The 125 Best Brain Teasers of All Time
Page 7
CLUE
ANSWER
108
Throwing a 6 or 7
MATH
Recall puzzle 98, taken from Mathematics and the Imagination by Edward Kasner and James Newman. This puzzle also comes from that book.
What is the probability of obtaining either a 6 or a 7 when throwing a pair of dice?
Augustus De Morgan (1806–1871) was a famous mathematician and founder of modern set theory. For puzzle aficionados, however, he is known as author of the marvelous compilation of challenging puzzles, A Budget of Paradoxes (1872), which distinguishes him as one of history’s great puzzle-makers.
CLUE
ANSWER
109
Horace Walpole’s Riddle
WORDPLAY
The following riddle comes from the English politician, writer, and man of letters, Horace Walpole (1717–1797). He is probably best known as the author of The Castle of Otranto (1764), identified by most literary historians as the first Gothic novel. This classic is a tough nut to crack!
Before my birth I had a name,
But soon as born I chang’d the same;
and when I’m laid within the tomb,
I shall my father’s name assume.
I change my name three days together,
yet live but one in any weather.
Who am I?
Riddles have been perceived as tests of intelligence since antiquity. Known as riddle games, these appear in many literary and musical forms. For example, there is a riddle scene in Richard Wagner’s (1813–1883) Siegfried (1857) and a riddle game in J. R. R. Tolkien’s (1892–1973) The Hobbit (1937).
CLUE
ANSWER
110
Alcuin Revisited
LOGIC
Recall puzzle 20, which was created by Alcuin in the 700s. River-crossing puzzles have turned out to be much more than mere exercises in logical thinking. Mathematical historians trace the conceptual roots of mathematical combination patterns to Alcuin’s “River Crossing Puzzles.” It is easy to recognize the roots of modern-day systems analysis, which is based on critical decision-making logic, in these simple, yet intriguing paradigmatic puzzles. Below is a version of the same concept, devised just for you.
The traveler from puzzle 20 reaches the same riverbank, with the same boat there. Along with him are his wolf, goat, head of cabbage, and this time, a mythical monster called the Wolf-Eater. The Wolf-Eater eats only wolves. In addition, when the Wolf-Eater is present on either side, he intimidates the goat, who will then not eat the cabbage. How does the traveler get them all across the river safely?
The first English translation of Alcuin’s Propositiones ad Acuendos Juvenes was produced by John Hadley and David Singmaster and published in volume 76 of The Mathematical Gazette in March 1992.
CLUE
ANSWER
111
Doublet: Flour to Bread
WORDPLAY
Some of Carroll’s doublet puzzles are undeniably challenging, as you will see in the following three puzzles that come directly from his pen!
Change flour to bread with the minimum number of steps between these two words.
Carroll was truly a genius. Incredibly, the fact that Carroll suffered from chronic migraines, epilepsy, stammering, and partial deafness did not deter the quickness of his intellect. It is recorded that he could write 20 words per minute, a page of 150 words in seven and a half minutes, and 12 pages in two and a half hours. He was a prolific letter writer, often writing more than 2,000 letters in a single year. He sometimes wrote backward, as well, forcing his reader to hold the letter up to a mirror in order to comprehend it.
CLUE
ANSWER
112
Doublet: Black to White
WORDPLAY
Here’s a second classic example in this sophisticated trio.
Change black to white with the minimum number of steps between these two words.
Despite being a brilliant mathematician and an unparalleled maker of ingenious puzzles, Carroll could not balance his bank account or carry out other everyday chores that we all take for granted. He often let his account go into overdraft, though he would pay it back faithfully on payday.
CLUE
ANSWER
113
Doublet: River to Shore
WORDPLAY
And now, the third doublet to complete the series.
Change river to shore with the minimum number of steps between these two words.
CLUE
ANSWER
114
Roman Numerals
MATH
This puzzle is a clever invention, although I am not sure of its original creator.
There is one four-digit number, and only one, which, when converted to a Roman numeral, becomes a common three-letter English word meaning “blend.” What number is that?
Did you know that the Rubik’s Cube appears throughout popular culture? It makes an appearance, for example, in the Spice Girls’ “Viva Forever” music video.
CLUE
ANSWER
115
House Numbers
MATH
This type of challenging puzzle particularly appeals to math educators. It requires some exact thinking.
There are 50 houses in a row, numbered consecutively from 1 to 50. How many times must the digit 1 be used?
CLUE
ANSWER
116
Missing Letters
LOGIC
This puzzle was invented by math wizard Theoni Pappas, as far as I can tell. It may look simple, but it is truly a brain teaser.
What two letters are missing in this set:
A, H, I, M, O, T, U, V, W, ?, ?
Following the invention of mass printing technology in the 1400s, collections of riddles were among the first books printed for popular entertainment.
CLUE
ANSWER
117
Doublet: Winter to Summer
WORDPLAY
Here is one final doublet from the pen of Lewis Carroll. It’s a monster.
Change winter to summer with the minimum number of steps between these two words.
Computer scientist, mathematician, and puzzlist Donald Knuth carried out a computer study of doublets, since he believed that three-letter doublets were too easy, even though Carroll found it required six steps to turn ape into man. He also felt that six-letter doublets were trivial, since relatively few six-letter words could be linked in the step-wise fashion stipulated by the doublet. Therefore, he identified the five-letter doublet as ideal. He used a collection of 5,757 common English five-letter words, determining when two words in the set could be linked in a word ladder via other words. Knuth discovered that most of the words in that set were semantically related to each other—an amazing discovery if you think about it! He also discovered that 671 of the words could not be used to form a word ladder with any others. He called these words “aloof”—one of the actual words in that set—which means, of course, “detached.”
CLUE
ANSWER
118
Relations: Daughter’s Mother
LOGIC
We’ve noted on several occasions throughout this collection Henry E. Dudeney’s distinction as one of the great puzzle-makers of all time. Before we close, here’s one last puzzle in his honor.
A woman is an only child and has herself only one child. She is looking at the photo of a woman: “That woman is my daughter’s mother.” Who is the woman in the photo?
In the introduction to his book, The Canterbury Puzzles, Dudeney wrote the following about puzzles: “Theologian, scientist, and artisan are perpetually engaged in attempting to solve puzzles, while every game, sport, and pastime is built up of problems of greater or less difficulty. The spontaneous question asked by the child of his parent, by one cyclist of another while taking a brief rest on a stile, by a cricketer during the luncheon hour, or by a yachtsman lazily scanning the horizon,
is frequently a problem of considerable difficulty. In short, we are all propounding puzzles to one another every day of our lives—without always knowing it.”
CLUE
ANSWER
119
Number Relations
MATH
Below is one final puzzle in this category of number game.
The following four numbers can be connected in only one way into an equation:
0, 13, 17, 30.
Can you figure it out?
Here’s something else that Dudeney wrote in his introduction to The Canterbury Puzzles that is of relevance: “Puzzles can be made out of almost anything, in the hands of the ingenious person with an idea. Coins, matches, cards, counters, bits of wire or string, all come in useful. An immense number of puzzles have been made out of the letters of the alphabet, and from those nine little digits and cipher, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. It should always be remembered that a very simple person may propound a problem that can only be solved by clever heads—if at all.”
CLUE
ANSWER
120
Anagram: Opposition
WORDPLAY
Remember the tricky type of anagram puzzle based on definitions I recently called the “final” one? Well, I take that title back. I’ve thought it over and am adding two more. These are really challenging.
Rearrange the letters in a word meaning “opposition to” to get a word meaning “family trees.”
Scientists such as Galileo, Christiaan Huygens, and Robert Hooke sometimes recorded their findings and empirical discoveries in anagram form to prevent others from stealing the credit.
CLUE
ANSWER
121
Anagram: Marked Down
WORDPLAY
This one really is the final anagram—I promise. Can you solve it?
Rearrange the letters in a word meaning “inferences” to get a word meaning “marked down.”
A blanagram is a word that is the anagram of another word except for one letter. An example is the following. The word claw has no anagram, but changing the c to k produces walk.
CLUE
ANSWER
122
Number Formation
MATH
This type of math puzzle is a favorite of math teachers the world over. It is yet another classic nut whose origin is unknown.
With six 1s and three plus signs, create a formula that will add up to 24.
Math teachers are also fond of magic squares. These are arrangements of numbers that add up to the same constant sum in the rows, columns, and diagonals of a square. Try to put the first nine digits into a three-by-three square (consisting of nine cells) so that they are placed according to this rule. You’ll likely find this exercise both challenging and fun. Magic squares have captured the fancy of many artists, architects, and writers. For example, a magic square is sculpted into the façade of the Passion in the Sagrada Familia church in Barcelona. The sculptor is the Catalan artist Josep Subirachs (1927–2014).
CLUE
ANSWER
123
Digit Addition
MATH
This puzzle is based on a series invented by the Indian mathematician D. R. Kaprekar (1905–1986).
What number comes next?
28, 38, 49, 62, 70, 77, 91 …
Some research exists suggesting that humor and puzzles may be related or located in the same area of the brain. Perhaps this is not so surprising after all: Humor makes us laugh out loud, “Ha-ha!” while solving a tough puzzle leads us to exclaim, “Aha!”
CLUE
ANSWER
124
Gangster Talk
LOGIC
This type of puzzle always presents a challenge. You’ve done a few like it, so enjoy it one last time.
Five gang members were brought in by the police yesterday for questioning. One was suspected of having murdered a rival in another gang. Here’s what each one said.
GARY: Hank did it.
WALTER: Yes, Hank is the killer.
JACK: Hank didn’t do it.
SAM: Gary did it.
HANK: Yes, Gary is the killer.
Four of the suspects lied and only one told the truth. Strangely, the single truth-teller was the murderer. Can you identify the killer?
Martin Gardner once made the following statement, which sums up the subtext of this book perfectly: “The sudden hunch, the creative leap of mind that ‘sees’ in a flash how to solve a problem in a simple way, is something quite different from general intelligence.”
CLUE
ANSWER
125
A Take on Phillips’s Masterpiece
LOGIC
Let’s end with a modified (and less complex) version of a masterpiece from the pen of British puzzle-maker Hubert Phillips, who we have met several times in this book. The reasoning seems harder than it is, in this case.
Before they are blindfolded, three women are told that each one will have either a red or a blue cross painted on her forehead. When the blindfolds are removed, each woman is then supposed to raise her hand if she sees a red cross and to figure out the color of the cross on her own head. Now, here’s what actually happens. The three women are blindfolded and a blue cross is drawn on each of their foreheads. The blindfolds are removed. After looking at each other, the three women do not raise their hands, of course. After a short time, one of the women says, “Our crosses are all blue.” How did she figure it out?
CLUE
ANSWER
Bonus Puzzle
LOGIC
A classic puzzle goes like this:
Each of three houses has three utilities: gas, electricity, and water. Connect each house to all three utilities, so each house has three lines, and each utility also has three lines. In setting this up, you cannot cross lines. You also cannot pass lines through houses or utilities. You cannot share lines either. Can you draw the nine lines required?
The answer to this puzzle is not provided here, since this is an “extra” for you to contemplate, but you can follow up on your own. Make no mistake, it’s a tough nut. You will find explanations on various websites, but before you do, try it out yourself.
CLUES
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LEVEL 1: SMARTYPANTS
1.If it helps, you can work backward, starting with a common word for “saliva.” Also keep in mind that there are four letters involved. Another clue for “stain” is “blemish.”
2.How would you describe the legal status of people who are husband and wife?
3.You really don’t need any help with this one—all you have to do is consider three coins (other than a nickel) that add up to 45 cents. You may have to try out a few combinations, if you do not immediately see it. That’s okay!
4.Think of how you are related to the male person who would have a mother-in-law in your family.
5.Keep in mind that the accountant is an only child. Which of the three people does this condition exclude for that position?
6.Here are two compound parts, in no particular order: look and store. Does this help?
7.Set each person in a left-to-right order with respect to each other using symbols, such as H = Hannah and G = Gina. For example, if you are told that Frieda beat Hannah, you can show it as: F—H, which means that F comes before H. Be careful though. In this type of puzzle such arrangements may be only temporary, since other people may come in between. But that is part of the fun of solving such puzzles.
8.Think about how each item would be classified scientifically, according to its physical composition.
9.Think of each letter as representing the first letter of a specific word. Also, keep in mind the words are connected in a logical sense, as well.
10.Start by calculating the amount Bill drank with respect to the number of pints that Lucy drank.
11.As indicated in the puzzle statement, you have to assume the worst-case scenario—drawing out two balls of different colors. What happens on your
next draw?
12.Like puzzle 11, assume the worst-case scenario—drawing out balls of different colors in a row.
13.The word to be added on would make each word a compound word. For example, the word hand can be added to kerchief or maiden to produce handkerchief and handmaiden. With some trial and error, you will have to narrow down the choice so that the word will make sense when added to all the given words.
14.Observe how each successive number in the sequence increases with respect to the numbers that come before it.
15.In this case, each number increases by a certain factor. Figure that out and you’ve solved it.
16.Keep in mind that the word refers to a type of vessel.
17.As with puzzle 16, keep the meaning in mind. The word means something that makes things go around.
18.Let the fish’s length be x. How would you represent half of this length? You can then set up an equation easily.
19.What letter in cold can be changed to form a legitimate word that will likely lead to warm? After deciding on that letter, just follow your word sense.
20.The key trip over is the first one, of course. Imagine what would happen if you started with the wolf, the goat, or the cabbage first. There is only one way to avoid dire consequences.
21.The word to be inserted contains four letters.
22.Consider very carefully what the statement 50 cents more than the eraser means. Note that the pencil does not cost 50 cents, but this much more than the other item.