Prove that a convex 13-gon cannot be cut into parallelograms.
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Solution
For a convex polygon with an odd number of sides, there is a side that is not parallel to any of the other sides, since the parallel sides of a convex polygon are divided into pairs. If a polygon can be cut into parallelograms, then for each of its sides, there will be a side parallel to it (see solutions to problems and ).
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