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Part of 1978 Miklós Schweitzer

Problems(1)

Miklos Schweitzer 1978_8

Source: n points in the unit square

1/25/2009
Let X1,…,Xn X_1, \ldots ,X_n be n n points in the unit square (n>1 n>1). Let ri r_i be the distance of Xi X_i from the nearest point (other than Xi X_i). Prove that the inequality r_1^2\plus{} \ldots \plus{}r_n^2 \leq 4. L. Fejes-Toth, E. Szemeredi
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