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?
First thing that came to my mind:
Divide the 10 pearls into 4 groups. 3,3,3, and 1.
Weigh each group. If one of the 3s is 29 weigh each pearl from there on it's own.
If you are very lucky you will get it at the first try (weighing the 1). If you're very unlucky, you'll get it at the 7th.
Chance
