Diophantus’ Age

No one knows much about Diophantus, the Greek mathematician, but in the sixth century a math puzzle purported to give his epitaph:

“This tomb holds Diophantus. Ah, what a marvel! And the tomb tells scientifically the measure of his life. God vouchsafed that he should be a boy for the sixth part of his life; when a twelfth was added, his cheeks acquired a beard; He kindled for him the light of marriage after a seventh, and in the fifth year after his marriage He granted him a son. Alas! late-begotten and miserable child, when he had reached the measure of half his father’s [total] life, the chill grave took him. After consoling his grief by this science of numbers for four years, he reached the end of his life.”

At what age did he die?

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He died at 84.

Unwanted

The maker doesn’t need it.

The buyer doesn’t use it.

The user doesn’t know he’s using it.

What is it?

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A coffin.

July 26, 2006January 15, 2013 | Puzzles

The Kayaker

A child releases a toy boat in a stream that flows at 3 miles an hour. At that instant, a kayaker 14 miles downstream begins paddling upstream at 7 miles per hour. How long will it take him to reach the toy?

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It will take 2 hours. We can ignore the speed of the stream, since it’s carrying both the kayaker and the toy. If he paddles at 7 mph, he’ll cover 14 miles in 2 hours.

June 27, 2006January 15, 2013 | Puzzles

Missing Square Puzzle

New York magician Paul Curry invented this puzzle in 1953. When the pieces of the triangle are rearranged as shown, suddenly a square is missing. How is this possible?

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It’s not a true triangle — the hypotenuse is bent just slightly, by about 1/28th of a unit, to permit the deception. If you can’t see the bend, there’s another giveaway: If it were a true triangle, the red and blue pieces would be similar. But the blue triangle has a ratio of 5:2, and the red triangle has the ratio 8:3.

May 26, 2006July 18, 2013 | Puzzles

Cryptarithm

A “cryptarithm,” originally published by Henry Dudeney in the July 1924 Strand:

cryptarithm

Each letter stands for a different digit. Can you identify them?

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O=0, M=1, Y=2, E=5, N=6, D=7, R=8, and S=9.

May 8, 2006January 15, 2013 | Puzzles

The Poe Cryptographic Challenge

Edgar Allan Poe was fascinated by cryptograms. He once offered a free magazine subscription to any reader who could stump him, and he claimed to have solved all 100 ciphers that were sent in.

That mania ultimately created a mystery that lasted 150 years after the writer’s death. In 1840 Poe published two ciphers sent in by a “Mr. W.B. Tyler” and challenged readers to solve them. No readers succeeded, and in fact the first cipher wasn’t cracked until 1992, when University of Illinois English professor Terence Whalen decoded a passage from Joseph Addison’s 1713 play Cato.

The second puzzle was even harder, a polyalphabetic substitution cipher using several different symbols for each English letter — and containing several mistakes. It was finally solved in 2000 by Toronto software engineer Gil Broza:

It was early spring, warm and sultry glowed the afternoon. The very breezes seemed to share the delicious langour of universal nature, are laden the various and mingled perfumes of the rose and the –essaerne (?), the woodbine and its wildflower. They slowly wafted their fragrant offering to the open window where sat the lovers. The ardent sun shoot fell upon her blushing face and its gentle beauty was more like the creation of romance or the fair inspiration of a dream than the actual reality on earth. Tenderly her lover gazed upon her as the clusterous ringlets were edged (?) by amorous and sportive zephyrs and when he perceived (?) the rude intrusion of the sunlight he sprang to draw the curtain but softly she stayed him. “No, no, dear Charles,” she softly said, “much rather you’ld I have a little sun than no air at all.”

Probably it’s a quote from a novel of the time.

Interestingly, some scholars think Poe himself composed the ciphers, as city directories show no W.B. Tyler in that period. We’ll never know for sure, but Poe himself once wrote:

Ye who read are still among the living; but I who write shall have long since gone my way into the region of shadows. For indeed strange things shall happen, and secret things be known, and many centuries shall pass away, ere these memorials be seen of men. And, when seen, there will be some to disbelieve, and some to doubt, and yet a few who will find much to ponder upon in the characters here graven with a stylus of iron.

May 4, 2006October 5, 2006 | Literature · Puzzles

The Monty Hall Problem

Suppose you’re a contestant on Let’s Make a Deal. Monty Hall shows you three doors. One hides a sports car; the other two hide goats. You choose Door #1.

Before opening Door #1, though, Monty opens Door #3, revealing a goat. Now you can stick with Door #1 or switch to Door #2. Which should you do?

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You should switch to Door #2. At the start, each door had a one-third chance of hiding the car. You chose Door #1, accepting a two-thirds chance that the car was really behind Door #2 or Door #3. In revealing the goat behind Door #3, Monty has helped you by removing that door from contention. Therefore the two-thirds chance now rests entirely with Door #2. This is counterintuitive, but it’s true. If you picture the universe of possibilities, you’ll see that in two-thirds of the cases you initially pick a goat, and Monty shows you where the car is by revealing the other goat. Only in one-third of the cases will you pick the car correctly on the first move, when switching is a bad idea.

Click for Answer

May 3, 2006May 23, 2013 | Puzzles

Hotel Puzzle

Three men stop at a hotel and agree to share a room for $30. Each gives the desk clerk $10.

Later, the clerk realizes he’s overcharged them for the room by $5. He gives the bellboy five $1 bills and tells him to return the money to the three men. The unscrupulous bellboy keeps $2 for himself and gives $1 to each of the three men.

So the men paid $9 each for the room, for a total of $27. The bellboy has $2. What happened to the other dollar?

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There’s actually no difficulty here. The desk clerk has $25, the guests have $3, and the bellboy has $2. The “trouble” arises only because we’re trying to add the bellboy’s $2 to the guests’ $27. Instead we should subtract it, giving $25 for the clerk, which is correct. In effect, the men paid $27 for a $25 room, and the clerk gave the change to the bellboy.

April 27, 2006January 14, 2013 | Puzzles

No Tips Either Way

Okay, you’re a chef. Which of these trays was requested for a singer’s dressing room, and which is the last meal of a Texas death-row inmate?

A. Neil Diamond (“Love on the Rocks”)
B. Nelly (“Hot in Herre”)
C. Smokey Robinson (“Tears of a Clown”)
D. B.B. King (“The Thrill Is Gone”)
E. Cornelius Goss (beat a Dallas homeowner to death with a board)
F. Gerald Mitchell (shotgunned two customers during a Houston drug deal)
G. James Collier (shot two Wichita Falls residents while stalking his daughter)
H. James Powell (raped and murdered a 10-year-old in Beaumont)
I. Paul Nuncio (strangled a 61-year-old in Plainview)

1. BBQ chicken wings, chips, fruit, ginger ale
2. 1 apple, 1 orange, 1 banana, coconut, peaches
3. One pot of coffee
4. Enchiladas, burritos, chocolate ice cream, cantaloupe (whole, split in half)
5. Chinese takeout, coffee
6. 1 bag of assorted Jolly Ranchers
7. Baked salmon, french fries, fruit platter, salad, soda
8. Nothing
9. Thirty jumbo shrimp, cocktail sauce, baked potato, French fries, ketchup, butter, one T-bone steak, one chocolate malt, one gallon of vanilla ice cream, and three cans of Big Red

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A. Neil Diamond (“Love on the Rocks”) 5. Chinese takeout, coffee B. Nelly (“Hot in Herre”) 7. Baked salmon, french fries, fruit platter, salad, soda C. Smokey Robinson (“Tears of a Clown”): 1. BBQ chicken wings, chips, fruit, ginger ale D. B.B. King (“The Thrill Is Gone”) 8. Nothing E. Cornelius Goss (beat a Dallas homeowner to death with a board): 2. 1 apple, 1 orange, 1 banana, coconut, peaches F. Gerald Mitchell (shotgunned two customers during a Houston drug deal) 6. 1 bag of assorted Jolly Ranchers G. James Collier (shot two Wichita Falls residents while stalking his daughter) 9. Thirty jumbo shrimp, cocktail sauce, baked potato, French fries, ketchup, butter, one T-bone steak, one chocolate malt, one gallon of vanilla ice cream, and three cans of Big Red H. James Powell (raped and murdered a 10-year-old in Beaumont) 3. One pot of coffee I. Paul Nuncio (strangled a 61-year-old in Plainview) 4. Enchiladas, burritos, chocolate ice cream, cantaloupe (whole, split in half)

Click for Answer

April 19, 2006January 14, 2013 | Crime · Entertainment · Puzzles

What’s Odd?

How quickly can you find out what is unusual about this paragraph? It looks so ordinary that you would think that nothing was wrong with it at all and, in fact, nothing is. But it is unusual. Why? If you study it and think about it you may find out, but I am not going to assist you in any way. You must do it without coaching. No doubt, if you work at it for long, it will dawn on you. Who knows? Go to work and try your skill. Par is about half an hour.

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The paragraph does not contain the letter e. I’m going to have to start finding some harder puzzles!

April 8, 2006January 14, 2013 | Puzzles