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Bottle Game is a puzzle in Professor Layton and the Last Specter.

## Puzzle

US Version

The hotel owner, Joseph, has challenged the professor to a little game.

There are 15 empty bottles on the counter. The players take turns removing one, two, or three bottles at a time. Whoever takes the last bottle loses the game.

Layton is going first. Can you help him win?

UK Version

The owner of the hotel, Joe, has challenged you to a little game.

There are 15 empty bottles on the counter. The players take turns removing one, two or three bottles at a time. Whoever takes the last bottle loses the game.

Layton is going first. Can you help him win?

## Hints

Click a Tab to reveal the Hint.

Experiment by taking different numbers of bottles. Can you make out any significant patterns?

It is possible for the player who goes first to win this game every time.

You need to be sure to leave only one bottle on your last turn. Think about how many bottles you would need to leave on the turn before last to make that possible.

US Version

If you can arrange it so that there are five bottles left before one of your opponent's turns, you can win. So how many bottles would you need to leave on the turn before that?

Just work your way backward until you know how many bottles you need to leave on the counter after your first turn.

UK Version

If you can arrange it so that there are five bottles left before one of your opponent's turns, you can win. So, how many bottles would you need to leave on the turn before that?

Just work your way backwards until you know how many bottles you need to leave on the counter after your first turn.

US Version

On your first turn, you should take two bottles, leaving 13. The number of bottles you should leave at the end of each turn is:
1st turn: 13 bottles
2nd turn: ? bottles
3rd turn: 5 bottles
4th turn : 1 bottle

Just work out how many bottles you should leave at the end of your second turn!

UK Version

On your first turn, you should take two bottles, leaving 13. The number of bottles you should leave at the end of each turn is as follows:

1st turn: 13 bottles
2nd turn: ? bottles
3rd turn: 5 bottles
4th turn: 1 bottle

Just work out how many bottles to leave at the end of your second turn!

## Solution

### Correct

Well done!

US Version

It's important to take two bottles on your first turn. Then if you leave 13 bottles, then 9, then 5, and then finally 1 bottle, you will win.

UK Version

It's important to take two bottles on your first turn, leaving 13. Then if you leave nine bottles, then five and finally one bottle, you'll win.

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