Choosing squares in an array that do not form a rectangle
Source: Czech-Polish-Slovak Match, 2010
August 8, 2011
geometryrectanglecalculuslinear algebramatrixanalytic geometrynumber theory
Problem Statement
Let be a prime number. Prove that from a array of squares, we can select of the squares such that the centers of any four of the selected squares are not the vertices of a rectangle with sides parallel to the edges of the array.