Shafted

dudeney drilled ball puzzle

From Henry Dudeney:

A ball 13 inches in diameter has a hole 5 inches wide drilled through the center. How deep is the hole?

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Pythagoras solves this neatly: x² + 25 = 169; x = 12. Curious addendum: If you now hold the hole’s depth constant at 12 and vary its width, adjusting the object’s diameter accordingly, the object’s volume remains constant. (Thanks, Thomas.)

January 23, 2010October 2, 2024 | Puzzles

A Riddle

At a Cambridge dinner, Arthur C. Clarke asked Clive Sinclair, “What was the first human artifact to break the sound barrier?”

What was it?

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The whip.

January 19, 2010January 23, 2013 | Puzzles

Fugue State

John lives in an East Coast state and Mary in a West Coast state. During a phone conversation one night, they realize that it is the same time in both locations. How can this be?

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John lives in Pensacola, Fla., which is in the Central time zone. Mary lives in Ontario, Ore., which is in the Mountain time zone. At 2 a.m. on the first Sunday in November, John sets his clock back 1 hour to standard time. One hour will pass before Mary too sets her clock back. So for one hour each year, they observe the same time. From Frank Morgan, The Math Chat Book, 2000. See also Four-Dimensional Basketball, Pop Fly, and A Freak of Navigation.

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January 16, 2010January 23, 2013 | Puzzles

A Vanishing

get off the earth

Patented in 1896, Sam Loyd’s “Get Off the Earth” puzzle reportedly sold more than 10 million copies during the puzzlemaker’s lifetime, making it one of the most popular puzzles of all time.

There are 13 men in the figure on the left. Rotating the earth produces the figure on the right — which has 12 men. What happened to the 13th man?

January 15, 2010September 3, 2010 | Puzzles

The Assassin

By Sam Loyd. Black to mate in four moves.

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1. … dxc5 2. (any) cxb4 3. (any) bxa3 4. (any) axb2#

January 9, 2010January 22, 2013 | Puzzles

A Day Trip

A man drives 1 mile to the top of a hill at 15 mph. How fast must he drive 1 mile down the other side to average 30 mph for the 2-mile trip?

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The answer is not 45 mph (with the idea that 15 + 45 / 2 = 30). In that event the man would cover 2 miles in 1/15 + 1/45 of an hour, for an average speed of only 22.5 mph. In fact he can’t possibly drive fast enough. To average 30 miles per hour, he would have to cover the 2 miles in 1/15 hour, or 4 minutes. But he’s already consumed 4 minutes in driving to the top of the hill (1 mile / 15 miles per hour = 1/15 hour, or 4 minutes). So it can’t be done.

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December 29, 2009January 22, 2013 | Puzzles

Stairway to Seven

You hate visiting your girlfriend because there’s no elevator in her apartment building. And now she’s moved from the fourth floor to the seventh. How many times longer does this make your ascent?

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It’s twice as long. You had to climb three flights to get from the first floor to the fourth; now you must climb six flights to get from the first to the seventh. That was the solution intended by Russian mathematician Boris Kordemsky, who invented the puzzle. It’s not valid in Britain, interestingly, which counts the ground-level story as the “ground floor,” the one above that as the first, etc. Evidently Russians and Americans have more in common than we thought.

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December 20, 2009January 22, 2013 | Puzzles

His and Hers

Many masculine nouns can be converted to feminine with a suffix, as HERO-HEROINE and HOST-HOSTESS.

Name a feminine noun that can be converted to masculine with a suffix.

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I was thinking of WIDOW-WIDOWER, but two readers point out that BRIDE-BRIDEGROOM also works if GROOM counts as a suffix.

December 14, 2009January 22, 2013 | Language · Puzzles

Open and Shut

Every room in my house has an even number of doors.

Prove that the house has an even number of exterior doors.

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Each door has two sides, so the total number of door sides is even. Since the number of door sides inside the house is even, the number on the exterior must be even as well. From L.A. Graham, Ingenious Mathematical Problems and Methods, 1959.