A stomachion (or ostomachion according to some, or syntemachion, or Loculus of Archimedes) is an ancient puzzle thought to be invented by Archimedes. A square is divided in 14 parts, the area of each exisiting in a rational proportion to the area of all others. Bill Cutler proved that there are 536 possible unique configurations of the stomachion tiles that will create a square.

Some would have it that the etymology of the name means ‘bone (osto) challenge (mákhion)’, as the original puzzles would have been made of ivory. In theory. Others hold the opinion that it means ‘problem (mákhion) which will drive you insane (stomachêin: be disgusted, resent)’. No doubt from empirical observation.

The puzzle is 7-3/4” square, and the tiles are made of 1/4” thick walnut. After many failed designs, botched efforts, and much sawdust, the final tray design was realized from scraps of birch plywood and 1/8” poplar. All pieces are shellaced, for the safety of young persons who may have a tendency to gnaw on the puzzle rather than be amazed by combinatorics.

The astute observer will no doubt realize that this ‘stomachion’ has only 11 pieces. It is, in fact, no stomachion at all, but a ‘STOMACH’, to use the terminology of Fan Chung & Ron Graham. Frankly, the prototype was built as a gift for a small child, and the ASTM deems some of the smaller pieces (of a 14-piece stomachion of this size) unsuitable for children under 3. The STOMACH is still capable of creating all 536 squares—however it cannot create some of the other classic arrangements, such as elephants and certain parallelograms.

Underneath the STOMACH is a second tray which holds a tangram. 5-1/2” square, also made of walnut.