Conway puzzle: Difference between revisions
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{{Short description|Three-dimensional packing problem}} |
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[[Image:Conway_puzzle_pieces.svg|thumb|Pieces used in the Conway puzzle]] |
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| ⚫ | '''Conway's puzzle''', or '''blocks-in-a-box''', is a [[packing problem]] using rectangular blocks, named after its inventor, mathematician [[John Horton Conway|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.<ref>{{MathWorld | urlname=ConwayPuzzle | title=Conway Puzzle}}</ref> |
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==Solution== |
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See also: [[Slothouber-Graatsma Puzzle]]. |
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[[Image:Conway puzzle_hint.svg|thumb|upright|A possible placement for the three 1×1×3 blocks – {{nowrap|the vertical}} block has corners touching corners of the two horizontal blocks]] |
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The solution of the Conway puzzle is straightforward once one realizes, based on [[parity (mathematics)|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.<ref>Elwyn R. Berlekamp, John H. Conway and Richard K. Guy: winning ways for your mathematical plays, 2nd ed, vol. 4, 2004.</ref> This is analogous to similar insight that facilitates the solution of the simpler [[Slothouber–Graatsma puzzle]].[[File:conway_puzzle_solution.svg|thumb|none|400px|A step-by-step solution to the Conway puzzle]] |
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==See also== |
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* [[Soma cube]] |
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==References== |
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{{reflist}} |
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==External links== |
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* [http://www.johnrausch.com/PuzzlingWorld/chap03.htm#p6 The Conway puzzle in Stewart Coffin's "The Puzzling World of Polyhedral Dissections"] |
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{{Packing problem}} |
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[[Category:Mechanical puzzle cubes]] |
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[[Category:John Horton Conway]] |
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Latest revision as of 19:58, 22 October 2023
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
[edit]
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
[edit]References
[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.