Unwound

You have 13 reels of magnetic tape, one empty reel, and a machine that will wind tape from a full reel to an empty one, reversing its direction. You need all 13 tapes reversed on their original reels. Show how this can be done, or prove that it’s impossible.

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It’s impossible. Each of the 13 reels must go through an even number of transfers in order to finish with its original tape. (Likewise, the empty reel must go through an even number of transfers to remain empty.) But each of the 13 tapes must be transferred an odd number of times to end up reversed. So the total number of transfers must be both even and odd, an impossibility.

July 23, 2012February 5, 2013 | Puzzles

Tall and Wide

tall and wide 1

Which of these triangles has the greater area?

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Each can be decomposed into two 3-4-5 triangles … so they’re equal.

July 21, 2012February 5, 2013 | Puzzles

Black and White

van beek chess problem

By H. Van Beek, Chemnitzer Wochenschach, 1926 (special prize). White to mate in two moves.

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1. Nc4 and White will mate by 2. d5, 2. Qg8, or 2. Qc8.

July 20, 2012February 5, 2013 | Puzzles

Outpourings

gedanken tank puzzle 1

A tank of water has two holes of equal area, one at top and one at bottom. The top one leads to a downspout, so that both holes discharge their water at the same level. Ignoring friction, which hole produces the faster flow of water?

You actually don’t need to know the physics in order to solve this — it yields to an insight.

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The water flows from both openings at the same rate. If it didn’t, we could connect the two to create a perpetual-motion machine. (From Lewis Epstein’s Thinking Physics Is Gedanken Physics, 1989.)

July 19, 2012February 5, 2013 | Puzzles · Science & Math

Substantial

Foaled in 1773, this thoroughbred racehorse bore the unlikely name of Potoooooooo.

How was it pronounced?

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“Potatoes.”

July 16, 2012February 5, 2013 | Puzzles

Black and White

By P. Klett. White to mate in two moves.

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1. Qh6 and the queen or knight will mate.

July 13, 2012February 5, 2013 | Puzzles

Tangled Tale

shoelace puzzle

A shoelace is lying on the floor, and I’m too nearsighted to see how the lace crosses itself at points A, B, and C. If I pull on the ends, what’s the probability that it will produce a knot?

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One in four. There are three intersections, so there are eight possible ways the lace can cross itself. Of these, only two (over/under/over and under/over/under) will produce a knot.

July 10, 2012February 5, 2013 | Puzzles

Black and White

schlechter chess problem

In 1908, two years before drawing against Emanuel Lasker for the world chess championship, Carl Schlechter published this problem in the Allgemeine Sportzeitung. White to mate in two moves:

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1. Qa6 and White will mate by 2. Qh6, 2. Nd3, or 2. Qa1.

July 6, 2012February 5, 2013 | Puzzles

Togetherness

distance sums problem

What location on this line segment has the smallest sum of distances to the labeled points?

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Consider first the endpoints, A and K: The sum of the distances to these two points will be the same for any point between them. Similarly, any point between B and J will have the same total distance to points A, K, B, and J. Proceeding in this way and taking the points in pairs, we find that every point between E and G produces the same total distance to the outermost 10 labeled points. That leaves only F. So the answer is that point F has the minimum total distance to the labeled points. Strangely, this means that we can shift the points around without affecting this result. If points A through E crowded F closely on the left, and point K were 90 light-years away on the right, point F would still yield the smallest total sum, so long as the points appeared in the order shown above.

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June 30, 2012February 5, 2013 | Puzzles

Black and White

By Herbert I. Ladd. In A Selection of Popular Two-Move Chess Problems (1887), Orestes Augustus Brownson calls this “a gem of purest ray serene.” White to mate in two moves.

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1. Ng6 and Black must lose by 2. Qd3#, 2. Qe5#, or 2. Qd6#.

June 29, 2012February 5, 2013 | Puzzles