olymmath

Putnam 1952 A6

  • Session A
  1. A man has a rectangular block of wood mm by nn by rr inches (m,n(m, n, and rr are integers). He paints the entire surface of the block, cuts the block into inch cubes, and notices that exactly half the cubes are completely unpainted. Prove that the number of essentially different blocks with this property is finite. (Do not attempt to enumerate them.)

Dataset text PutnamGAP. Quoted with source.

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