# Finding upper and lower bounds of a problem [closed]

We have n balls where 1 is a little heavier than the others and we want to find that heavier ball. We can only put some balls on one side of the scale and some on the other side and see if it leans and to which side. How can we find lower and upper bounds for this problem? We want upper and lower bounds to be equal.

## closed as off-topic by Emil Jeřábek, D.W., Jan Johannsen, Hsien-Chih Chang 張顯之, András SalamonJun 27 '18 at 19:50

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Theorem 1: Let $S$ be a set of coins, one lighter than the rest. The least number of weighings on a beam balance in which the light coin can be found is the unique $n$ satisfying $3^{n-1} < |S| \le 3^n$.