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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 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.
The Conway puzzle in Stewart Coffin's "The Puzzling World of Polyhedral Dissections"
{{Packing problem Packing problems Recreational mathematics Tiling puzzles Mechanical puzzle cubes John Horton Conway
Solution
The solution of the Conway puzzle is straightforward once one realizes, based onparity
Parity may refer to:
* Parity (computing)
** Parity bit in computing, sets the parity of data for the purpose of error detection
** Parity flag in computing, indicates if the number of set bits is odd or even in the binary representation of the r ...
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.
See also
*Soma cube
The Soma cube is a solid dissection puzzle invented by Danish polymath Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg.
Seven pieces made out of unit cubes must be assembled into a 3×3×3 cube. The pie ...
References
External links
The Conway puzzle in Stewart Coffin's "The Puzzling World of Polyhedral Dissections"
{{Packing problem Packing problems Recreational mathematics Tiling puzzles Mechanical puzzle cubes John Horton Conway