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?
(In reply to
re(5): solution (plus one)--Even More by Charlie)
Good ideas! Here are some more:
Start with 153 bags.
Start by setting aside 68 bags. Take the other 85 and split them as you said. The only difficulty is if these 85 are OK and the 68 are light.
If the 68 are light, set aside 15. Of the remaining 53, split them into sets A, B, C, D with 15 each of A, B, C and 8 in set D. Take one each from A, two each from B, three each from C, and four each from D. Total weight should be 1464 (at most). If A is light, the total would be 15 grams low, B 30, C 45, and D 32. You can then do the 1,2,3,... trick with the proper remaining pile (A,B,C,D or the one set aside, each of which have at most 15 coins in them).
Bummer though -- since we can get 68 bags in two weighings, it is too bad we can't put 136 in the first A,B pairing instead of only 85. Also, I'd really like to be able to use those last 36 grams in ABCD weighing above, but don't see how at the moment....
re(6): solution (plus one)--Still more
