Gateways To Joy
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Puzzles
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Set 7
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Rectangle with Integer Side
Rectangle with Integer Side
17 Aug 2011
Puzzle

A big rectangle is composed of smaller non-overlapping rectangles, each having integer width or integer height or both. Prove that the big rectangle enjoys the same property.

Source

Do not remember.

Solution

  1. Fourteen Proofs of a Result about Tiling a Rectangle by S Wagon, The American Mathematical Monthly, vol. 94, 1987, pp. 601-617. The article won the MAA Writing Award in 1988.
  2. Solution by David McKay.
  3. Solution by E W Dijkstra.
  4. Solution by Ulrich Berger.
  5. Solution at cut-the-knot.

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