Conway puzzle
{{Short description|Three-dimensional packing problem}}
Image:Conway_puzzle_pieces.svg
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.{{MathWorld | urlname=ConwayPuzzle | title=Conway Puzzle}}
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.Elwyn R. Berlekamp, John H. Conway and Richard K. Guy: winning ways for your mathematical plays, 2nd ed, vol. 4, 2004. This is analogous to similar insight that facilitates the solution of the simpler Slothouber–Graatsma puzzle.File:conway_puzzle_solution.svg
See also
References
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External links
- [http://www.johnrausch.com/PuzzlingWorld/chap03.htm#p6 The Conway puzzle in Stewart Coffin's "The Puzzling World of Polyhedral Dissections"]
{{Packing problem}}