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Turning to four cubes, we find that there are six different ways to form irregular shapes by joining the cubes face to face. These are pieces 2 to 7 in the illustration. To identify the seven pieces Piet Hein labels them with numerals. No two shapes are alike, although 5 and 6 are mirror images of each other. Piet Hein points out that two cubes can be joined only along a single coordinate, three cubes can add a second coordinate perpendicular to the first, and four cubes a r e necessary to supply the third coordinate perpendicular to the other two.

T 19 - Aldous Huxley, Brave New World H E CHINESE puzzle game called tangrams, believed to be thousands of years old, employs a square of thin material that is dissected into seven pieces (see Chapter 18). The game is to rearrange those pieces to form other figures. From time to time efforts have been made to devise a suitable analog in three dimensions. None, in my opinion, has been as successful as the Soma cube, invented by Piet Hein, the Danish writer whose mathematical games, Hex and Tac 66 The Soma Cube Tix, are discussed in the first Scientific A m e r i c a n Book of Mathematical Puzzles.

167 per cent. Maybe the moral for international politics is even better here. The problem, in variant forms, appears in several puzzle books. The earliest reference known to me is Hubert Phillip's Question Time, 1938, Problem 223. A different version of the problem can be found in Clark Kinnaird's Encyclopedia of Puzzles and Pastimes, 1946, but the answer is incorrect. Correct probability figures for Kinnaird's version a r e given in The American Mathematical Monthly, December 1948, page 640. CHAPTER SIX rn The Soma Cube ".

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