Talk:2010 USAMO Problems/Problem 6
The solution given is written horribly, and appears to be wrong. I'm actually unsure what the answer is, but I know it's at most 46. For any positive integers a and b, (-a,-a), (-b,-b), (a,b) prevents you from taking one from more than two. This can be done for 22 sets of 3 pairs. It's also obvious that the answer is at least 34. Pick 34 different pairs where there is a positive element. Delete that positive element. If this is impossible, instead do it for negatives.