Math puzzle involving the game Connect 4

[Blue_Jaunte]

I was playing Connect 4 the other day, and I started to wonder how you could fill the board entirely without connecting 4. I haven't tackled the problem so I don't know if it's of general interest at all, or if it yields any interesting results...but I thought I'd share it with you all.

Perhaps you can think of more interesting problems with this game (since, now that I think about it, I'm basically asking all the ways you can fill a slightly larger tic-tac-toe board)?

For those who don't know what connect 4 is:
http://www.oldeducator.com/connect4.jpg
2 players take turns dropping their checkers into the board. The goal is to make 4 of your pieces connect in any direction (vertically, horizontally, diagonally).

 

[DavidSnider]

http://www.connectfour.net/Files/connect4.pdf

This paper shows a strategy to force a draw or a win for white.

 

[n1person]

I think perhaps the simplest pattern for not connecting for is where you make a column 2 or 3 thick, alternating one way, then the adjacent column you alternate it the other way.

00XX00XX
XX00XX00
00XX00XX
XX00XX00

etc for the entire board (it if has odd dimensions then you can just have it one thick at the end

it sort of reminds me of the Four color map problem...

 

[Blue_Jaunte]

Wow, thanks guys. I should've known that someone would be on the case. DavidSnider, i noticed that the paper is a "Master's Thesis" from a university in Amsterdam. Is that comparable to a Master's thesis in the states or PhD? I'm just wondering because of the length.