1. Finding the Counterfeit Coin. You have 5 coins. You know that one of them is counterfeit and weighs less than the others. Suppose also that you have a balance scale. Is there a strategy for finding the counterfeit coin using the balance scale only twice? If yes, what is the strategy?
2. Finding the Counterfeit Coin Revisited. Suppose you have 9 coins that look identical. Suppose, however, that eight are genuine (and identical) but one is counterfeit. The only clue to the counterfeit coin is that it weighs slightly more than the genuine coins. Suppose also that you have a balance scale. Can you find a way to determine which coin is counterfeit using the balance scale only twice?
3. Finding the Counterfeit Coin – Part 3. Suppose you have 12 coins that look identical. Suppose, however, that eleven are genuine (and identical) but one is counterfeit. The only clue to the counterfeit coin is that it has a different weight. I.e., it weighs either slightly more or slightly less than the genuine coins but you don’t know which. Suppose also that you have a balance scale. Can you find a way to determine which coin is counterfeit and tell whether it is heavier or lighter using the balance scale only three times?
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