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. Weigh pearls 1, 2, and 3 against 4, 5, and 6. If 1-2-3 weighs less than 4-5-6, then 1-2-3 contains the fake pearl. If 1-2-3 weighs more, than 4-5-6 contains the fake. If they weigh the same, then 7-8-9 contains the fake.
Call the three pearls in the group containing the fake a, b, and c. Weigh a and b against one another. If a weighs less, then it is fake. If b weighs less, than it is the fake. If they weigh the same, then c is the fake.
Solution
