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How Many Friends? is a puzzle in Professor Layton and the Last Specter.

Puzzle

US Version

A girl is having some friends from school over for a party and wants to share her special chocolates with them. If she gives them out so that everyone has three chocolates each, there will be six left over. However, if she tries to give everyone five chocolates each, she'll be short by six chocolates.

How many friends are coming to her party?

UK Version

A girl is having some friends from school round for a party and wants to share her special chocolates with them. If she shares them out so that everyone has three chocolates each, there will be six left over. However, if she tries to give everyone five chocolates each, she'll be short by six chocolates.

How many friends are coming to her party?

Hints




Click a Tab to reveal the Hint.

US Version

For these kinds of problems, you need to make some equations. Including the girl, the number of people at the party will be A. Then, if each person gets three chocolates and six are left over, the total number of chocolates can be expressed as 3A + 6.

UK Version

For these kinds of problems you need to make some equations. Including the girl, the number of people at the party will be A. Then, if each person gets three chocolates and six are left over, the total number of chocolates can be expressed as 3A + 6.

US Version

It's not possible for all guests to be given five chocolates, because the girl is short by six. This means that the total number of chocolates can be expressed as 5A - 6.

Since both this expression and the one from Hint 1 represent the number of chocolates, we can say:
3A + 6 = 5A - 6

Solve this equation to find A.

UK Version

It's not possible for all guests to be given five chocolates because the girl is short by six. This means that the total number of chocolates can be expressed as 5A - 6.

Since both this expression and the one from Hint 1 represent the number of chocolates, we can say:
3A + 6 = 5A - 6

Solve this equation to find A.

US Version

5A - 3A = 6 + 6
2A = 12
A = 6

The number of people at the party, including the little girl, will be six.

UK Version

3A + 6 = 5A - 6
5A - 3A = 6 + 6
2A = 12
A = 6

The total number of people at the party, including the little girl, will be six.

US Version

If you thought the answer was six, you'll have to think again. Reread the question. It asks for how many friends will come to the party.

That means you have to take the little girl away from the total. The answer is six people minus one.

UK Version

If you thought that the answer was six, then you'll have to think again. Read the question again. It asks for how many friends will come to the party.

That means you have to take the little girl hosting the party away from the total. The answer is 6 - 1 people.


Solution

Incorrect

US Version

Too bad!

Try turning some of the numbers you've been given into equations.

UK Version

Bad luck.

Try turning some of the numbers you've been given into equations.

Correct

Correct!

The answer is five friends.

Apart from the girl herself, there will be five other people at the party.

LS097S

A big thanks to http://professorlayton4walkthrough.blogspot.com

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