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.
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: