So with this class of problem you have a number of items and one of them is a fake. All the real items weigh the same, and the fake one weighs less than the real ones.
Twelve item version of the problem:
You have twelve pearls, eleven are real and one is fake. All the real items weigh the same, and the fake one weighs less than the real ones.
Nine item version of the same problem:
You have nine pearls, eight are real and one is fake. All the real items weigh the same, and the fake one weighs less than the real ones.
Eight item version of the problem:
Eight eggs look identical except one is lighter.
How can you find the fake with a scale?
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