Solution to Riddle of the Week

Solution to Riddle of the Week: The Thief and the Scale

Difficulty level: Moderate

Michael Stillwell
 
By Jay Bennett

This one is tricky, so don't feel bad about stepping away from it for a while to ponder. You can revisit the question and a hint here, so spend a little time thinking about how you could figure out exactly what you want to know—which sack has gold coins—by combining coins from multiple sacks and weighing them.

SOLUTION

Label the sacks 1 to 100, and take a number of coins out of each sack equal to the number on the label. So take 1 coin out of the first sack, 2 coins out of the second sack, and so on up to 100. Weigh all these coins together on the scale.

If all the coins weighed exactly 1 ounce, then you would get 5050 ounces. (You can crank this out on a calculator, or use this math equation to quickly calculate your answer: 100 x 101 / 2 = 5050.) But the gold coins weigh 1.01 ounces. So, if you weigh your pile of coins and get 5050.01 ounces, then the gold coins are in the sack labeled 1. If you get 5050.42 ounces, the gold coins are in the sack labeled 42. If you happen to get 5051 ounces, the gold coins are in the sack labeled 100.

Note: For a quick getaway, you might want to keep all the coins from separate sacks in different piles so you can immediately grab the ones you know are gold, throw them in with the rest of the gold coins, and flee.