Your enemy chooses 10 points on an infinite tabletop and gives you 10 coins of the same size (let’s say U.S. quarters). Can you always place the coins on the tabletop in such a way that all 10 points are covered, but no two coins overlap?
If your enemy puts all 10 points far away from each other, you can just put one quarter over each point. If he scrunches them up real near each other, you can just put one quarter over all of them, and put the other nine quarters anywhere you want. But if he’s clever enough, can he make your job impossible?
Edit: I originally described the tabletop as “big”; I’ve edited this post to change it from big to infinite, in order to be true to the puzzle as Kariv originally posed it. My apologies for the original inaccurate transcription.