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How to Cut a Rug
By Solomon Golomb '51

The carpet in your living room is in good condition, but you are moving to a new place. You discover that the new living room needs a carpet of the same area, but a different shape.

In each of the following problems, it is possible to cut the old carpet into only two pieces, which can then be reassembled to cover the new shape. Here is a simple example, from 6' x 12' to 9' x 8'.

See how many of the following carpets you can cut into only two pieces that can then be reassembled to cover the required shape. Regions in black are missing from your old carpet. (The problems get progressively harder.)

Follow this link to solutions.

Return to April 2008 Table of Contents

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