Three Riddles

From Henry Dudeney’s 300 Best Word Puzzles:

What is that from which you may take away the whole and yet have some left?
What is it which goes with an automobile, and comes with it; is of no use to it, and yet the automobile cannot move without it?
Take away my first letter and I remain unchanged; take away my second letter and I remain unchanged; take away my third letter and I remain unchanged; take away all my letters and still I remain exactly the same.

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The word wholesome. Noise. A postman. (Ha!)

July 9, 2013July 19, 2013 | Puzzles

Black and White

huggins chess problem

By A.Z. Huggins. White to mate in two moves.

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1. Qa1! and the queen will mate. From Nordisk Skaktidende, 1875.

July 5, 2013July 12, 2013 | Puzzles

Pillow Talk

In 1951 James Thurber’s friend Mitchell challenged him to think of an English word that contains the four consecutive letters SGRA. Lying in bed that night, Thurber came up with these:

kissgranny. A man who seeks the company of older women, especially older women with money; a designing fellow, a fortune hunter.

blessgravy. A minister or cleric; the head of a family; one who says grace.

hossgrace. Innate or native dignity, similar to that of the thoroughbred hoss.

bussgranite. Literally, a stonekisser; a man who persists in trying to win the favor or attention of cold, indifferent, or capricious women.

tossgravel. A male human being who tosses gravel, usually at night, at the window of a female human being’s bedroom, usually that of a young virgin; hence, a lover, a male sweetheart, and an eloper.

Unfortunately, none of these is in the dictionary. What word was Mitchell thinking of?

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Disgrace.

July 3, 2013July 12, 2013 | Language · Puzzles

15 Puzzle

A problem from the 1999 Russian mathematical olympiad:

Show that the numbers from 1 to 15 can’t be divided into a group A of 13 numbers and a group B of 2 numbers so that the sum of the numbers in A equals the product of the numbers in B.

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Suppose this were possible, and let x and y be the numbers in B. Then: (1 + 2 + … + 15) – x – y = xy 120 = xy + x + y 121 = (x + 1)(y + 1) We know that x and y fall between 1 and 15, so the only possible solution is (x, y) = (10, 10). But x and y must be two different numbers. So the task is impossible.

July 2, 2013July 12, 2013 | Puzzles

Cold Case

Enigma, the official publication of the National Puzzlers’ League, published this item in the “Chat” column of its August 1916 issue:

“The police department of Lima, O., is greatly puzzled over a cryptic message received in connection with the robbery of a Western Ohio ticket agent. Here it is: WAS NVKVAFT BY AAKAT TXPXSCK UPBK TXPHN OHAY YBTX CPT MXHG WAE SXFP ZAV FZ ACK THERE FIRST TXLK WEEK WAYZA WITH THX.”

As far as I can tell, in the ensuing 97 years it has never been solved. Any ideas?

June 29, 2013June 28, 2013 | Puzzles

Black and White

challenger chess problem

By Alfred Clement Challenger. White to mate in two moves.

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White wins with the quiet 1. g5!: 1. … Kf5 2. Bc2# 1. … Kd5 2. Bf3# 1. … e5 2. Qf3# From the American Chess Magazine, 1897.

June 28, 2013July 5, 2013 | Puzzles

In a Word

carfax
n. a place where four roads meet

Traveling between country towns, you arrive at a lonely crossroads where some mischief-maker has uprooted the signpost and left it lying by the side of the road.

Without help, how can you choose the right road and continue your journey?

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You know the town you just came from — use that knowledge to orient the signpost.

June 27, 2013July 25, 2013 | Language · Puzzles

A Martian Census

A room contains more than one Martian. Each Martian has two hands, with at least one finger on each hand, and all Martians have the same number of fingers. Altogether there are between 200 and 300 Martian fingers in the room; if you knew the exact number, you could deduce the exact number of Martians. How many Martians are there, and how many fingers does each one have?

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The key is that the number of fingers can tell us uniquely the number of Martians. That’s a tall order. It eliminates, say, 246 fingers, because that’s too ambiguous: There might be 82 Martians with 3 fingers each, or 3 Martians with 82 fingers each, and so on. The only possibility that avoids this uncertainty is that the quantity of Martians and the quantity of fingers per Martian are expressed by the same number, and that this number is not composite. That means we’re looking for the square of a prime number, and the only such number in the range 200-300 is 289, or 17². So there are 17 Martians, each of which has 17 fingers. This is the only number between 200 and 300 that permits such a definite assertion.

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June 25, 2013July 5, 2013 | Puzzles

Black and White

Bachmann chess problem

By Ulrich Bachmann. White to mate in two moves.

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1. Rd6! and White will mate with the knight or the bishop. From Der Schachfreund, 1898.

June 21, 2013June 28, 2013 | Puzzles

Three by Three

three by three puzzle

What’s the ratio between the areas of the two triangles?

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Invert the smaller triangle and it becomes clear that the ratio is 4 to 1.

June 17, 2013June 28, 2013 | Puzzles