Black and White

orbán chess puzzle

Tibor Orbán offered this puzzle in Die Schwalbe in 1976. The position above can be reached in exactly 3 moves in several ways — for example:

1. e4 c6 2. Bb5 e6 3. Bxc6 dxc6
1. e4 e6 2. Bc4 c6 3. Bxe6 dxe6

How can it be reached in exactly 4 moves?

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Trip Planning

mouse puzzle

A mouse wants to eat his way through a 3 × 3 × 3 cube of cheese, starting in one of the corners and tunneling through all 27 1 × 1 × 1 sub-cubes, visiting each once. Can he arrange his route so that he finishes at the center of the cube? Assume that he always moves between orthogonally adjacent cubes, traveling through walls but not through edges or corners.

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Containing an Arc

arc puzzle

University of Illinois mathematician John Wetzel called this one of his favorite problems in geometry. Call a plane arc special if it has length 1 and lies on one side of the line through its end points. Prove that any special arc can be contained in an isosceles right triangle of hypotenuse 1.

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A Triangle Puzzle

posamentier puzzle

In isosceles triangle ABC, CD = AB and BE is perpendicular to AC. Show that CEB is a 3-4-5 right triangle.

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Black and White

neuhaus chess problem

By Eugene Neuhaus Jr. White to mate in two moves.

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Escalation

Let’s play a game. You name an integer from 1 to 10. Then we’ll take turns adding an integer from 1 to 10 to the number our opponent has just named, giving the resulting sum as our answer. Whoever reaches 100 first is the winner.

You go first. What number should you choose?

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The Slothouber-Graatsma Puzzle

A deceptively simple packing problem by Dutch architects Jan Slothouber and William Graatsma: How can you assemble six 1 × 2 × 2 blocks and three 1 × 1 × 1 blocks into a 3 × 3 × 3 cube? There’s no trick to it, but it can be quite difficult to solve — the solution is unique, not counting mirror reflections and rotations.

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Black and White

korolikov chess problem

A curiously ambiguous problem by V.A. Korolikov. Mate in 1. Either side can fulfill this easily — but which has the move?

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