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Part of 1984 IMO Longlists

Problems(1)

2m gon with exactly one pair of parallel sides

Source:

10/10/2010
Given a regular convex 2m2m- sided polygon PP, show that there is a 2m2m-sided polygon π\pi with the same vertices as PP (but in different order) such that π\pi has exactly one pair of parallel sides.
modular arithmeticgeometry unsolvedgeometry