Show that among any n+2 integers, either there are two whose difference is a multiple of 2n, or there are two whose sum is divisible by 2n.

Chose any (n+1)-element subset from \{1,2, \ldots, 2n\}. Show that this subset must contain two integers that are relatively prime.

(Putnam 1994) Prove that the points of an [right] isosceles triangle of side length 1 cannot be colored in four colors such that no two points at distance at least 2-\sqrt{2} from each other receive the same color.

Wording found on the 1994 Putnam: Show that if the points of an isosceles right triangle of side length 1 are colored with one of four colors, then there must be two points of the same color which are at least a distance s-\sqrt{2} apart.