You have three bags of coins with an unspecified number of coins in each bag. One of the bags consists entirely of counterfeit coins weighing 55 grams each; the other two bags contain all genuine coins weighing 50 grams each.

Using a weighing machine ONCE only, how can you identify the bag of counterfeit coins?

Take one coin from bag one, two coins from bag two and three from bag three and weigh all six coins together. If they weigh 305 grams the first bag contains the counterfeit coins; if they weigh 310 grams the second bag does, and if they weigh 315 grams the third bag does.