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Slothouber–Graatsma puzzle
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).
The puzzle is essentially the same if the three 1 × 1 × 1 blocks are left out, so 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 nontrivial 3D packing problem.
==Solution==
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, as each of the 3 x 3 layers in the various directions needs to contain such a unit block. 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.〔Elwyn R. Berlekamp, John H. Conway and Richard K. Guy: Winning ways for your mathematical plays, 2nd ed, vol. 4, 2004.〕
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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