Slothouber–Graatsma puzzle

The solution to this puzzle is unique (up to mirror reflections and rotations).

This follows from parity considerations, because the larger blocks can only fill an even number of the 9 cells in each 3 x 3 layer.

More general puzzles involving the packing of convex rectangular blocks exist.

The best known example is the Conway puzzle which asks for the packing of eighteen convex rectangular blocks into a 5 x 5 x 5 box.

A harder convex rectangular block packing problem is to pack forty-one 1 x 2 x 4 blocks into a 7 x 7 x 7 box (thereby leaving 15 holes); the solution is analogous to the 5x5x5 case, and has three 1x1x5 cuboidal holes in mutually perpendicular directions covering all 7 slices.