Three cups problem
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Starting with three cups place one upside down and two right side up. The objective is to eventually turn all cups right side up in six moves. You are only able to and have to turn two cups over each turn.
[edit] Solution
The puzzle is impossible because you have an even number of cups facing up and you are allowed to turn two over at a time so 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. You need an odd number of cups facing up so the problem is impossible. The possible version of this puzzle is to start with two cups facing down and one cup facing upward. This is possible because 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.
