Take Three From Five Jenny

Any set of five numbers must include at least one subset of three numbers that sum to a multiple of three.

It works because of the pigeonhole principle. When you divide any integer by three, the remainder is 0, 1, or 2. So, with five numbers, there must be at least three numbers in there that, when their remainders are added, total to a multiple of three.

(not) fun fact: my sister posed me this as a challenge when I was about seven years old and got annoyed when I found out it was impossible