MathDB

We call a coloring

f

of the elements in the set

M = \{(x, y) | x = 0, 1, \dots , kn - 1; y = 0, 1, \dots , 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 \leq n(n + 1).

Problem Statement