Doublet: Four to Five
WORDPLAY
Try your hand at the following doublet devised by the inventor of the genre, Lewis Carroll.
Change four to five with a minimal number of steps between the two words.
Did you know that President Bill Clinton is a crossword puzzle aficionado? He even composed an online crossword puzzle for the New York Times in 2007.
CLUE
ANSWER
90
Carroll’s Bag of Marbles
MATH
Lewis Carroll was truly a brilliant puzzle-maker in all genres, not just a maker of doublets. Here’s another example from his cunning imagination.
A bag contains one marble, known to be either white or black. A white marble is dropped inside, the bag shaken, and one drawn out, which also proves to be white. What is now the chance of drawing another white marble?
Did you know that Carroll was also a photographer at around the time that photography was invented? He took many photographs that still exist today and are appreciated as art photography. He photographed famous personages, including Lord Salisbury and Alfred, Lord Tennyson.
CLUE
ANSWER
91
Doublet: Wheat to Bread
WORDPLAY
Here’s yet another of Carroll’s inspired doublets.
Change wheat to bread with a minimal number of steps between the two words.
Riddles are found throughout our literary tradition, attesting to their perceived importance in human life. Works of literature that contain riddles range from Ulysses (1922) by James Joyce (1882–1941) and Emma (1815) by Jane Austen (1775–1817) to Wizard and Glass: The Dark Tower IV (1997) by Stephen King.
CLUE
ANSWER
92
Codes and Ciphers
LOGIC
Given the extraordinary ingenuity that has gone into inventing and breaking secret military and other codes over the centuries, it is little wonder that cryptography has given rise to a genre of puzzles called, appropriately enough, cryptograms. These became very popular in the 19th century after Edgar Allan Poe used a cryptogram in his story “The Gold-Bug” (1843). The most common type of cryptogram puzzle is the letter-to-letter substitution, known as a Caesar cipher, because it was Julius Caesar who apparently used this as a technique. Here’s how this type of puzzle works. What three-word simple phrase does the following encode: H KNUD XNT? The hidden phrase, technically called the plain-text, is I LOVE YOU. It was encoded by replacing each letter with the letter immediately before it in the normal alphabet. So I was replaced with H (the letter just before it), L with K, O with N, and so on. That is the code.
Try your hand at the following cryptogram.
This Caesar cipher hides a quotation by Mark Twain from his short novel The Refuge of the Derelicts (1905):
RFCPC UYQ LCTCP WCR YL SLGLRCPCQRGLE JGDC.
Can you decipher it?
Cryptography originated as a form of secret writing, not mental recreation. The writers of sacred Jewish texts, for example, often concealed their messages by substituting one letter of the Hebrew alphabet with another—the last letter in place of the first, the second last for the second, and so on. That method of cryptography was called atbash.
CLUE
ANSWER
93
Sarah’s Climbing Escapade
MATH
Rate and distance puzzles populate the universe of mathematics. The first such puzzles go back to antiquity and can be found in collections such as the Ahmes Papyrus and Fibonacci’s Liber Abaci, mentioned several times in this book. Here’s a typical example.
My friend Sarah is a mountain climber. She can hike uphill at an average rate of 2 miles per hour, and downhill at an average rate of 6 miles per hour. If she hikes uphill and then continues downhill, without spending time at the top, what will be her average speed for the whole trip?
As you may know, Pythagoras loved mystery and puzzles and formed a secret society to study both, now called the Pythagorean Brotherhood—though in all likelihood this name is a mistranslation, because Pythagoras encouraged full participation by women. Late in life, he married one of his students, Theano. An accomplished cosmologist and healer, Theano headed the Pythagorean society after her husband’s death, and even though she faced persecution, she continued to spread the Pythagorean philosophy throughout Egypt and Greece alongside her daughters. A basic tenet of the Pythagoreans was that each natural number held symbolic significance. They claimed, for instance, that the number 1 stood for unity, reason, and creation. This is why they believed the single horn of the unicorn possessed magical powers. Today it continues to have this meaning in many cultures, where, in the form of a cordial, it is purported to cure diseases, as well as to neutralize the poisons of snakes and rabid dogs.
CLUE
ANSWER
94
Anagram: Shred
WORDPLAY
Here is an anagram with an extra twist: You are not provided with the words that need transforming from one to the other. Instead, you must start with the definitions to decipher what these words are.
Rearrange the letters in a word meaning “shred” to produce a word meaning “prominent or important.”
Sir Arthur Conan Doyle (1859–1930) was intrigued by puzzles, incorporating them in several of his Sherlock Holmes mysteries. He seems to have been particularly captivated by cryptograms, following in the footsteps of Edgar Allan Poe.
CLUE
ANSWER
95
Anagram: Incentive
WORDPLAY
Here is another anagram in the same format as the previous one. You are not given the words in question, so you have to figure them out using the given definitions.
Rearrange the letters in a word meaning “inventive” to produce a word meaning “responsive.”
The New York Times, which is emblematic as the publisher of the crossword puzzle, wrote in 1924 that crossword puzzles were “a sinful waste” in futility. How the times [pun intended] have changed.
CLUE
ANSWER
96
Anagram: Fatherly
WORDPLAY
Here is one more puzzle demonstrating this format of anagram.
Rearrange the letters in a word meaning “fatherly” to produce an adjective referring to a mother and a father.
In the 1999 movie The Matrix, the place between the real world and the Matrix is cleverly named Mobil. This is actually an anagram of limbo, a region between heaven and hell.
CLUE
ANSWER
97
Gardner’s Sock Puzzle
LOGIC
Let’s do another puzzle in Martin Gardner’s genre of drawing items from a box.
In a box are 30 pairs of socks: 10 green, 10 red, and 10 yellow. In each case 5 are of one orientation (for the left foot) and 5 are of the other (for the right foot). Assuming you are blindfolded, what is the least number you must draw to get a pair of socks that match in color (2 green, 2 red, 2 yellow) and orientation (a pair of green left and right socks, and so on)?
Puzzles and games of all kinds are of interest to computer scientists as a means to develop algorithms. For example, Mastermind is a popular game for two players. It is played with pegs and resembles a pen and paper puzzle called “Bulls and Cows” that potentially dates back more than a hundred years. Mastermind is particularly appealing to computer scientists, since they can create algorithms to play it.
CLUE
ANSWER
98
An Ace or a King
MATH
In 1940, Edward Kasner (1878–1955) and James Newman (1907–1966) published their famous work, Mathematics and the Imagination. In the book, the two mathematicians made the following apt statement: “The theory of equations, of probability, the infinitesimal calculus, the theory of point sets, of topology, all have grown out of problems first expressed in puzzle form.” The following puzzle comes from that b
ook.
Since there are 4 aces in a deck, the probability of drawing an ace from 52 cards is . But what is the probability of drawing either an ace or a king from the deck in one draw?
CLUE
ANSWER
99
Dudeney’s Kinship Masterpiece
LOGIC
Recall from puzzle 4 that the inventor of complicated kinship puzzles was Henry Dudeney. His original invention is now considered a masterpiece in the genre. Here it is (slightly modified)—see if you can crack it.
A boy is looking at a photo: “Brothers and sisters have I none, but this man’s son is my father’s son.” Who is the person in the photo?
Well-known writer Marilyn vos Savant, also known for having the highest recorded IQ, gives the following good advice about crossword puzzles: “People who work crossword puzzles know that if they stop making progress, they should put the puzzle down for a while.” This sound advice applies to puzzles of all kinds.
CLUE
ANSWER
100
Time Logic
LOGIC
This next puzzle will truly test your wits.
Jason works every third day at a department store as a part-time sales clerk. Alicia also works there, but only on Saturdays. The store stays open seven days a week. This week, Jason worked on Monday, October 1. On what date will the two be working together?
Before embarking on the toughest puzzles in level 5, you might wonder: Is the ability to solve puzzles specific to humans? Maybe not. Incredibly, researchers found in 2010 that an ant species successfully solved the three-disk version of the Tower of Hanoi puzzle, invented by French mathematician Édouard Anatole Lucas (1842–1891). The puzzle uses three rods and a stack of disks in increasing sizes, which can slide onto any of the rods. It begins with the disks in increasing order, from top to bottom, on the left-most rod—the smallest disk on top and the largest on the bottom. The goal is to move all the disks to the third rod on the right, according to three rules:
1.Only one disk can be moved at one time.
2.Each move consists of taking the upper disk from one of the stacks and placing it on another rod or stack.
3.No disk can be placed on top of a smaller disk.
With three disks, the puzzle can be solved in seven moves. It is truly amazing that ants were able to solve this!
CLUE
ANSWER
101
Ancient Math
MATH
The Ahmes Papyrus, as discussed earlier, is one of the first known collections of math problems and puzzles. Since what we have is a version copied by a scribe, we know it was written even earlier than 1650 BCE. Among its puzzles, one finds conundrums dealing with fractions and early equations. The following puzzle has been created in the same spirit of the papyrus. The idea is to connect the given numbers with the relevant arithmetical signs into an equation. You must use all the numbers. Before you try solving it, here’s an example. The numbers 13, 75, 248, and 4 can be combined to form a legitimate equation as follows: 4(75 - 13) = 248.
How can the numbers 10, 0, 22, and 12 be logically combined into an equation, using each number only once?
CLUE
ANSWER
102
A Polybius Cipher
LOGIC
A popular type of cryptogram puzzle is the number-to-letter cipher, known as a Polybius cipher because its invention is attributed to the Greek historian Polybius (200–118 BCE). One simple Polybius code would be to replace each letter of the plaintext with digits in numerical order. For example, if the plaintext is I LIKE LIFE, the code would replace I with 1 being the first letter in the text, L with 2 being the second letter in the text, and so on. The end result is the ciphertext 121342154. Note that the same number is used for the same letter, no matter where it appears.
The following cipher encodes a quotation by American author Erica Jong from her book Fear of Flying (1973):
20 12 8 8 18 11 18 8 7 19 22 12 11 18 26 7 22
12 21 7 19 22 12 11 11 9 22 8 8 22 23.
Can you decode it?
The first evidence of the use of cryptograms for recreational purposes dates to a ninth-century manuscript found in Bamberg, Germany, which contains a cryptogram puzzle that transposes Latin letters into Greek.
CLUE
ANSWER
103
Trainspotting, Logically Speaking
MATH
The following is a tricky puzzle in computation. I am not sure where the prototype for the puzzle comes from, but it appears in different guises in many classic collections, so I’ve included it here.
A train leaves New York for Washington every hour on the hour. Similarly, a train leaves Washington for New York, but it does so every hour on the half-hour. The trip takes five hours each way. If you are on the train from New York bound for Washington, how many of the trains coming from Washington going toward New York would you pass?
The great composer and crossword puzzle-maker Stephen Sondheim once said, “The nice thing about doing a crossword puzzle is, you know there is a solution.” Maybe the fact that puzzles have solutions—unlike many other things in life—is what makes them so addictive.
CLUE
ANSWER
104
Which Offer?
MATH
The following is a classic nut in computation—I’m unaware of this one’s origin, as well, but it is found all over the puzzle universe. Here’s your chance to solve it.
You are offered a part-time job as a pizza delivery person, working only on weekends. Your boss gives you a choice of the following two salary options: (1) $4,000 for your first year of work, and a raise of $800 for each year after the first, or (2) $2,000 for your first six months of work, and a raise of $200 every six months thereafter. Which is the better offer?
Listening to classical music, such as to the symphonies of Wolfgang Amadeus Mozart (1756–1791), seems to reap many cognitive benefits. This is known, rather appropriately, as the “Mozart Effect.” Puzzles can also enhance our intellectual skills and can thus be viewed, analogously, as producing the “Puzzle Effect.”
CLUE
ANSWER
105
Duma or Ruma?
LOGIC
Recall Hubert Phillips’s clever logic puzzle 49. This one is somewhat more difficult, but the reasoning is the same.
Recall that in the village described in puzzle 49, the members of the Bawi clan always tell the truth while those of the Mawi clan always lie. While visiting this village, Dr. Brown ran into a woman and a man. They spoke a different dialect of the village language than the one spoken by her previous informants. She asked the woman, “Are you a truth-teller?” “Ruma,” she replied in her dialect. Dr, Brown then asked her partner, a man who spoke English, what she had said. “She said yes,” he replied, “but she is a liar.” Can you figure out the clan(s) to which this man and woman belonged?
Most historians of philosophy maintain that one of the founders of logic as a reasoning system was Aristotle (384–322 BCE), even though similar concepts have been found before Aristotle and in other parts of the world. He was certainly the inventor of the syllogism, which displays how some aspects of logical thinking unfold. For example: (A) All cats are mammals; (B) Pumpkin is a cat; (C) Conclusion: Pumpkin is a mammal.
CLUE
ANSWER
106
What Day Is It?
LOGIC
Remember the liar-detection puzzles from before? Well, here is one real tough nut for you in this genre. However, it may not be so tough by now, since you might have gotten the hang of it.
Alma, Barb, Charlene, Dina, Emma, and Fanny are good friends, but they love to argue—literally over the time of the day! Here they are arguing over what day of the week it is, only confusing the issue further.
ALMA: Yesterday was Friday.
BARB: Today is Saturday.
CHARLENE: No, today is not Saturday. Nor is it Monday or Wednesday.
DINA: The day after tomorrow is Tuesday.
EMMA: Tomorrow is Wednesday.
FANNY: Tomorrow is Friday.
Only one of their statements is true. All the others are false. Can you determine which day of the week it is?
One of the most fascinating puzzle books ever written has the enigmatic title What Is the Name of This Book? (1978) by the late logician and mathematician Raymond Smullyan (1919–2017). It is a fascinating book because it allows readers to grasp a famous theorem in logic (called Gödel’s theorem), without any background in this complicated field, simply by solving the logic puzzles that Smullyan provides.
CLUE
ANSWER
107
Racing: Five International Runners
LOGIC
As promised, here is your final puzzle in this genre (see also 7, 32, 54, 78).
Five runners competed at an international race. On their shirts they bore the numbers 1, 2, 3, 4, and 5. No runner finished according to his or her number; that is, the one who wore number 1 did not come in first, the one who wore number 2 did not come in second, and so on. Number 1 and number 5 came in one after the other. Numbers 3, 4, and 5 finished one after the other, with 3 coming in just ahead of 4, who came in after 5. Number 3 was not the winner. So, who won the race?
The Sudoku Cube, created by Jay Horowitz in 2006, is a version of the Rubik’s Cube. In this case, the faces or facets have the numbers one to nine on the sides instead of colors. The object is to solve the puzzle as you would sudoku, while keeping track of the cube structure, as well.
The 125 Best Brain Teasers of All Time Page 6