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Conway's puzzle, or blocks-in-a-box, is a packing problem using rectangular blocks, named after its inventor, mathematician John Conway. It calls for packing thirteen 1 × 2 × 4 blocks, one 2 × 2 × 2 block, one 1 × 2 × 2 block, and three 1 × 1 × 3 blocks into a 5 × 5 × 5 box.

Solution

The solution of the Conway puzzle is straightforward once one realizes, based on parity considerations, that the three 1 × 1 × 3 blocks need to be placed so that precisely one of them appears in each 5 × 5 × 1 slice of the cube. This is analogous to similar insight that facilitates the solution of the simpler Slothouber–Graatsma puzzle.

See also

• Soma cube

References

1. Weisstein, Eric W. "Conway Puzzle". MathWorld.
2. Elwyn R. Berlekamp, John H. Conway and Richard K. Guy: winning ways for your mathematical plays, 2nd ed, vol. 4, 2004.

External links

• The Conway puzzle in Stewart Coffin's "The Puzzling World of Polyhedral Dissections"

• Packing problems
• Tiling puzzles
• Mechanical puzzle cubes
• John Horton Conway