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With 3 weighings you can find one ball out of a total of 12 balls that are all of the same weight except one, and in addition determining whether the odd one is lighter or heavier than the other 11.

Similarly with 4 weighings you can solve the problem with 38 balls, 5 weighings for 118 balls, etc. More generally one can deduce a formula for the number f(n) of balls for n weighings, where n is any positive integer.

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