Stomachion Puzzle – Play Online

An ancient dissection puzzle associated with Archimedes, also called Ostomachion. A simple square with a wonderfully difficult question: how many ways can you put it back together?

11 pieces are locked in place. Fit the remaining 3 to finish the square. Rotate and flip pieces — turning them over is allowed.

3 ·5 ·6 ·7 ·8 ·9 ·10 ·11 ·12 ·13 ·14 ·Piece numbers11 locked

Piece tray

124

Select a piece

Can it be finished?HintReveal solutionReset

About the puzzle and its 536 solutionsBill Cutler’s enumeration found 17,152 labeled arrangements, or 536 distinct solutions when rotations and reflections of the whole square and swaps of the two pairs of identical pieces are counted as the same. Piece flips are allowed here. The square is checked by geometry; the numbered library identifies your solution, not whether it is accepted.

Coordinates snap to the exact 12 × 12 integer lattice of the classical dissection. There is no rounding tolerance in the completion check: all 14 authentic pieces must lie inside the square with disjoint interiors and total area 144. Reference hints need not match your partial arrangement.

Your attempts, times, and full-challenge solution numbers stay in this browser. Guided results are separate; hints have their own best times, and revealed solutions are never recorded as solves.

Prefer permanent, more thorough storage of your solving history than this browser can offer? We are considering user accounts for exactly that — let us know you are interested through our contact form.

All About Stomachion — history, geometry, and the story behind 536 solutions

References: Drexel’s Archimedes collection, Wolfram MathWorld, and Laurent Lessard’s computational study.