Chameleon Coins


You cannot find the chameleon coin in a mix with real coins if it does not want to be found, because it can consistently behave as a real coin. Let’s add classic fake coins to the mix, the ones that are lighter. Still the task of identifying the chameleons using a balance scale cannot be achieved: the chameleons can pretend to be fake coins. We can’t identify the fake coins either, as the chameleons can mess things us up by consistently pretending to be fake.





One Comment

  1. Felix:

    Let A, B, C, D be the four coins.
    First, weigh A+B against C+D. If one side is lighter, then the side is guaranteed to have the fake coin. If not, then we know the chameleon was behaving as a fake coin, and it’s not on the same side as the fake coin.
    Then, weigh A against B. We know at least one of them is real. If one side is lighter, then we have found the fake coin. Otherwise, the other has to be the chameleon, and we know the fake coin is either C or D.

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