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I forgot to answer for which values of n this would hold true.
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N=3, N-1=2. There are 2 real coins and 1 fake coin. The 2 real coins will balance against each other and the other one is fake. This process will hold true for all values of N where N is greater than or equal to 3.

N=3, N-1=2. There are 2 real coins and 1 fake coin. The 2 real coins will balance against each other and the other one is fake.

N=3, N-1=2. There are 2 real coins and 1 fake coin. The 2 real coins will balance against each other and the other one is fake. This process will hold true for all values of N where N is greater than or equal to 3.

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N=3, N-1=2. There are 2 real coins and 1 fake coin. The 2 real coins will balance against each other and the other one is fake.