Problem

Source: Romanian JBTST III 2007, problem 3

Tags: modular arithmetic, induction, combinatorics proposed, combinatorics



Consider a $n$x$n$ table such that the unit squares are colored arbitrary in black and white, such that exactly three of the squares placed in the corners of the table are white, and the other one is black. Prove that there exists a $2$x$2$ square which contains an odd number of unit squares white colored.