Conway puzzle
Three-dimensional packing problem From Wikipedia, the free encyclopedia
Three-dimensional packing problem From Wikipedia, the free encyclopedia
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]
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.
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