Watch this animation. In six moves, turning two
cups at a time, I turned them all right-side-up. Now you try it, using real
cups or glasses. Can't do it, in any number of moves? See the solution
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© Copyright 2002, Jim Loy
Watch this animation. In six moves, turning two
cups at a time, I turned them all right-side-up. Now you try it, using real
cups or glasses. Can't do it, in any number of moves? See the solution
below:
Solution: This kind of thing is sometimes called a "bar bet." Another description would be "scam." It can't be done in any number of moves, from the position shown above (two up and one down). But you saw me do it in six moves. Well, I didn't start with the same position. I started with one up and two down. Then I could have done it in any number of moves. I could have done it in one move, but then you would have noticed the scam, because starting with two up and one down, you cannot do it in one move.
Starting with one up and two down, there are three different pairs of cups that I can flip. If I flip the two on the left, the position goes from one up and two down to one up and two down, same situation, different cups. Same thing with the two on the right. But if I move the two on the opposite ends, I go from one up and two down to three up. However, if we start with two up and one down, we can get either another two up and one down, or three down. In that case, we cannot ever get three up, or one up and two down. This is an example of mathematical parity (see Dominoes On a Checker Board and The 15 Puzzle). Any move maintains the parity.
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