You have 10 stacks of 10 coins. You know how much the coins should weigh. You know all the coins in one stack of ten are exactly a hundredth of an ounce off, making the entire stack of ten coins a tenth of an ounce off. You also know that all the other coins weigh the correct amount. You are allowed to use an extremely accurate digital weighing machine only once.
How do you determine which stack of 10 coins is faulty?
Answer:
One coin from the first stack is placed on the scale along with two coins from the second stack and three coins from the third stack etc…
If the weight is off by one hundredth of an ounce then it is the first stack that is faulty.
If the weight is off by two hundredths of an once then it is the second stack that is faulty.
If the weight is off by three hundredths of an once then it is the third stack that is faulty.
Etc.