You have nine pearls, one of which is (as is usually the case in these problems) fake. You know that the fake pearl weighs less than the others, but it is (of course) impossible to distinguish from the others in any other way.

What is the minimum number of weighings that must be performed to find the fake pearl? How would you go about it?

Two weighings.

Since you know that the fake is lighter (a definite plus), as soon as you get an imbalance, you know which pan the fake is in.

First, put 3 pearls in each pan. If they balance, the fake is one of the three not being weighed. If they don't balance, the fake is one of the three in the lighter pan. Either way, you have eliminated all but three pearls.

Now put one of those pearls in each pan. If they balance, the fake is the third. If they don't balance, the fake is the lighter one.

Posted by TomM on 2002-05-23 13:22:50