A deceptively simple packing problem by Dutch architects Jan Slothouber and William Graatsma: How can you assemble six 1 × 2 × 2 blocks and three 1 × 1 × 1 blocks into a 3 × 3 × 3 cube? There’s no trick to it, but it can be quite difficult to solve — the solution is unique, not counting mirror reflections and rotations.

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The key is to notice that the 1 × 1 × 1 blocks must fall along a diagonal of the finished cube, to ensure that each 3 × 3 × 1 “slice” of the cube (in every orientation) can contain an odd number of blocks: