Hole Hearted

gardner geometric vanish

Martin Gardner called this the proudest puzzle of his own devising. When the pieces on the left are rearranged as on the right, a hole appears in the center of the square. How is this possible?

“I haven’t the foggiest notion of how to succeed in inventing a good puzzle,” he told the College Mathematics Journal. “I don’t think psychologists understand much either about how mathematical discoveries are made. … The creative act is still a mystery.”

Set Theory

A puzzle by Polish mathematician Paul Vaderlind:

Andre Agassi and Boris Becker are playing tennis. Agassi wins the first set 6-3. If there were 5 service breaks in the set, did Becker serve the first game?

(Service changes with each new game in the 9-game set. A service break is a game won by the non-server.)

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Black and White

keym chess puzzle

By Werner Keym, from Die Schwalbe, 1979. What were the last moves by White and Black?

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The Lock Key


Two adjoining lakes are connected by a lock. The lakes differ by 2 meters in elevation. A boat can pass from the lower lake to the upper by passing through the lock gate, which is closed behind it; then water is added to the lock chamber until its level matches that of the upper lake, and the boat can pass out through the upper gate.

Now suppose two boats do this in succession. The first boat weighs 50 tons, the second only 5 tons. How much more water must be used to raise the small boat than the large one?

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No Touching


This scale balances a cup of water with a certain weight. Will the balance be upset if you put your finger in the water, if you’re careful not to touch the glass?

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Counter Play


A puzzle by Lewis Carroll:

A bag contains one counter, known to be either white or black. A white counter is put in, the bag shaken, and a counter drawn out, which proves to be white. What is now the chance of drawing a white counter?

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Spear Fight


A puzzle by Henry Dudeney:

A lady is accustomed to buy from her greengrocer large bundles of asparagus, each twelve inches in circumference. The other day the man had no large bundles in stock, but handed her instead two small ones, each six inches in circumference. “That is the same thing,” she said, “and, of course, the price will be the same.” But the man insisted that the two bundles together contained more than the large one, and charged a few pence extra. Which was correct — the lady or the greengrocer?

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