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It is easy to cut a loaf of bread into 8 pieces using 3 straight cuts. How many pieces can you get from a doughnut (torus) using three straight cuts, the idea being to get as many as possible?

Note: Pieces may not be repositioned between cuts.(A proof of optimality is not expected, though I believe it has been done in this case. Citations to the literature are welcome.)

(I would rather not mention in the official problem statement that two pieces that have a single point in common are considered disconnected -- because it gives too much of a hint and seems reasonably obvious.....)

Source: This problem goes back a few years and was mentioned in Martin Gardner's Scientific American column at some point. I was reminded of it in the nice new problem book by Ed Barbeau (U. of Toronto) titled "Aftermath: Puzzles and Brainteasers" (Wall & Emerson, Toronto (416) 467-8685). That book contains several nice problems, some quite original, and I anticipate using a few more from there this season.

© Copyright 1998 Stan Wagon. Reproduced with permission.

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2 October 1998