If a finite number of rectangles, every one of which has at least one integer side, perfectly tile a big rectangle, then the big rectangle also has at least one integer side. I present two proofs of this theorem, both accessible to a ten-year-old. The proofs generalize to other situations.

[Also, a one-page introduction to this
problem is here:
(pdf)
(postscript)]

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David MacKay's: home page, publications. bibtex file.

Canadian mirrors: home page, publications. bibtex file.