You have been given 10 bags of pearls. You are told that one of the bags is full of those cheap plastic kind of pearls, but the other nine are the real deal. Naturally, you cannot tell the difference just by looking. However, you know that the fake pearls weigh 9 grams each, while the real ones are one gram heavier and weigh 10.
Armed with a very presice scale, you could weigh a pearl from each bag until you find the fake one by weight, but that would take up to 10 weighings. Can you do it in less?
Take a pearl from bag 1, 2 pearls from bag 2, 3 pearls from bag 3, etc.
Weigh this pile of pearls you have. If they were all real, the result would weigh 10*(1+2+3+4+...+10) = 550 grams.
Because some of the pearls are fake, your result will be less.
If it's one gram less, then the bad pearls are in bag 1. If the difference is 2 grams, then bag #2 is the culptit, etc.
Thus the problem is solvable in one weighing.
Puzzle Thoughts
