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A4

Part of 1968 Putnam

Problems(1)

Putnam 1968 A4

Source: Putnam 1968

2/19/2022
Let S2⊂R3S^{2}\subset \mathbb{R}^{3} be the unit sphere. Show that for any nn points on S2 S^{2}, the sum of the squares of the n(n−1)2\frac{n(n-1)}{2} distances between them is at most n2n^{2}.
Putnamgeometry3D geometrysphere