Each point in the plane is colored either red or green. Let ABC be a fixed triangle. Prove that there is a triangle DEF in the plane such that DEF is similar to ABC and the vertices of DEF all have the same color.I think I was assigned to grade it since it looks like the kind of problem I would make up, even though I didn't. It was problem 5 (out of 5) and hence it was what we thought was the hardest problem. About 100 people tried it, and less than 5 got it right, and less than 10 got partial credit (and they didn't get much).
I got two funny answers:
All the vertices are red because I can make them whatever color I want. I can also write at a 30 degree angle to the bottom of this paper if thats what I feel like doing at the moment. Just like 2+2=5 if thats what my math teacher says. Math is pretty subjective anyway. (NOTE- this was written at a 30 degree angle.)
I like to think that we live in a world where points are not judged by their color, but by the content of their character. Color should be irrelevant in the the plane. To prove that there exists a group of points where only one color is acceptable is a reprehensible act of bigotry and discrimination.Were they serious? Hard to say, but I would guess the first one might have been but the second one was not.