Ninety-nine points on one of the diagonals of a unit square
Source: Austrian Mathematical Olympiad 1999, Part 2, D2, P1
June 28, 2011
combinatorics proposedcombinatorics
Problem Statement
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 .