychologist Jean Piaget (1896–1980) put it aptly: “Logic and mathematics are nothing but specialized linguistic structures.”
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6
Compound Words
WORDPLAY
A compound word is the combination of two individual words to create an entirely new meaning. For example, the noun handkerchief is made up of two nouns: hand + kerchief. So, a handkerchief is a kerchief held in one’s hand. Puzzles that play on this feature involve figuring out the compound word by relating the definition of its two parts. For example, can you determine the compound word made up of two distinct parts meaning “inside” and “place something?” The answer is input, since in = “inside” and put = “place something.” It’s as simple as that. Here are a few puzzles of this kind to challenge your brain.
What compound words do these suggest?
(1) companion + sailing vessel, (2) volume + retail establishment, (3) leaf color + abode, (4) gaze + away
The 1511 collection titled Amusing Questions was published by a printer called, rather appropriately, Wynkyn de Worde. It was among the first books printed after the invention of the printing press.
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7
Racing: Three Runners
LOGIC
This form of logic puzzle is a real brain teaser. No one knows for sure who invented it, but it has been around for quite some time. This is the first of several such puzzles in this book, each successive example increasing in level of difficulty.
Three runners—Frieda, Hannah, and Gina—competed in a high school race. Frieda beat Hannah, but not Gina. Which runner came in first?
For some reason people have always been attracted to racing games, typically played with objects on surfaces and boards. Today, many of
the most popular board games fall into this category, such as Parcheesi and backgammon.
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8
Odd-One-Out: Materials
WORDPLAY
If you have ever taken an IQ test, you are familiar with the “odd-one-out” format. For example, in the set of words baseball, tennis, helmet, football, hockey, the word helmet, unlike the other four words, does not refer to a specific sport. Therefore, logically, it is the odd one out. While these puzzles commonly appear on IQ tests and are used to assess candidates for various purposes, surprisingly, nothing is known about their origin.
Which one of the words in this set does not belong conceptually to the others?
sand
iron
gasoline
copper
steel
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9
Lateral Thinking: Seven Letters
LOGIC
You’ve heard of the expression lateral thinking, haven’t you? It comes from psychologist Edward de Bono’s work in the late 1960s, showing that sometimes we have to think outside the box a bit, as the expression goes. Since then, the lateral-thinking puzzle has become a genre all its own. One subgenre involves decoding the meaning of seemingly random symbols. This is the first of three classified here under the category of lateral thinking—with just a touch of poetic license.
What could the following sequence of letters possibly mean?
MTWTFSS
The classic example of lateral thinking is a story about a truck stuck under a low bridge. As a group of people tried to think of some way to force the truck out, a little boy, using lateral thinking, suggested a solution that is obvious, believe it or not. This puzzle will be presented to you later as number 57.
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10
Coffee Math
MATH
Puzzles can be found in one of the first math textbooks ever devised, known as the Ahmes Papyrus from Egypt (1650 BCE). Throughout this puzzle collection, we will refer to this fascinating papyrus. The following puzzle has been created in the style of the puzzles in that book, focusing on fractions and ratios.
Bill, Arnie, Lisa, and Lucy went to a coffee shop last night. Lucy drank 6 pints of coffee (an awful lot, don’t you think?). Bill drank half of Lucy’s amount, Arnie drank half of Bill’s, and Lisa drank half of Arnie’s. How many pints did Lisa drink?
Incidentally, the textbook is called both the Ahmes Papyrus, after the Egyptian scribe Ahmes, who copied it, and the Rhind Papyrus, after the Scottish lawyer and antiquarian, Alexander Henry Rhind (1833–1863), who purchased it in 1858 while vacationing in Egypt. The papyrus had been found a few years earlier in the ruins of a small building in Thebes in Upper Egypt.
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11
Matching Colors: 20 Balls
LOGIC
The following puzzle genre was invented by the late Martin Gardner (1914–2010), who was the puzzle columnist for Scientific American for 25 years, starting in 1956. Gardner is acclaimed as one of the modern era’s best puzzle-makers.
For this kind of puzzle, you must consider the “worst-case scenario”; in other words, do not assume that you will be lucky and draw out the matching balls with your first two draws. The worst-case scenario means that you need to envision yourself unlucky to the maximum.
In a box there are 20 balls: 10 white and 10 black. The balls are equally spherical, and both weigh and feel the same. If you are wearing a blindfold, what is the least number of balls you must draw from the box to get a pair of balls matching in color (two white or two black)?
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12
Matching Colors: 30 Balls
LOGIC
Let’s do another one in this genre, perhaps adding some complexity to it!
In a box are 30 billiard balls—10 white, 10 black, and 10 red—scattered haphazardly. Again, they all weigh and feel the same. If you are wearing a blindfold, what is the least number of balls you must draw out to get a pair that matches: that is, two white balls, two black balls, or two red balls?
As you can see, logic can be confusing. Lewis Carroll made this rather appropriate statement, albeit rather tongue-in-cheek: “Contrariwise, if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.”
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13
A Common Word
WORDPLAY
The study of how words form their own associations and semantic patterns is the basis of rhetoric, the art of using persuasive and effective language. The associative aspect of language is also the basis for various word puzzles. Consider this one below.
What single word can be added to all of the following words to create legitimate new compound words?
jail, cage, brain, call, song
The first book of crossword puzzles was published by Simon & Schuster in 1924. Titled The Cross Word Puzzle Book, it consisted of a compilation of crossword puzzles from the newspaper New York World and was an overnight best seller.
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14
Fibonacci’s Legacy
MATH
Leonardo Fibonacci of Pisa (1170–1250) made many original contributions to mathematics, including his legendary Fibonacci sequence. Here is a stretch of his original sequence in the form of a puzzle.
What number comes next?
1, 1, 2, 3, 5, 8, 13, 21, 34, 55 …
IQ tests typically use sequences similar to this one. The first widely used IQ test was prepared by French psychologists Alfred Binet and Théodore Simon in 1905. Their aim was to measure intelligence independently of social class, ethnicity, or any other social variable.
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15
A Trickier Fibonacci
MATH
Sequence puzzles require a combination of math and logic. Here’s another one for you to try.
What number comes next?
3, 4, 6, 9, 13, 18, 24, 31 …
Did you know that there is a branch of mathematics, called recreational mathematics, which studies the history, structure, and meaning of mathematical puzzles?
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16
Palindrome: Vessel
WORDPLAY
A palindrome is a word or expression that reads the same backward as forward. Here’s a famous example of a palindrome: A man, a plan, a canal, Panama! Note how adjusting the punctuation and the spaces between the words allows one to read the sentence in either direction.
What five-letter English word starting with k can be read forward and backward and refers to a type of vessel?
Palindromes were important in antiquity, as a famous acrostic, known as the Sator Acrostic, reveals, found among the ruins of Pompeii (and other ancient places). The word acrostic derives from the Greek term akrostikhis, which is a combination of akron (“head”) and stikhos (“row, line of verse”). Literally, therefore, it meant “the line at the head,” pointing out the fact that in addition to horizontal rows, an acrostic contains a vertical row formed by the letters at the “head” of each line. The word found its way into English in the 16th century, suggesting that anagrams had become popular during that period.
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17
Palindrome: Round and Round
WORDPLAY
Now, try your hand at this palindrome.
What seven-letter English word starting with r can be read forward and backward, and refers to something that makes things go round and round?
Ralph Waldo Emerson (1803–1882) once wrote that “a character is like an acrostic or Alexandrian stanza; read it forward, backward, or across, it still spells the same thing.” Incidentally, one of the most interesting problems in mathematics is to find palindromic prime numbers (numbers that have no factors other than themselves and 1).
For example, 101 is a prime number and its digits can be read forward and backward. Another such number is 919. Can you find others?
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18
Fishy Size
MATH
The following puzzle is a classic one in simple mathematics, but a tricky one nonetheless. Puzzles like this reach considerably far back in history.
The other day my friend went fishing. She caught an enormous trout that was 20 feet long plus half of its own length. What was its total length?
The term enigmatology was coined by Will Shortz, puzzle editor at the New York Times, to draw attention to the importance of studying puzzles systematically and examining them just like any other type of human intellectual or creative artifact. The word is defined simply as “the study of puzzles.”
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19
Doublet: Cold to Warm
WORDPLAY
Lewis Carroll was not only a great writer of children’s books and a mathematician, but also one of the most brilliant puzzle creators in history. His “doublet” puzzle has become a staple in the category of word games. The challenge is to transform one word into another by changing only one letter at a time, forming a genuine new word (not a proper name) with each letter change. For example, turn the word grow into flop in just two steps between the beginning and ending words: GROW—(1) glow—(2) flow—FLOP. The first step is to change the r in grow to l to get glow. The second step is to change the g in glow to f to get flow. Finally, by changing the w in flow to p, we get the final world flop.