For 5 coins, put 2 on each side of the balance. If they match, they are real, and you just compare one of them to the fake. If they don’t match, compare the 2 coins from the lighter side. If they match, they are real and the fake is heavy. If they don’t match, the fake is light.

You can use a ≤ b ≤ 2a for N=5 since the piles are impossible to arrange. If a=1, then b=3, and b>2a. If a=2, then b=1, and a>b.

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