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?

Since we can always divide the number of pearls into three comparable piles and deduce which of the piles contains the fake pearl after one weighing, the number of necessary weighings is determined by powers of 3. That is to say if P is less than or equal to 27, it will require 3 weighings, likewise if less than or equal to 81, it will require 4 weighings. We can extend this to say:

If 3^(x-1)<P<=3^x, then it will require x weighings to determine the fake pearl.

Edited on November 30, 2005, 11:22 pm

Posted by Eric on 2005-11-29 23:21:44