Each of the cells of a table 2014 x 2014 is colored in white or black. It is known that each square 2 x 2 contains an even number of black cells and each cross (3 x 3 square without its corner cells) contains an odd number of black cells. Prove that the 4 corner cells of the table are in the same color.
Problem
Source: V International Festival of Young Mathematicians Sozopol 2014, Theme for 10-12 grade
Tags: combinatorics, table, Coloring