## Wednesday, July 16, 2008

### Diffferent Type of Game

In Greenwich Village, tic-tac-toe is played in an atypical way. At each turn a player marks as many squares as he wishes provided they are in the same vertical or horizontal row (they need not be adjacent). The winner is the one who marks the last square.

Which player has the advantage, and what strategy should he employ?

1. The first player has the advantage as they can take all but TWO squares which are in no line to each-other (diagonal or straight)

May looks something like:
x|x|
x|x|x
x| |x

2. Sorry; disregard the above answer. I read the question wrong. *oops*.

3. If the 1st player marks 1 square, the 2nd marks two to form a connected right angle. If instead he marks 2 or 3 squares, the 2nd player marks as many as necessary to complete either an L or a T of 5 squares. In either occasion, the 2nd player wins.

4. Fancy a game Mike?? I'll go first -
| |
|x|
| |

5. I get the feeling this is going to be an object lesson.

And since I'm thinking about it, I think I know what you're getting at. I messed up. If you start off with just one. In that case, marking two O's won't cut it. Instead I'll mark three.

| |o
|x|o
| |o

Thanks for pointing this out. I love it when people really think about my answers!

What about the possibility of starting with three X's?

x| |
x| |
x| |

Is there any way for player two to win?

6. I can give it a go

x| |
x|o|o
x| |

7. x|x|x
x|o|o
x| |

8. x|x|x
x|o|o
x|o|o

So player 2 will always win (if played properly)!

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