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A5

Part of 1967 Putnam

Problems(1)

Putnam 1967 A5

Source: Putnam 1967

5/13/2022
Show that in a convex region in the plane whose boundary contains at most a finite number of straight line segments and whose area is greater than π4\frac{\pi}{4} there is at least one pair of points a unit distance apart.
Putnamgeometrydistance