Archimedes' (O)stomachion (metal pieces)

The first puzzle in history

It was a spiritual game, predecessor of the puzzle. It probably resulted from a mathematical problem of Archimedes, or vice versa. The game consists of a square base divided into 14 geometric pieces. The aim of the game was to reshape, in as many ways possible, using all the pieces, the square or (like tangram) some particular figures (e.g. a helmet, a goose in flight, a tower, a column, an elephant, a boar, a barking dog, a stalking hunter). In the problem, Archimedes demonstrates that each of the pieces has an area that is a rational fraction of the total area of the initial square and searches for the number of possible combinations for recreation. In 2003, through a dedicated computer program (Bill Сutler), it was proved that there are 536 unique combinations or 17.152 if all symmetrical (by rotation, mirroring or identical triangles' swaping) are included.