Solution #89: The Mongolian Postal Service

Boris placed the flute diagonally in a suitcase that measured 1 meter by 1 meter. This suitcase was quite acceptable to the postal officials its sides measured 1 meter. From corner to corner, it measures 1.414 meters -- the square root of two.

Incidentally, if his flute had measured 1.7 meters, he could have fitted it across the diagonal of a box whose sides were 1 meter long. The diagonal of a cube is the square root of the three times its side -- 1.73 meters.

From a theoretical mathematical viewpoint, there is no reason why this process cannot be extended indefinitely. If Boris could construct a four-dimensional box with 1-meter sides, then he could get a 2-meter flute in it (square root of 4) and a 25-dimensional construction could contain a 5-meter flute while still meeting the rules of having no side longer than 1 meter.

Source: Sloane, Paul
Categories: Clever, Algebra, Geometry and Space, Pythagorean theorem, Favorite
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