A Geometric Paradox

a geometric paradox

May 15, 2014May 14, 2014 | Puzzles · Science & Math

Black and White

elekes chess problem

By Dezso Elekes. White to mate in two moves.

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1. Qf6! forces the knight to move, permitting 2. Qg7#. From The Chess Amateur, 1921.

May 9, 2014May 18, 2014 | Puzzles

Black and White

carpenter chess problem

By George Edward Carpenter. White to mate in two moves.

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1. Qd1! and the queen will mate. From The Dubuque Chess Journal, 1872.

May 3, 2014May 11, 2014 | Puzzles

Separate Quarters

separate quarters puzzle

Nine wolves share a square enclosure at the zoo. Build two more square enclosures to give each wolf a pen of its own.

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May 1, 2014May 11, 2014 | Puzzles

Nob’s Number Puzzle

nob's number puzzle

A conundrum by the late brilliant Japanese puzzle maven Nob Yoshigahara.

Lee Sallows writes, “You have to solve this yourself, otherwise you won’t see how beautiful it is.”

April 30, 2014April 29, 2014 | Puzzles

Black and White

petkovic chess problem

A cylindrical problem by Miodrag Petkovic: Imagine that the board is rolled into a cylinder, with the a-file adjoining the h-file. How can White mate in two moves?

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1. Nb5! Kxb5 2. Qa4#. If 1. … Kd5 then 2. Qe6#. From Mathematics and Chess, 1997.

April 25, 2014May 4, 2014 | Puzzles

Black and White

griswold chess problem

By John Griswold White. White to mate in two moves.

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The quiet 1. Kg5! forces Black to move a knight, permitting White to mate from e6 or g6. (Note that 1. Ke5 won’t work because of 1. … Nc6+!) From Canadian Illustrated News, 1880.

April 18, 2014April 27, 2014 | Puzzles

No Attraction

Kepler’s second law holds that a line segment connecting an orbiting planet to its sun sweeps out equal areas in equal periods of time: In the diagram above, if the time intervals t are equal, then so are the areas A.

If gravity were turned off, would this still be true?

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Yes. The planet would pass into space in a straight line, and each time interval would define a triangle with height h and base t. Since a triangle’s area is half the product of its height and base, these are all equal.

April 12, 2014March 5, 2015 | Puzzles · Science & Math

Black and White

loyd chess problem

By Sam Loyd. White to mate in two moves.

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Typically for Loyd, the answer is the least likely move on the board: 1. Nd2! (threatening 2. Rxe2#) If 1…Kxf2 then 2.Qg3# If 1…Kxd2 then 2.Qc3# If 1…Rxe3 then 2.Qxe3#

April 11, 2014April 20, 2014 | Puzzles

Math Notes

Prove that log₁₀ 5 is irrational.

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Suppose it’s rational. Then log₁₀ 5 = a/b, where a and b are positive integers. Then 10^a/b = 5 and 10^a = 5^b. But these two values can never be equal — any positive integral power of 10 will end in 0, and any such power of 5 will end in 5. So log₁₀ 5 cannot be rational.

April 10, 2014April 13, 2014 | Puzzles