Question

Consider the following numbers 3, 6, 9, 12, . . . , 75. Show that if we pick 15 arbitrary numbers from them, then we will find two that have sum equal to 81. I understand that there are 12 distinct sets containing pairs that sum to 81 plus a singleton subset {3}. but wouldn't this mean that there are 2 remaining "empty holes" that need to be filled? Not sure how to apply the pigeonhole principle here.

Answer 1