6.BC. HOFFMAN'S CUBE
This consists of 27 blocks, a x b x c, to make into a cube a+b+c on a side. It was first proposed by Dean Hoffman at a conference at Miami Univ. in 1978. See S&B, p. 43. The planar version, to use 4 rectangles a x b to make a square of side a + b is easy. These constructions are proofs of the inequality of the arithmetic and geometric means. Sometime in the early 1980s, I visited David Klarner in Binghamton and Dean Hoffman was present. David kindly made me a set of the blocks and a three-sided corner to hold them.
D. G. Hoffman. Packing problems and inequalities. In: The Mathematical Gardner, op. cit. in 6.AO, 1981. Pp. 212 225. Includes photos of Carl Klarner assembling the first set of the blocks. Asks if there are analogous packings in n dimensions.
Berlekamp, Conway & Guy. Winning Ways. 1982. Vol. 2, pp. 739 740 & 804 806. Shows all 21 inequivalent solutions.
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