olymmath

ÖMO 1999 Problem 4

  • Day 2

Ninety-nine points are given on one of the diagonals of a unit square. Prove that there is at most one vertex of the square such that the average squared distance from a given point to the vertex is less than or equal to 1/21/2 .

Dataset text AI-MO AoPS. Quoted with source.

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