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Stomachion

The stomachion  ( from Greek for stomach but the connections are unclear)  is an ancient puzzle game, and as it seems the oldest puzzle game.  The puzzle was discovered accidentally, in 1846, but then fall into oblivion for over a century . It consists of 14 flat (possibly ivory) pieces of various polygonal shapes which together can be arranged in the shape of a square. The object of the game to rearrange the pieces to form an interesting shape .  Roman poet and statesman Magnus Ausonius (310-395 AD)   mentioned this puzzle for the first time in his book Liber XVII Cento nuptalis.  He listed several animal shapes (e.g. the elephant given below) and human figures.

In Latin texts the puzzle is also referred to as the loculus of Archimedius  (i.e. Archimedes' box) or syntemachion and Ausonius refers to it as ostomachion. The name Archimedes’ box indicates connections to Archimedes but it is not known whether Archimedes is the inventor of the game . It is more probable that only explored some geometrical aspects of the puzzle. Two fragmentary manuscripts discovered in Constantinople in 1899    and attributed to Archimedes survived,  one is an Arabic translation   and the other is a Greek manuscript   dating from the tenth century .  The Greek manuscript is rather incomplete and describes the relationships between various angles of the pieces. The Arabic manuscript contains more information. Gives a construction of the Stomachion and determines the areas of its pieces.

Taking  a square the pieces have integer areas 3, 3, 6, 6, 6, 6, 9, 12, 12, 12, 12, 12, 21 (cf. Pick’s Theorem ).

In 2003 using  a computer program Bill Cutler found that there are, barring rotations and reflections, 536 possible distinct arrangements of the pieces into a square         .  Here are three of them:

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