Imagine that there are three kinds of coins: real coins, fake coins, and an alternator coin. The fake coins are lighter than the real ones. The alternator coin is a peculiar coin that exists only in a mathematician’s mind, as it can change its weight at will. When you put the alternator on the scale, it can either weigh the same as a real coin or a fake coin. Now, here is our puzzle. There are four identical-looking coins: two real, one fake, and one alternator. We know that the alternator coin strictly alternates its weight each time it is put on the scale. How do you find the alternator using a balance scale at most three times?
The puzzle is from Tania Khovanova's blog.
Solution
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