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Nine Pearls Puzzle - Solution
The Puzzle:
You have nine pearls.
Eight of them are real pearls, and one of them is a fake.
The eight real ones all weigh exactly the same. But the fake pearl weighs slightly less than the real ones.
With no more than two uses of a balance scale, how can you find the fake pearl?
(The difference in weight is so small that you must use the scale. The only way to decipher the fake pearl is by weight.)
Our Solution:
Place three pearls on one side and three pearls on the other side, if the scale remains balanced then those pearls are all real, and the fake pearl is one of the three you left out.
If the scale becomes off balance then the raised pile is the lightest, and that means that the fake pearl is in that set of three.
Now we are down to just three pearls that may be fake.
Now place one pearl on one side of the scale and one on the other side of the scale, leaving one out.
Again, if the scale is even then the fake pearl is the one you left out, and if the scale is unbalanced then the raised pearl is the fake one.
If the scale becomes off balance then the raised pile is the lightest, and that means that the fake pearl is in that set of three.
Now we are down to just three pearls that may be fake.
Now place one pearl on one side of the scale and one on the other side of the scale, leaving one out.
Again, if the scale is even then the fake pearl is the one you left out, and if the scale is unbalanced then the raised pearl is the fake one.