# 2002 IMO Problems/Problem 1

is the set of all with non-negative integers such that . Each element of is colored red or blue, so that if is red and $h′ ≤ h,k′ ≤ k$ (Error compiling LaTeX. ), then $(h′,k′)$ (Error compiling LaTeX. ) is also red. A type subset of has blue elements with different first member and a type subset of has blue elements with different second member. Show that there are the same number of type and type subsets.