Change a letter in the word for “monetary aid to help someone” to produce a new word meaning “perspicuity.”
The English word riddle comes from an Old English word meaning “sieve,” indicating that a riddle is indeed a puzzle from which one has to “sift out” its meaning.
CLUE
ANSWER
67
A Bigger Fibonacci
MATH
Recall the Fibonacci sequence. Here is another puzzle based on the same principle.
What number logically comes next?
2, 4, 12, 48, 240, 1440 …
Many discoveries in mathematics surface from puzzles. A puzzle known as the Königsberg Bridge Problem, devised by the mathematician Leonhard Euler (1707–1783), influenced the development of modern-day graph theory and topology, both of which are crucial for many scientific disciplines. The puzzle basically asks you to traverse a network of seven bridges without repeating any portion of your route. This puzzle is available on numerous websites if you’d like to try it yourself.
CLUE
ANSWER
68
Which Colors Make a Couple?
LOGIC
Recall puzzle 5, Dudeney’s marvelous deduction puzzle. These are now very popular and classified under the general rubric of “logic puzzles.” Here’s another one for you.
Last week, three couples made dates to go to the prom. One girl was dressed in red, one in green, and one in blue. The boys also wore outfits in the same three colors. While the three couples were dancing, the boy in red said to the girl in green and her partner: “Not one of us is dancing with a partner dressed in the same color.” Can you tell who went with whom to the prom?
Here’s an interesting fact: One of the best-selling puzzle-games of all time is the Rubik’s Cube, which has sold over 500 million copies. Have you ever played with the Cube? Solving it requires a combination of logic and visual reasoning in large doses, so I always find it difficult to crack, but some people can achieve it literally in seconds.
CLUE
ANSWER
69
Sequence: Four Words
WORDPLAY
By this point in the collection, you have solved a few number sequence puzzles. Now that you’ve familiarized yourself with that format, it’s time to try your hand at word sequences.
Which word logically comes next?
spot, tops, pots, opts …
CLUE
ANSWER
70
Lies, Lies
LOGIC
Recall the various liar puzzles you have solved so far, including 48, 49, and 60. Most of them are descendants of the original prototype by Hubert Phillips. Here’s another one to keep you on your toes.
Yesterday a bank was robbed. Four suspects were rounded up and interrogated. One of them was indeed the robber. Here’s what they all said under questioning by the police:
ALEX: Daniela did it.
DANIELA: Tara did it.
GARY: I didn’t do it.
TARA: Daniela is a liar. I am innocent.
Only one of these four statements turned out to be true; the others were false. Can you figure out who the robber was?
CLUE
ANSWER
71
Signs, Signs
MATH
This type of puzzle was a favorite of some of the great puzzlists, including Loyd and Dudeney. It can certainly be a head scratcher.
Provide the missing signs (+, −, ×, ÷) that would make the numbers provided work in the following equation:
34 ? 43 ? 6 = 71
Here’s another interesting fact about mathematicians and their love of games. Invented by Danish mathematician Piet Hein (1905–1996), Hex is a board game played on a hexagonal grid. Players take turns placing a stone of their color on a single cell of the board. The objective is to form a connected path of stones before one’s opponent does. Apparently, the game was also invented independently by John Forbes Nash Jr. (1928–2015), the subject of the movie A Beautiful Mind (2001).
CLUE
ANSWER
72
Math Signs
MATH
Here’s a similar puzzle requiring the insertion of math signs.
Provide the missing signs (+, −, ×, ÷) that will lead to a correct equation:
72 ? 8 = 7 ? 2
Sometimes mathematical puzzles show up in the most unexpected places. The Monty Hall Problem was named after Monty Hall, the host of the TV quiz show Let’s Make a Deal. It goes like this: Suppose you are given the choice of three doors. Behind one door is a car; behind each of the other two doors is a goat. You pick, say, door number 1, but the host, who knows what’s behind the doors, opens a different door, number 3, which is hiding a goat. He then asks you, “Would you like to pick door number 2 instead?” What would you say? Is it to your advantage to switch your choice? In fact, it is. It turns out that those who change their answer have a two-thirds chance of winning the car, while those who stick to their choice have only a one-third chance.
CLUE
ANSWER
73
Change-a-Letter: Paramour
WORDPLAY
This type of puzzle is a favorite of many puzzle-makers. Here’s one more of this kind for you to try.
Change one letter in a word referring to a glandular organ and you will get a word meaning “paramour.”
Puzzles that trick us can also frustrate us. Three posts, colored red, white, and blue cast a shadow. Which shadow is the darkest? Shadows are, in fact, all the same hue (dark). But the answer is frustrating if you didn’t figure it out yourself, right?
CLUE
ANSWER
74
Change-a-Letter: Caring
WORDPLAY
Here’s another change-a-letter puzzle.
Change one letter in a word referring to an emitter and you will arrive at a word meaning “caring.”
CLUE
ANSWER
75
Musicians
LOGIC
Recall the brilliant inventions of Henry Dudeney. As we’ve already seen in several cases (such as puzzles 4, 5, and 68), he intended these puzzles to test our logic skills in ingenious ways. Here’s another one in a similar vein, with the difficulty level raised a notch or two.
Bernard, Peter, Rhonda, and Selena are musicians. One is a drummer, one a pianist, one a singer, and one a violinist, though not necessarily in that order. Selena and Bernard play often with the violinist. Selena also plays and performs often with the drummer. Both Peter and the violinist have attended many concerts of the pianist. Peter is not the drummer. What is each person’s musical field?
Puzzles of all kinds are found in literature, the arts, and even music. An example of the latter is Edward Elgar’s (1857–1934) beautiful Enigma Variations, a work that has been characterized as a “musical cryptogram.” Its unknown solution still challenges us today, as many have come forward with plausible explanations.
CLUE
ANSWER
76
Zeno’s Conundrum
LOGIC
The following puzzle goes back to ancient times. Historians attribute it to Zeno of Elea, who lived in the fifth century BCE and was the originator of the well-known paradoxes of motion, four of which have survived and have become important in the development of both logic and mathematics.
Consider two coins of equal size, A and B, touching each other. If B remains fixed and A is rolled around B without slipping, how many revolutions will A have made around its own center when it returns its original position?
Zeno’s class paradox states that a runner who begins running at a starting line will never reach the finish line, because the runner must cover half the distance first; then from that half distance point, the runner must traverse another half distance, and from that new position another half distance, and so on ad infinitum. Conclusion? The half-distance intervals become smaller and smaller, but they go on forever. Using this reas
oning, which is perfectly logical, the runner will never cross the finish line, even though, in reality, we know that the runner will indeed cross it (unless some other factor happens to stop the runner along the way).
CLUE
ANSWER
77
Ladder Rungs
MATH
This puzzle has become a classic one, even though no one knows who invented it as far as I can tell. It reminds us in a fundamental way of the snail problem (puzzle 52), doesn’t it?
During a warehouse fire, a firefighter stood on the middle rung of a ladder, pumping water into the burning warehouse. A minute later, she stepped up 3 rungs, and continued directing water at the building from her new position. A few minutes after that, she stepped down 5 rungs, and from this new position continued to pump water into the building. Half an hour later, she climbed up 7 rungs and pumped water from that new position until the fire was extinguished. She then climbed the remaining 7 rungs up to the roof of the warehouse. How many rungs were on the ladder?
Greek philosopher Pythagoras (570–495 BCE) offers us the following cogent thought, which is relevant to everything in this book: “Reason is immortal, all else mortal.”
CLUE
ANSWER
78
Racing: Six Runners
LOGIC
As promised in level 1’s first racing puzzle, here is a more difficult challenge in this genre than the previous three (puzzles 7, 32, and 54).
Six runners squared off at the annual meet held in their small town. Jerry beat Bob, who beat Paula, who beat Sarah, who beat Tim. Lorraine came in right after Tim. Who won the race?
As you now know, Lewis Carroll was one of the greatest puzzle-makers of all time, if not the greatest. In his book The Game of Logic (1886), he introduced a type of puzzle based on logical deduction by which a solver was expected to reach a conclusion such as “Some greyhounds are not fat,” from premises such as “No fat creatures run well,” and “Some greyhounds run well.”
CLUE
ANSWER
79
Number Riddle: A Warm-Up
MATH
Here is an unusual type of puzzle. It is a number puzzle in the form of a riddle, thus making it twice as hard.
I am a number between 20 and 50. If you multiply me by 3 and divide the result by 9, you’ll get 11. What number am I?
There seems to be a general unstated principle of puzzles: The clearer the puzzle’s guidelines, the more people like to attempt it. Thus, puzzles like crosswords and sudoku likely experience such popularity because the rules for solving them are so straightforward and easy to understand. Of course, this does not make them any simpler to solve.
CLUE
ANSWER
80
Number Riddle: Prime
MATH
Now that you have gotten the hang of it, here’s one more math puzzle in this genre. By the way, if you have forgotten this definition, a prime number is a number that is not divisible by any number other than itself and 1.
I am a prime number less than 100. If you add 2 to me, you will get the next prime number greater than me. If you multiply me by 3, you will get a number which, if you subtract me from it, will give you 34. What number am I?
In the ninth volume of his book the Elements, Euclid (c. 300 BCE) proved that the number of primes is infinite, even though they become scarce as we move up the number line: For example, 25 percent of numbers between 1 and 100 are prime, 17 percent of numbers between 1 and 1,000 are prime, and only 7 percent of numbers between 1 and 1,000,000 are prime.
CLUE
ANSWER
81
Matching Colors: 30 More Balls
LOGIC
Recall Martin Gardner’s famous puzzle, drawing balls from a box (puzzle 11). Here’s a trickier version.
In a box are 30 balls: 10 white, 10 black, 5 green, 3 blue, and 2 yellow. What is the least number you must draw, with a blindfold on, to get a pair of balls matching in color (2 white, 2 black, 2 green, 2 blue, or 2 yellow)?
Ernő Rubik, the creator of the Rubik’s Cube, once wrote that with a good puzzle “nobody is lying.” In fact, puzzles do not lie, but they may sometimes deceive us with their wording and their twists.
CLUE
ANSWER
82
Matching Colors: 25 Balls
LOGIC
Now try your hand at this more complex version of Gardner’s puzzle.
A box contains 25 balls: 5 white, 5 black, 5 green, 5 blue, 2 yellow, 2 brown, and only 1 red. With a blindfold on, what is the least number of balls you must draw to get a pair that match in color (2 white, 2 black, 2 green, 2 blue, 2 yellow, or 2 brown)?
Above all else, Gardner is known for his ingenious mathematical games. But he was also a renowned debunker and skeptic, writing against the pseudo-science that is frequently presented as fact rather than fiction. His 1952 book, Fads and Fallacies in the Name of Science, led to the establishment of the skeptical movement, which promotes scientific inquiry and the use of reasoning in examining all claims.
CLUE
ANSWER
83
Number Riddle: Three Digits
MATH
Now that you have become familiar with this type of numeric puzzle, we will move on to the first of three in a new format. Here the object is to identify a mysterious number. These will really give you a brain workout, and maybe even a headache.
I am a three-digit number, whose digits follow one another in numerical sequence. If you multiply me by 2, and then subtract 1 from the result, you get 245. What number am I?
Previously, we mentioned that Dudeney invented alphametics. However, an example of a verbal arithmetic puzzle like the alphametic was recently discovered from 1864. It was found on page 349 of American Agriculturist magazine, volume 23, published in December of that year. But, in my view, it is unlikely that Dudeney would have had access to the magazine. Moreover, his puzzle is somewhat different. Maybe some puzzles are “archetypes” that recur throughout time and cultures. Could this be such an archetype?
CLUE
ANSWER
84
Number Riddle: A Second Prime
MATH
Here’s the next in this series of numeric riddles. This one focuses on primes.
I am a prime number less than 100. If you add my two digits and then multiply me by the number that results from it, you will get 52. What number am I?
Here are a few other fascinating facts about primes. Two primes that differ by 2, such as 5 and 7 or 17 and 19 are called twin primes; however, it is not yet known whether the number of twin primes is infinite. What can be shown is that each even number (after 2) is the sum of two primes; however, this conjecture has never actually been proven. Though many conjectures about primes continue to be unsolved, primes remain among the most fascinating numbers—they are the atomic particles of all number systems.
CLUE
ANSWER
85
Number Riddle: Single Digit
MATH
Finally, here is the third and last puzzle in this mind-twisting genre.
I am a number between 1 and 5. First, add me to the next number above me. Next, multiply the result by me and add me again. Finally, add the digits in the result, and you will get a number that is twice me. What number am I?
The discovery of mathematical patterns raises some fundamental questions. Are we constituted by our nature to discover it? Do the patterns discovered by mathematicians mirror the patterns hidden in nature? One thing is certain—the discovery of a pattern is a fascinating event in and of itself, as you may have experienced throughout this book.
CLUE
ANSWER
86
Relations: Sister’s Nephew
LOGIC
Here is another version of Dudeney’s marvelous kinship relations puzzle. It’s the first of three in a row.
A married woman who has only one child looks at a photo of a man and thinks, “Th
is man’s son is my sister’s nephew.” What relation does the woman have to the man in the photo?
In 1893 Dudeney struck up a friendly correspondence with renowned American puzzle-writer Sam Loyd, sharing many ideas. However, a rift soon developed after Dudeney discovered that Loyd was publishing many of Dudeney’s puzzles under his own name. One of Dudeney’s daughters recalled that her father once equated Loyd with the devil.
CLUE
ANSWER
87
Relations: Mother’s Grandson
LOGIC
Here’s the second in this clever genre.
Mary has one sister and no brothers. She herself has no children. So, what relation does Mary have to her mother’s grandson?
CLUE
ANSWER
88
Relations: Mother’s Niece
LOGIC
Here’s the third and final puzzle in the Dudeney relations series.
A girl looks at the photo of a woman and thinks: “This woman’s daughter is my mother’s niece.” What relation does the girl have to the woman in the photo?
Lewis Carroll once wrote, “Who in the world am I? Ah, that’s the great puzzle.”
CLUE
ANSWER
89
The 125 Best Brain Teasers of All Time Page 5
