The Three Cups Problem

Here are three cups, one upside down.

Turning over exactly two cups with each move, can you turn all cups right-side-up in no more than six moves?

If it’s possible, show how; if it’s not, say why.

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It’s not possible. Denote by W the number of cups that are upside down. At the start W is 1, and each move changes W by an even number. So we can never arrive at 0 (in any number of moves).