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The Fake Coins is a puzzle in Professor Layton and the Diabolical Box.

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




Click a Tab to reveal the Hint.

US Version

The bag of fake coins contains ONLY fake coins, each of them one unit lighter than a real coin. So you could take one coin out of each bag and weigh them each in turn, using the scale five times.

But that wouldn't make for a very interesting puzzle, would it?

UK Version

The bag of fake coins contains only fake coins, each of them one gram lighter than a real coin. So, you could take one coin out of each bag and weigh them each in turn, using the scale five times.

But that wouldn't make for a very interesting puzzle, would it?

US Version

Think about how to accomplish your goal in less than five weighings. If you tried to weigh all the bags at once, you would go over the scale's measuring capacity.

UK Version

Think about how to accomplish your goal in fewer than five weighings. If you tried to weigh all the bags at once, you would go over the scale's measuring capacity.

US Version

Hint Two had the idea of weighing all the bags at once. There are 10 10-unit coins in each of the five bags, for a total of 500 units. But one bag contains fake coins, so the weight is actually less than that.

Perhaps the key to solving this really is to weigh all the bags at once, in a sense?

UK Version

Hint 2 had the idea of weighing all the bags at once. There are 10 10-gram coins in each of the five bags, for a total of 500 grams. But one bag contains fake coins, so the weight is actually less than that.

Perhaps the key to solving this really is to weigh all the bags at once, in a sense?


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.

DB119S

A big thanks to http://professorlayton2walkthrough.blogspot.com

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