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?

The best way to go about this is to take 1 coin from bag 1, 2 coins from bag 2, 3 coins from bag 3 etc. until you cannot add any more because of the weight limit. If you've placed x coins on the scale, then the coins would be 12x if they were all real.

If the amount is Y lower than x then the fake coins are in bag Y, as you would have placed Y coins from bag Y on.

I'll leave someone else to do the calculations. :)

Posted by Lewis on 2003-07-25 09:49:02