IMO 1974 LL USS43

An (n2 +n+1) imes(n2 +n+1) matrix of zeros and ones is given.

IMO 1974 LL USS43

Origin: USS

Problem

An (n2 +n+1)\times(n2 +n+1) matrix of zeros and ones is given. If no four ones are vertices of a rectangle, prove that the number of ones does not exceed (n + 1)(n2 + n + 1).