Conway puzzle

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.[1]

Pieces used in the Conway puzzle, one of each kind

Solution
A possible placement for the three 1×1×3 blocks. The vertical block has corners touching corners of the two horizontal blocks.

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.[2] This is analogous to similar insight that facilitates the solution of the simpler Slothouber–Graatsma puzzle.

See also

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.
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