HARD PUZZLE 6

Mr Smith has lots of pound coins, ten boxes in all. Each box contains 100 pound coins, but one box contains coins which are counterfeit and are slightly lighter, 1/16 of an ounce lighter to be exact. The problem lies in the fact that they all look identical, the only way to tell them apart is to weigh them. Mr Smith knows the correct weight for a box, but how many weighings are required to determine which box contains the counterfeit ones?

a]One weighing is enough. Take one coin from the first box, two from the second and so on. Now when the coins are weighed, the number of 1/16ths light will tell us which box contains the counterfeits. For example if it was box 5, the weighing would be 5/16 too light.