After figuring out the Trickier pearls problem you've just realized something. Being a pearl expert you know there are two types of oysters which each produce pearls exactly the same in every aspect except for weight. The pearls produced by the blue oysters weigh 10 grams and the ones produced by the black oysters weigh 11 grams, and of course fake pearls weigh 9 grams.

You have 5 bags and each of them either contains all fake pearls, all black oyster pearls or all blue oyster pearls. You have to find out which bags contain which kinds of pearls in the least amount of weighings possible. Assume every bag of pearls has an infinite amount of pearls.

Weigh 1 pearl from bag 1
100 pearls from bag 2
10,000 pearls from bag 3
1,000,000 pearls from bag 4
100,000,000 pearls from bag 5

If every bag held pearls from blue oysters, the total weight should be 1010101010 grams ("10" repeated 5 times). If any of the pairs of digits reads 09 or 11, the corresponding bag holds fakes or pearls from black oysters, respectively. There are other solutions that use far fewer pearls, but this one is easy to explain.

Posted by Bryan on 2003-04-02 07:49:53