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Problem of the Week 865

The Opaque Square

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The owner of a square piece of land of unit size knows that a straight telephone line is running across the land at a depth of 30 cm. To find the line, one can dig a ditch (of total length 4) once around the square. But digging up three sides of the square (total length 3) will also uncover the telephone line. The prize goes to the student(s) who produce a ditch of shortest length which will uncover the line.

Source: Bernd Kawohl (Math. Institut Universitaet zu Koeln), The Mathematical Intelligencer, Vol 20, 1998, 16-21.

© Copyright 1998 Stan Wagon. Reproduced with permission.

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2 October 1998