You have N large bags of coins. All of the bags contain real 12 gram coins except for one, that one contains fake 11 gram coins.

To help you find the bag of fake coins, you have a digital scale which will give you the exact weight of any amount of coins up to 1500 grams. Any amount over 1500 grams will cause the scale to spit out a random value.

How many bags (N) can you have and still be able to tell which bag contains the fake coins if you can only use the scale three times?

i think the answer is 8 total bags of coins.
you start out with 7 bags of 12 gram coins and 1 bag of 11 gram coins.
split the 8 bags into groups of 2 and weigh one of the groups of 4 bags. if the weight is divisible by 12 then the other group has the bag of fake coins. if not, then the group weighed has the fake coins.
then split the group with the fake coins in 2, and weigh one of the groups with 2 bags. if the weight is divisible by 12 then the other group has the fake coins.
you are then left with 2 bags. one with real coins and one with fake. weigh either one of them and divide the weight by 12. you will then know which is fake and which is real.

Posted by Angel on 2003-08-25 01:56:26