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Divide the pearls into three groups: pearls A:(1,2,3) B:(4,5,6) and C:(7,8,9).
First, weigh the three pearls of A against the three pearls of B. If one of them weighs less than the other, then the fake pearl is in that group. Otherwise, it's in group C.
Having determined which group the pearls are in, take two pearls of that group, and weigh them. If one is lighter, then that one is fake. If they are both the same weight, then the fake one is the one you didn't put on the scale.
Thus we can determine the fake pearl in only two weighings. |
