Stomachion, Fourteen Pieces and One Square

We’re introducing a new online puzzle at PuzzleWhere: Stomachion. It’s free to solve, right in your browser, without an account. Start with a few pieces and work up to the full fourteen-piece challenge.

A square cut into fourteen pieces sounds simple enough. Put the pieces back, and the square should return. But Stomachion — also called Ostomachion — has been inviting people to think harder for more than two thousand years.

The puzzle is associated with Archimedes, whose surviving discussion also examines the areas of its pieces. Our version uses the classical dissection, not an approximation.

See the fourteen-piece Stomachion square

A gentle way to begin

Introduction 1 leaves eleven pieces in place and asks you to fit the remaining three. Solve it to unlock Introduction 2: six open spots, with rotation and flipping needed to finish. Once unlocked, both introductions are available to revisit, each with its own saved attempt and best times.

You can take on the full challenge at any time. It clears the square and puts all fourteen pieces in your tray. Move the pieces, rotate them, or flip them top-to-bottom. The goal is exact: no gaps, no overlapping interiors, and every piece inside the square.

Compare the two guided introductions and the full challenge

Not just one answer

Bill Cutler’s computer enumeration found 17,152 labeled arrangements. Treat turns and reflections of the whole square and swaps of identical pieces as equivalent, and there are 536 distinct solutions. We independently enumerated the integer-grid arrangements and obtained those same counts.

There is no single arrangement you have to copy. Our solver checks the actual geometry; the numbered library identifies the arrangement you found. Finish a square and you’ll be congratulated on your solution number. In the full challenge, your browser also keeps track of the numbered solutions you’ve discovered.

Help that follows your square

Wondering whether your current arrangement can still work? Can it be finished? checks whether the square can be completed with every placed piece left exactly where it is. It doesn’t move anything. If the answer is no, you’ll need to reposition or return a piece to the tray before continuing.

Hint uses only a solution compatible with your placed pieces. The first press identifies a next piece and offers a clue; a second press shows its placement as an outline. If no completion fits your current board, it tells you to move a piece first instead of pointing to an impossible spot.

Reveal solution follows the same rule: it preserves your placed pieces and fills in the rest from a compatible solution. If none fits, your board stays unchanged and you’re asked to move a piece before trying again. A reveal never counts as a solve or a personal best.

Hints and the completion check mark an attempt as assisted. Assisted and unassisted results are kept separate, so you can choose whether to work entirely on your own or take a little help along the way.

Your next square

Your attempts, progress, and times stay in this browser. Each guided introduction has its own history, separate from the full challenge. That means you can return to a square without starting over, but clearing browser storage or switching devices won’t bring that history with you.

If you’d like user accounts for more permanent, detailed history across devices, let us know through our contact form.

Ready to fit your first pieces? Find Stomachion on our Solve page, or go straight to the puzzle below — free, without an account.

Solve Stomachion at PuzzleWhere

Further reading

Drexel’s Archimedes collection and Wolfram MathWorld discuss the historical construction and the counting convention.