Conway puzzle on:
[Wikipedia]
[Google]
[Amazon]
Conway's puzzle, or blocks-in-a-box, is a
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
packing problem
Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few conta ...
using rectangular blocks, named after its inventor, mathematician John Conway
John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches ...
. 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.
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.
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