Nice, and very typical of the Olympiads.

We were discussing one of the questions after we did it, and one student said, "Oh, I knew this one from a book, but I didn't think it was fair to use that."

We were all skeptical so he told us the answer. In one sentence. Many facepalms.

Our supervisor said, "Next time, write the answer, and if you like, tell them you read it in a book."

Here's the problem! In hindsight, it seems so obvious.

You have N red dots and N blue dots in the plane, no three in a straight line.

Prove that it is always possible to partition the set of dots into pairs of red and blue dots, and then connect each pair with a line segment, such that those line segments don't intersect.