Conway puzzle

Conway's puzzle 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.

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 at least one of them appears in each 5 × 5 × 1 slice of the cube.

The letters a, b, and c represent 1 × 1 × 3 blocks, and everything else is represented by an *.

Slice #
  1     2     3     4     5
aaa** ***** ***** ***** *****
***** ***b* ***b* ***b* *****
***** ***** ***** ***** ****c
***** ***** ***** ***** ****c 
***** ***** ***** ***** ****c 

See also

• Slothouber–Graatsma puzzle