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]
![](http://178.128.105.246/cars-http-upload.wikimedia.org/wikipedia/commons/thumb/5/58/Conway_puzzle_pieces.svg/220px-Conway_puzzle_pieces.svg.png)
Solution
editThe 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
editReferences
edit- ^ 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.