High Hopes

A worm crawls along an elastic band that’s 1 meter long. It starts at one end and covers 1 centimeter per minute. Unfortunately, at the end of each minute the band is instantly and uniformly stretched by an additional meter. Heroically, the worm keeps its grip and continues crawling. Will it ever reach the far end?

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Black and White

wheeler sui-mate

By C.H. Wheeler, from the Dubuque Chess Journal, December 1877. “White to play and compel self-mate in two moves” — that is, White must force Black to checkmate him in two moves.

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Heads and Tails

Let’s play a coin-flipping game. At stake is half the money in my pocket. If the coin comes up heads, you pay me that amount; if it comes up tails, I pay you.

Initially this looks like a bad deal for me. If the coin is fair, then on average we should expect equal numbers of heads and tails, and I’ll lose money steadily. Suppose I start with $100. If we flip heads and then tails, my bankroll will rise to $150 but then drop to $75. If we flip tails and then heads, then it will drop to $50 and then rise to $75. Either way, I’ve lost a quarter of my money after the first two flips.

Strangely, though, the game is fair: In the long run my winnings will exactly offset my losses. How can this be?

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Black and White


“The Forlorn Hope,” by J. Paul Taylor, 1878. White to mate in two moves.

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Cries logical Bobby to Ned, will you dare
A bet, which has most legs, a mare, or no mare.
A mare, to be sure, replied Ned, with a grin,
And fifty I’ll lay, for I’m certain to win.
Quoth Bob, you have lost, sure as you are alive,
A mare has but four legs, and no mare has five.

The Panorama of Wit, 1809

Ball Juggling

Image: Wikimedia Commons

In a solar eclipse, the moon casts its shadow on Earth. In a lunar eclipse, Earth casts its shadow on the moon.

Solar eclipses are more common than lunar eclipses, but we tend to have the opposite impression. Why?

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Up From Down

Mount Everest rises 29,029 feet above sea level, and Ecuador’s volcano Chimborazo rises only 20,702 feet. But because Earth bulges at the equator, Chimborazo is actually farther from the center of the planet. If we could connect the two peaks with a water pipe, in which direction would the water flow?

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