**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]}

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

## See also

## References

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