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Puzzle page

May 2002

Mathematical Misfits


Which fits best - a square peg in a round hole, or a round peg in a square hole? To be more precise, if you take a circle and fit inside it the largest possible square, and then take a square and fit inside it the largest possible circle, which leaves proportionally least space?

Which fits best?

Which fits best?


Which fits best in a sphere - a dodecahedron or an icosahedron? That is, if you fit the largest possible dodecahedron and icosahedron inside a given sphere, which leaves least space?





You can see rotating versions of these here (70k download each).

(Both images copyright by Rüdiger Appel)

You can send your solution by e-mail to

If you are stumped by last issue's puzzle, here is the solution.

For some challenging mathematical puzzles, see the NRICH puzzles from this month or last month.


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