Conway's puzzle is a packing problem

Packing problem

Packing problems are a class of optimization problems in mathematics which involve attempting to pack objects together , as densely as possible. Many of these problems can be related to real life packaging, storage and transportation issues...

 using rectangular blocks, named after its inventor, mathematician John Conway

John Horton Conway

John Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...

. 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 when one realizes 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.

External links

• The Conway puzzle in Stewart Coffin's "The Puzzling World of Polyhedral Dissections"