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?
You do indeed take 1 from the 1st bag and 2 from the second and so on.
The equation for a sum of a series of consecutive positive integers starting with 1 is:
n(n+1)/2
Solving for this where the equation ≤ 1500 gives n=54. So with 3 uses of the scale 3*54=162.
You could test up to 55 bags at one time if there were some way to make sure that the bag with the fake coins was bag no. 40 or greater. Because, the fake coins are 1 gram lighter each. But there isn't, so tough.
the math
