Simple Proofs of a Rectangle Tiling Theorem

David J C MacKay

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)]

html postscript pdf

html version (created Tue 27/5/03) (Cambridge UK).

postscript (Cambridge UK).

pdf (Cambridge UK).

html version (Canada mirror).

postscript (Canada mirror).

pdf (Canada mirror).

All postscript files are compressed with gzip - see this page for advice about gzip, if needed.


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