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Problem 2 (due Monday, February 17)
Let d(n) be the smallest number such that among any d(n) points inside a regular n-gon with side of length 1 there are two points whose distance from each other is at most 1. Prove that
(a) d(n)=n for 4≤n≤6.
(b) limn→∞d(n)n=∞.
For a complete solution see the following link Solution.