Hoffman's packing puzzle

[2][3] Hoffman (1981) writes that the first person to solve the puzzle was David A. Klarner, and that typical solution times can range from 20 minutes to multiple hours.

Although the puzzle can be constructed with any three different edge lengths, it is most difficult when the three edge lengths of the blocks are close enough together that x + y + z < 4 min(x,y,z), as this prevents alternative solutions in which four blocks of the minimum width are packed next to each other.

Additionally, having the three lengths form an arithmetic progression can make it more confusing, because in this case placing three blocks of the middle width next to each other produces a row of the correct total width but one that cannot lead to a valid solution to the whole puzzle.

The fact that the pieces have less total volume than the cube follows from the inequality of arithmetic and geometric means.

In d dimensions the puzzle asks to pack dd identical blocks into a hypercube.