Fake coins

[kate]

We have 10 bags with coins which are looking the same. One of the bags contains only fake coins. The coins in the other bags are original. The fake coins' weight is 4 grams and the original coins' weight is 5 grams. You have a scale which measures in grams. How can you guess which is the bag with the fake coins with only one measurement with the scale.

[Fed_BG]

So we construct a set of coins the following way: we take 1 coin trom the first bag, 2 from the second and so on. If all the bags were with origin coins we would have a total weight of (1+2+...+10)*5 = 275 grams. The actual weight will differs from the "perfect" weight with exactly the count of fake coins in the set (5-4=1 gram difference), but respectively the number of the bag with fake coins.