At this point, students are ready to talk about the mathematics involved in the trick. This trick is related to odd and even numbers. Since the goal is to get all three cups facing up (an odd number) and you start with one cup facing up (also an odd number) you must turn up an even number (two) of cups, because an odd plus an even is an odd. Likewise, in the students’ impossible starting position with one cup down and two cups up, no number of even flips will get all three cups facing up. This is because you start with an even number of cups facing up and you must flip an even number of cups over on each move and an even plus an even is an even, not an odd.