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. Unknown error_msg), then $(h′,k′)$ (Error compiling LaTeX. Unknown error_msg) 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.