Shifting Gears


A puzzle by French puzzle maven Pierre Berloquin:

Timothy rides a bicycle on a road that has four parts of equal length.

The first fourth is level, and he pedals at 10 kph.

The second fourth is uphill, and he pedals at 5 kph.

The third fourth is downhill, and he rides at 30 kph.

The fourth fourth is level again, but he has the wind at his back, so he goes 15 kph.

What is his average speed?

Click for solution …

Cruel and Unusual


A king is angry at two mathematicians, so he decrees the following punishment. The mathematicians will be imprisoned in towers at opposite ends of the kingdom. Each morning, a guard at each tower will flip a coin and show the result to his prisoner. Each prisoner must then guess the result of the coin flip at the other tower. If at least one of the two guesses is correct, they will live another day. But as soon as both guesses are incorrect, they will be executed.

On the way out of the throne room, the mathematicians manage to confer briefly, and they come up with a plan that will spare them indefinitely. What is it?

Click for solution …


Items requested in the 2000 Baylor College Linguistic Scavenger Hunt:

  1. the word for “cheese” in Estonian
  2. the longest word in English that uses no letter more than once
  3. a nine-letter English word that has only one syllable
  4. the sound that a dog makes in Swedish
  5. the regional word for “drinking fountain” that’s used in Wisconsin
  6. the language that Jesus spoke
  7. the American equivalent of the British word “ex-directory”
  8. five words that are legal plays in Scrabble and that have only two letters, one of which is “x”
  9. the motto of the Klingon Language Institute
  10. identity of the person who said, “England and America are two countries divided by a common language.”

Click for solution …

Black and White

kraemer chess problem

By Adolf Kraemer. White to mate in two moves.

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Getting More Fiber

You’re locked on the roof of a building that’s 800 feet tall, and you want to reach the ground uninjured. You can safely fall only about 5 feet. The walls of the building are completely smooth and featureless, except that one wall has a small ledge that’s 400 feet above the ground. There’s a hook on this ledge, and another hook directly above it at the edge of the roof.

You have 600 feet of rope and a knife. How can you reach the ground?

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Heart and Head

Just offering this as a curiosity:

ohnishi cryptarithm

It was devised by the late Japanese cryptogramist Kyoko Ohnishi, and praised by puzzle maven Nob Yoshigahara. If each letter stands for a unique digit, what product is encoded here?

When this appeared in MIT Technology Review in November 2012, it attracted 20 responses, but it appears that all of them used computers to find the solution. If there’s a way to reason it out, I don’t think anyone has found it yet.

If we assume that neither of the factors has a leading zero, and that the partial products have five and four digits, as shown, then the solution is unique. I’ll put it in the spoiler box below, in case you want to work on it yourself.

Click for Answer

Black and White

techritz problem

By M. Techritz. Place the black and white kings on the board so that White can mate in one move.

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In a Word

n. enrichment

adj. unprofitable

Another puzzle by Yakov Perelman:

“Two fathers gave their two sons some money. One gave his son 150 rubles and the other 100 rubles. When the two sons counted their finances, they found that together they had become richer by only 150 rubles. What is the explanation?”

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Russian science writer Yakov Perelman asks: How many times must an 8-toothed cogwheel rotate on its axis to circle around a 24-toothed cogwheel?

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Black and White

tanner chess problem

By John Tanner. White to mate in two moves.

Click for Answer