Stomachion.
A place for every piece.

How to play Stomachion

1. Fill the outline with all fourteen pieces. Pale pieces are already in place and stay fixed.
2. Drag a loose piece from the tray into an open space. Release it near a legal position and it settles into place.
3. Select a piece to Rotate it a quarter-turn or Turn over to flip it. You can select and drag a piece already on the board. If there is no room to turn, choose Lift first.
4. Pieces must stay inside the outline and must not overlap. Every complete arrangement that fits is accepted.
5. For precise positioning, open Adjust position. Change Column and Row to move a live preview across the visible grid, then choose Place piece. The values mark the top-left of the piece’s surrounding box.
6. Hint draws the outline of a suggested placement. It leaves you to find the piece’s rotation and side.

Placement guidance shows gold when a piece can fit and muted crimson when it would overlap or leave the outline. A legal placement can be part of a different valid solution; the colours never judge it against one secret answer. Turn guidance off for a harder challenge. The game still prevents overlapping pieces.

Soft paper-like sounds accompany a placement, with a lower sound for a piece that cannot fit. You can switch sound off in Game settings. Undo and Restart are always there when you want to try another approach.

A Greek puzzle with a Roman afterlife

Stomachion belongs to the mathematical world associated with Archimedes. Its familiar square is divided into fourteen geometric pieces. Research on the Archimedes Palimpsest connects the surviving treatise with the question of how those pieces can be rearranged. Modern analysis counts 536 different square arrangements when rotations, reflections and exchanges of identical pieces are treated as equivalent.

The puzzle also appears in Roman literature. In the introduction to his Nuptial Cento, the fourth-century poet Ausonius describes fourteen pieces of bone forming animals, people and objects. He compares the skill of joining those pieces with assembling a poem from fragments of earlier verse.

Roman Empire Times’ game uses the fourteen-piece square shown in mathematical studies of Stomachion. The numbered lessons and partly completed boards are our teaching format: a way to begin with one satisfying fit before taking on larger gaps.

Choose a shape, find your pace

Choose square, step, corner or sail in Collection, then choose one of its twenty levels. Each shape begins with three simple fits. From level four you will need to turn pieces; from level six you will also need to turn them over. The final two levels leave all fourteen pieces for you to place.

The original fourteen pieces remain the same. Roman Empire Times’ silhouettes and lessons are modern challenge designs, following the ancient idea of making figures from a set of pieces. Every level has a checked solution.

After level twenty, try Remix. It chooses from verified arrangements and reshuffles the pieces, with at least two complete solutions compatible with the fixed clues. You can return for another variation whenever you like.

Create your free Roman Empire Times account to keep every fit and finished level, or sign in to continue your puzzle.

Sources and further reading

ETH Library: Stomachion, its pieces and mathematics

Reviel Netz: How many ways can you have a stomach ache?

Fan Chung and Ron Graham: A tour of Archimedes' Stomachion

Ausonius, Nuptial Cento, introduction; H. G. Evelyn White translation, printed page 375