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(2): solution (plus one) by Charlie)
Sorry, I just couldn't let this go....how about 83 bags?
Set one aside. Split the rest into two groups A and B. Take one from each of A and two from each of B. Total weight should be 1476. If it is, the one you set aside is light. Else it is light by 41 or 82 grams. So now you are down to at most 41 bags. Split the rest into 3 groups a, b ,c. Take one from each of a, two from each of b, three from each of c (a and b have 14 each, c has 13). Total weight should be 12 grams*(14+28+39)=950 grams. You can immediately determine which group is light. Then use the 1, 2, 3, 4, .... trick for that set. Since each set has less than 15, you are fine.
re(3): solution (plus one)
