Solution
The problem is impossible to solve. An even number of cups are facing up, and you must turn over exactly two cups at each move. Since an even plus an even is an even, not an odd, no number of even flips will ever get all the three cups right-side up. To solve the problem, you need an odd number (i.e., three) of cups facing up, so the problem is impossible.
The solvable (but trivial) version of this puzzle starts with two cups upside down and one cup right-side up. To solve the puzzle in a single move, you need only turn up the two cups that are upside down — after which all three cups are facing up.
Read more about this topic: Three Cups Problem
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