Hoffman-Knuth Puzzle

In 1978, Dean Hoffman posed the following problem to a conference at Miami University.

“Fit twenty-seven blocks, measuring A x B x C into a cubic box with sides of A

• B + C. A, B and C must be different and the smallest dimension must be larger than (A + B + C) / 4.”

Knuth modified the condition to be A = (A+B+C)/4 so that we can fit four boxes in a stack. For certain combinations, we can pack 28 blocks.

But some A, B, C have no solution need an additional condition 3B <= A + B + C

• b c a ——- 4a/3 …… 5a/3 ——- 2a