The 125 Best Brain Teasers of All Time Page 3
Change cold to warm in just three steps (between the starting and ending words, of course).
Lewis Carroll himself stated that he invented the doublet game on Christmas Day of 1877. Actually, the first mention of the doublet appears in an entry in his diary of March 12, 1878, in which he calls it word links, describing it as a two-player game. He uses the name doublet for the first time in the March 29, 1879, issue of Vanity Fair, for which he wrote many such puzzles.
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20
Alcuin’s Masterpiece
LOGIC
This puzzle is one of a set of three called the “River Crossing Puzzles,” posed originally by the famous English scholar and ecclesiastic Alcuin (735–804 CE). The puzzle below—one of the greatest puzzles of all time—comes from this manual. Can you solve it?
A traveler comes to a riverbank with a wolf, a goat, and a head of cabbage. To his delight he sees a boat that he can use for crossing to the other bank, but to his dismay, he notices that it can carry no more than two—the traveler himself, of course, and just one of the two animals or the cabbage. As the traveler knows, if the two are left alone together, the goat will eat the cabbage and the wolf will eat the goat. The wolf does not eat cabbage. How does the traveler transport his animals and his cabbage to the other side intact in the minimum number of back-and-forth trips?
This puzzle is seen by mathematicians as providing the initial insight into the theory of permutations and combinations. Remember those from school?
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21
Word Chains
WORDPLAY
The number of ingenious puzzles invented to challenge our knowledge of language associations is quite large, attesting to the enormous appeal that wordplay holds for us. One clever type of word puzzle sometimes found in cryptic crosswords (i.e. crosswords with trick clues) is the word chain. This format provides two words separated by a space. Your challenge is to fill that space with a word that produces a legitimate word or expression that relates to both the given words: for example, key _______ link. Inserting chain in the space produces two legitimate words: keychain and chainlink. That’s all there is to it.
Which word inserted in the space produces two legitimate words when combined with the given words?
wild _______ style
The 2006 film Wordplay, directed by Patrick Creadon, is an enlightening documentary on the appeal of crossword puzzles focusing on Will Shortz, the New York Times puzzle editor and founder of the annual crossword tournament. The movie tracks Shortz’s lifelong interest in puzzles and takes a look at the puzzle tournament he founded in 1978.
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22
Count Carefully
MATH
Here’s a tricky puzzle in arithmetic. I am unaware of who first devised this one, but it appears frequently in all kinds of puzzle collections and websites. Be careful!
A pencil and eraser together cost 55 cents. The pencil costs 50 cents more than the eraser. How much does the eraser cost?
Does emotion play a role in puzzles? It does. Not only do puzzles typically bring about a feeling of satisfaction from successfully finding a solution, or a feeling of frustration from not getting it—research also shows that they activate specific emotional centers in the brain.
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23
Trainspotting
LOGIC
This is a classic puzzle that always seems to stump solvers. It has appeared in collections since at least the mid-20th century. Though it’s actually an easy puzzle, it can definitely appear complicated.
A train leaves New York for Chicago traveling at the rate of 75 miles an hour. Another train leaves Chicago for New York an hour later, traveling at the rate of 50 miles per hour. When the two trains meet (cross each other), which one is nearer to New York?
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24
Rebus: Popular Expression
WORDPLAY
Do you know what a rebus is? It is a form of writing that suggests a meaning or message through a combination of symbols and words. Rebus writing goes back considerably in time, but the puzzle version is a relatively modern phenomenon. It can consist of pictures, letters, and numbers in some combination, or a layout of words and symbols that hide some message. It also might involve a play on the sounds of the letters, on the location of words and symbols with respect to each other, or on the pronunciation of the symbols used. The trick is to “read” the message to literally “see” what it yields. For example, what expression does W1111HILE hide? Look closely and we can see that ones have been inserted in the word while—giving us “ones in while.” With some minor adjustment, we arrive at the hidden phrase “once in a while.” Here is a simple rebus for you to try.
What expression does the following rebus suggest?
BRIDGE
DUCK
Rebuses were popular in the Middle Ages and were used to write names, perhaps because they are easier to figure out if one is illiterate.
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25
The Riddle of the Sphinx
WORDPLAY
No book of classic puzzles worth its salt would neglect to include the first documented riddle in history. As already discussed, according to legend, when Oedipus approached the city of Thebes, he encountered a gigantic Sphinx guarding the entrance to the city. The menacing beast confronted Oedipus, posed the following riddle to him, and warned him that if he failed to solve it, he would die instantly at the Sphinx’s hands. Oedipus answered it correctly, and the rest is history.
What creature moves on four legs at dawn, two at noon, and three at twilight?
The main character of the Saw movie series is a figure called Jigsaw. He poses puzzles to people who must solve them in order to save their lives. In essence, Jigsaw is a modern descendant of the Sphinx.
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26
Anagram: Dormitory
WORDPLAY
Throughout history, many famous personages avowed their belief in the divinatory power of anagrams. During the siege of the city of Tyre, Alexander the Great (356–323 BCE) had a dream in which a satyr appeared before him. Troubled by this occurrence, Alexander summoned his soothsayers the next morning to interpret the dream. They pointed out that the word satyr itself contained the answer, because the Greek word for satyr was an anagram of “Tyre is thine.” Reassured, Alexander went on to conquer the city the subsequent day. The point is that anagrams may reveal truth indirectly, as the following puzzle will illustrate. It is a classic anagram, found throughout wordplay collections.
The letters of the word dormitory can be rearranged to produce a two-word phrase that describes a typical dormitory. What is that phrase?
To reiterate here, anagrams might be prophetic after all. An anagram of radioactivity pioneer Marie Curie (1867–1934) is “Me, radium ace.” How accurate!
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27
Odd-One-Out: Shapes
LOGIC
Recall the odd-one-out puzzle from level 1 (puzzle 8). Here’s a slightly tougher one for you to try. Also bear in mind that this type of puzzle is enjoyed enormously by children learning to read and write.
Which of the words in this set does not conceptually belong?
triangle, cube, square, octagon, pentagon
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28
Portia’s Dilemma
LOGIC
Are you familiar with The Merchant of Venice by William Shakespeare (1564–1616)? A highlight of that play is the scene in which Portia’s potential suitors have to choose among three caskets composed of gold, silver, and lead. The one who chooses the correct casket containing Portia’s portrait and a scroll will win her hand in marriage. This kind of puzzle has inspired many variations. Here’s one made up just for you.
Imagine t
hree boxes: a box with two black ties in it, a second box containing two white ties, and a third box with one white and one black tie. The boxes are labeled, logically enough, BB (= two black ties), WW (= two white ties), and BW (= one black tie, one white tie). However, someone has switched the labels, so that now each box is labeled incorrectly. Can you determine the actual contents of each box after one draw? And from which box should you make that draw?
Here is a sage thought from Shakespeare: “There is nothing either good or bad, but thinking makes it so.”
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29
Weighing Conundrum
MATH
Here is a classic puzzle whose origin is unknown. Is it a math puzzle or is it a logic puzzle? Maybe both.
I have seven billiard balls, one of which weighs less than the other six. Otherwise, they all look exactly the same. How can I identify the one that weighs less on a balance scale, using that scale no more than two times?
Math and reason are certainly connected, aren’t they? English mathematician James Joseph Sylvester (1814–1897) put it perfectly when he stated, “Mathematics is the music of reason.”
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30
Don’t Smoke
MATH
Here’s a kind of puzzle that requires some truly clever thinking. It also bears an implicit warning about the dangers of smoking.
Jack used to smoke. One day he decided to quit, cold turkey, after smoking the 27 cigarettes that remained in his pocket. He took out the 27 cigarettes and started to smoke them, one by one. Since it was his habit to smoke only ⅔ of a cigarette, Jack soon realized that he could glue three butts together to make another cigarette. So, before giving up his bad habit, how many cigarettes did he end up smoking?
On the subject of arithmetic, poet Carl Sandburg (1878–1967) offered the following witticism: “Arithmetic is where the answer is right and everything is nice and you can look out of the window and see the blue sky—or the answer is wrong and you have to start over and try again and see how it comes out this time.” It rings true, doesn’t it?
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31
Iron to Lead
WORDPLAY
Recall Carroll’s doublet from puzzle 19. Carroll later modified the rules to make his puzzles more difficult. Here is the example he used to introduce a new version of the doublet. Can you solve it? Rearranging the letters of a word is, of course, making an anagram of the word.
Change iron into lead by introducing a new letter or by rearranging the letters of the word at any step. You may not do both in the same step. Each time you must create a genuine word, of course.
According to some scholars, anagrams originated in the writings of the Greek poet Lycophron (320-280 BCE) who lived in Alexandria. Lycophron’s two most famous anagrams were on the names of Ptolemy (100–170) and his queen, Arsinoë, in his famous poem on the siege of Troy titled Cassandra. It seems that we have been playing with words forever!
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32
Racing: Four Runners
LOGIC
Recall puzzle 7. As promised, here is a slightly trickier puzzle in this genre.
Armand, Claudio, Shirley, Dina, and Elgin competed against each other in a high school race. Elgin beat Claudio, Shirley beat Elgin, Dina came in right after Shirley, and Armand beat Shirley. In which order did they all finish?
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33
Lateral Thinking: Frank’s Children
LOGIC
As promised, here is your second puzzle in lateral thinking. Again, you might find the same form of puzzle under a different rubric in other puzzle collections. But I certainly think it involves lateral thinking. Try it yourself and you be the judge. This one is a classic, by the way.
Frank has three daughters, each of whom has a brother. How many children did Frank have altogether?
The expression thinking outside the box likely comes from the way in which the famous nine-dot puzzle is solved: Connect nine dots arranged in a square alignment using four lines, without the pen leaving the paper or any dots left over. One of the first appearances of this puzzle is in a collection by puzzlist Sam Loyd (1841–1911) dating back to the late 1800s.
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34
Missing Number
MATH
Here’s another type of math puzzle that IQ test constructors love to pose. It is actually quite simple, if you know your basic math.
What number completes the following sequence?
3, 9, 27, 81, 243 …
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35
Alphametic: Three Letters
MATH
The following puzzle is called an alphametic, since it replaces numbers with letters—hence a blend of alpha(bet) + (arith)metic. It belongs to a puzzle genre called cryptarithmetic, developed by two great puzzle-makers, the American Sam Loyd and the Englishman Henry Dudeney. This puzzle is actually rather simple, but if you are unfamiliar with this type, it can be quite challenging.
What numbers do the following letters stand for?
TIP + PIT = APA (A = 5)
One of Sam Loyd’s best chess puzzles is the following one: Place the Queen on any chessboard square and then move her over the 64 squares and back again to the starting square in 14 moves. Can you solve it?
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36
Alphametic: Four Letters
MATH
Now, try your hand at this one, which increases the difficulty level a notch or two.
What numbers do the following letters stand for?
SLOB + BLOL = KOOK
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37
A Classic Nursery Rhyme
LOGIC
The following nursery rhyme appeared in 18th-century England. It has become a classic conundrum with a twist, so be careful!
As I was going to St. Ives, I met a man with seven wives. Each wife had seven sacks. Each sack had seven cats. Each cat had seven kits. Kits, cats, sacks, wives, how many were going to St. Ives?
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38
Voltaire’s Riddle
WORDPLAY
The following riddle was composed by the great French satirist Voltaire (1694–1778).
What of all things in the world is the longest, the shortest, the swiftest, the slowest, the most divisible and most extended, most regretted, most neglected, without which nothing can be done, and with which many do nothing, which destroys all that is little and ennobles all that is great?
As seen in the Riddle of the Sphinx, riddles in the ancient world were regarded as coded messages from the gods. This is because the ancients viewed riddle talk as the gods’ natural language. They therefore believed that only those equipped with special knowledge, such as the Greek oracles who spoke in riddles, could truly understand the message. In later years however, prophets such as Nostradamus (1503–1566) wrote in riddles, as well.
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39
Jumble: A Proverb
WORDPLAY
This genre of puzzle was created in 1954 by Martin Naydel (1915–2006), who is better known for his comic books. It consists of the letters of words all scrambled up. The challenge is to unscramble the letters to find the original words. For example, one way to scramble the letters of the word FRIEND is DFRNEI. There are various versions of this game, including one in which you are provided with several scrambled words, and your goal is to reconstruct a phrase or expression. Here is an example for you to try.
The letters in the words of a famous proverb have been scrambled. Can you figure out what the proverb is?
WOT WSRGON OD OTN KEAM A GHTIR.
The English writer John Dryden (1631–1700) once wrote that anagrams “torture one poor word ten thousand ways.”
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40
Jumble: Alexander Pope
WORDPLAY
Here is another jumble puzzle for you.
Unscramble the letters to get a famous quotation by Alexander Pope:
OT RER SI UHAMN; OT ROFIGEV, NEVIDI.
You might find it interesting that wordplay comes in many varieties and with ingenious twists. A pangram, for instance, is a sentence using every letter of the alphabet at least once. The best-known English example is The quick brown fox jumps over the lazy dog, which uses all 26 letters.
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41
Most Frequent Number?
MATH
This is a math puzzle found commonly in puzzle collections. Here’s our version.
What digit between 1 and 1,000 (inclusive) is the most frequent?
There are many games based on mathematics. One is a two-player mathematical game called Grundy’s Game, which starts with a heap of objects such as checker pieces. The two players take turns splitting the heap into two piles of different sizes. The game ends when the piles can no longer be split into different sizes, such as when one pile consists of only two pieces. Try it with a partner—you’ll find it stimulating and fun. But first, look up the simple rules on the Internet.