We call a coloring f of the elements in the set M={(x,y)∣x=0,1,…,kn−1;y=0,1,…,ln−1} with n colors allowable if every color appears exactly k and l times in each row and column and there are no rectangles with sides parallel to the coordinate axes such that all the vertices in M have the same color. Prove that every allowable coloring f satisfies kl≤n(n+1). geometryrectangleanalytic geometrycombinatorics unsolvedcombinatorics