Slothouber–Graatsma puzzle

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The Slothouber–Graatsma puzzle is a packing problem that calls for packing six 1 × 2 × 2 blocks and three 1 × 1 × 1 blocks into a 3 × 3 × 3 box. The solution to this puzzle is unique (up to mirror reflections and rotations).

Note that the puzzle is essentially the same if the three 1 × 1 × 1 blocks are left out, such that the task is to pack six 1 × 2 × 2 blocks into a cubic box with volume 27. The Slothouber–Graatsma puzzle is regarded as the smallest non-trivial 3D packing problem. Its solution is unique (up to rotational and mirror symmetries).

See also: Conway puzzle.

The solution of the Slothouber–Graatsma puzzle is straightforward when one realizes that the three 1 × 1 × 1 blocks (or the three holes) need to be placed along a body diagonal of the box.