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
devide the 9 pearls into three piles of three.
weigh two piles agains each other.
If they balance they are all good, return them to your jewel box. then take the remaining three and place one on each side of the scale resrving the third. If the scalle balances, the enwieghed pearl is the clunker. If the scale does not balance than obviously the lighter pearl is the clunker.
If the scal did not balance on the first weigh, use the lighter pile ans do as described above for the unweighed pile.
Solution
