Question: Twenty-five students attend a class reunion and shake hands with each other. If no student shakes hands with the same person twice, explain why two students will have shaken the same number of hands.
So far, the furthest I've gotten is finding the number of possible handshake combinations which would be (25 x 24)/2 = 300 (using n(n-1)/2). This question seems to be a pigeonhole principle question. I am new to this topic however, so my understanding is elementary and insufficient to answer this.