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.

P.S. This is the second time I submitted this because I don't think it worked the first time. If you find somebody with the same details, please ignore this or the other one. If you don't, then don't worry and carry on.