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Puzzle
- US Version
There are 10 coins in each of the five bags below. One of these bags is filled with fake coins that are lighter than the real ones. A real coin weighs 10 units, but a fake coin is one unit lighter. If you're using a scale that can register up to 200 units, what is the fewest number of times you could use the scale to find the one bag filled with fake coins?
- UK Version
There are 10 coins in each of the five bags below. One of these bags is filled with fake coins that are lighter than the real ones. A real coin weighs 10 grams, but a fake coin is one gram lighter. If you're using a scale that can register up to 200 grams, what is the fewest number of times you could use the scale to find the one bag filled with fake coins?
Hints
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Solution
Incorrect
Too bad!
- US Version
Stick with it until you figure it out!
- UK Version
Stick with it until you work it out!
Correct
You got it!
You only need to use the scale once. From every bag, remove the number of coins indicated by the bag's number. Then you just weigh these 15 coins once.
- US Version
If all of the coins were real, their combined weight would be 150 units, but you'll end up with a weight less than this. The difference between this actual weight and 150 units corresponds to the number on the bag of fake coins.
- UK Version
If all of the coins were real, their combined weight would be 150 grams, but you'll end up with a weight less than this. The difference between this actual weight and 150 grams corresponds to the number on the bag of fake coins.
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