A Chess Maze

wurzburg chess puzzle

By O. Wurzburg, 1919. If Black does not move at all, in how few moves can the white king reach f4? White can move only his king; as in regular play, it can capture enemy pieces but cannot enter check.

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Quick Thinking

Some “ridiculous questions” from Martin Gardner:

1. A convex regular polyhedron can stand stably on any face, because its center of gravity is at the center. It’s easy to construct an irregular polyhedron that’s unstable on certain faces, so that it topples over. Is it possible to make a model of an irregular polyhedron that’s unstable on every face?

2. The center of a regular tetrahedron lies in the same plane with any two of its corner points. Is this also true of all irregular tetrahedrons?

3. An equilateral triangle and a regular hexagon have perimeters of the same length. If the area of the triangle is 2 square units, what is the area of the hexagon?

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What’s the Angle?

what's the angle puzzle

AB = XY. Find z°.

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More Fun

If the proportion of blonds among blue-eyed people is greater than among the population as a whole, is it also true that the proportion of blue-eyed people among blonds is greater than among the population as a whole?

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Earnings Report


My employer has nine workers. The nine of us want to determine what our average salary is, but none of us wants to divulge his own salary. Can we find the average without doing so?

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Black and White

von meyenfeldt chess puzzle

A poser by F.H. von Meyenfeldt, 1967. What move must Black play to enable a forced mate in two by White?

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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?

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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?

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