Stupid cheater

Here's a simple logic puzzle I picked up randomly on the Net. There once a sultan who asked his 10 goldsmiths to make 10 gold coins each. Each coin was to have exactly 10 grams of gold exactly. But one of them was a bad goldsmith. He decided to make all of his coins with only 9 grams of gold each. The sultan caught wind of the plot, and knew that there was one bad goldsmith. So on the day when all the goldsmiths presented their work before the sultan, the sultan took some gold coins from each goldsmith. Then he weighed them on the scale. With that, he identified the cheating goldsmith. How did he accomplish that?







Simple. The sultan needs a way to label each of his goldsmith, goldsmith 1, goldsmith 2, etc. If the bad guy contributes 1 coin, the total weight would be 1 gram less. If he contributes 2 coins, the total weight would be 2 grams less. Combining these 2, gives us a method. Get one goldsmith to contribute 1 coin, the second to contribute to contribute to 2, and so on. If none of them cheated, then the total weight should be 550 grams. Count the shortfall. If the shortfall is 1 gram, then the goldsmith who only contributed 1 coin is the bad guy. If the shortfall is 10 grams, then the guy who contributed 10 coin is the bad guy.