Riddle of the Week

Riddle of the Week: The Thief and the Scale

Difficulty level: Moderate

Michael Stillwell
 
By Jay Bennett

This week's riddle requires a clever bit of thinking and a little bit of math. At first it may seem impossible, but don't give up.

PROBLEM

You're a thief, and you've managed to break into the vault of an ancient bank filled with 100 sacks of coins. One of the sacks contains gold coins, while the other 99 are filled with counterfeit gold coins. You cannot tell the difference between the gold coins and the fakes by handling the coins, looking at them, biting them, or testing them.

The fake coins weigh exactly 1 ounce each, while the real gold coins weigh 1.01 ounces. There is a large scale with enough room for all the sacks in the vault, but as soon as you weigh something it will trigger an alarm, so you can use the scale just once before you must flee the vault.

How can you figure out which sack of coins contains the real gold by only weighing something on the scale once?

Note: The scale tells you the exact weight of whatever you put on it, it is not a balance scale.

HINT

You might want to consider labeling the sacks. And remember, you can take coins out of the sacks and weigh a combination of them. Once you come up with your strategy, you will need to make a calculation