Question

Suppose 9 coins are identical in appearance. Eight of these are identical in weight but the ninth is lighter than the others because it is counterfeit. Explain how it is possible to identify the counterfeit coin by using a balance scale just twice. (Using a strategy similar to a Tower of Hanoi problem)

Answer 1

We divide them into three groups in such a way that each group consists of three coins . We place two sets in the balance if one is of less weight then we consider that.

or if both are of equal weight, then the third set contains the lighter coin.Thus we select the set that contains the lighter coin by weighing once

now we take those three and keep one in the plates of the balance keeping the third on the floor. If there is imbalance, then the plate with lighter coin will go up. If there is balance , then the one on the floor is the lighter coin.

Thus , we select the coin by weighing exactly twice