Number of Solutions to the 3D Squares Puzzle (Soma Cube): 240 Distinct Solutions

The Soma Cube (7 pieces, 27 cubelets → 3×3×3 cube) has 240 distinct solutions.

Details

• Pieces: All 7 non-convex tetracubes (4 cubes each) + 1 tricube (3 cubes) = 27 cubes total.
• Distinct = not identical under rotation/reflection of the assembled cube.
• Conway & Guy (1961) enumerated by hand; verified by computer.
• Each solution can be rotated 24 ways (cube symmetries) → 240 × 24 = 5,760 oriented solutions.

Related Counts

• Pentominoes (12 pieces, 60 squares): 2,339 solutions (6×10 rectangle).
• Bedlam Cube (13 pieces, 4×4×4): 19,186 solutions.
• Diabolical Cube (6 pieces, 3×3×3): 13 solutions.

Why 240 Matters

Small enough to exhaust manually (with notation), large enough for replayability. The Soma Cube is the platonic ideal of 3D dissection puzzles — minimal pieces, maximal variety.

Piet Hein invented it in 1933 during a quantum mechanics lecture (Heisenberg). "A beautiful freak of nature."