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Suppose You Have 50 Coins, One of Which Is Counterfeit

Question 54

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Suppose you have 50 coins, one of which is counterfeit (either heavier or lighter than the others). You use a pan balance scale to find the bad coin. Prove that 4 weighings are not enough to guarantee that you find the bad coin and determine whether it is heavier or lighter than the other coins.

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Four weighings yield a 3-ary t...

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