2002 IMO Problems/Problem 1

Revision as of 23:26, 18 November 2023 by Tomasdiaz (talk | contribs)

Problem

$S$ is the set of all $(h,k)$ with $h,k$ non-negative integers such that $h + k < n$. Each element of $S$ is colored red or blue, so that if $(h,k)$ is red and $h' \le h,k' \le k$, then $(h',k')$ is also red. A type $1$ subset of $S$ has $n$ blue elements with different first member and a type $2$ subset of $S$ has $n$ blue elements with different second member. Show that there are the same number of type $1$ and type $2$ subsets.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See Also

2002 IMO (Problems) • Resources
Preceded by
First Question
1 2 3 4 5 6 Followed by
Problem 2
All IMO Problems and Solutions