There are 10 identical bags of coins. Each bag contains 100 coins. In one bag the coins are silver, in the others gold. All the coins are identical. A gold coin weigh 10 grams and a silver coin weigh a gram less.
Given a regular measurement scale, how would you determine in one weighing which bag does not have the gold coins?
Take one coin from the first bag, two from the second, three from the third, and so on, until you have ten coins from the tenth.
Then stack and weigh the 55 coins (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10). Since each gold coin weigh ten grams, if all had been gold, the scale would have read 550 grams.
The amount by which the weight was too light indicated the number of silver coins and the number of the the silver bag. For instance, if the weight was 543 grams, it would indicate that 7 silver coins (550 – 543 = 7) had been weighed with the gold coins and that the rest of the silver coins were in the seventh bag.