The reason for this is quite simple once you think about it. Consider the original orientation of cups. It is possible to get all three cups facing up in just one move by flipping the outside two cups; doing it in three moves is another deliberate distraction. Because you are always flipping two at a time, starting with two cups facing up or two cups facing down will determine the final possibilities. Whenever two cups are facing down at the beginning, you will always be able to get all three facing up, and never all three facing down. Likewise, whenever you begin with two cups facing up at the beginning, you will always be able to get all three facing down, and never all three facing up.