# math question?

You have 45 silver coins but one of them is a lighter weight counterfeit. How can you determin the counterfeit coin in a maximum of 3 weighings on a balance scale?

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I don’t think you can; I think it takes n=ceil(log(45)/log(3))=4:

#1: Weigh 15 on each side of the scale. If they weigh the same, put those 30 in your pocket and get the remaining 15. If they don’t, put the heavier 15 and the 15 you didn’t weigh in your pocket and get the lighter 15.

#2: Weigh 5 on each side; do the same thing to narrow the lighter coin to one of the groups of 5.

#3: Weigh 2 on each side. If they balance, the leftover is it; if not:

#4: Weigh the 2 of the lighter side against each other.