16 Aug '08 16:34

Connect is a pencil and paper game, played between two players (I'll call them red and blue) on slightly out-of-phase rectangular grids, like this:

http://img390.imageshack.us/img390/9779/grid1nh2.jpg

The red player only uses the red dots, and the blue player only uses the blue dots. They take it in turns to draw a line between any two of their dots that are one space apart, so if blue goes, then red, then blue again, you might get a grid that looks like this:

http://img516.imageshack.us/img516/4074/grid2ud3.jpg

The aim for blue is to draw a line from left to right. The aim for red is to draw a line from top to bottom. In the following game, red has won:

http://img141.imageshack.us/img141/1531/grid3te6.jpg

Firstly, this is a brilliant game and you will have fun playing it without knowing the solution.

Secondly, there is a 100% winning strategy for the first player. What is it? And can you prove it wins? Including winning on bigger boards?

http://img390.imageshack.us/img390/9779/grid1nh2.jpg

The red player only uses the red dots, and the blue player only uses the blue dots. They take it in turns to draw a line between any two of their dots that are one space apart, so if blue goes, then red, then blue again, you might get a grid that looks like this:

http://img516.imageshack.us/img516/4074/grid2ud3.jpg

The aim for blue is to draw a line from left to right. The aim for red is to draw a line from top to bottom. In the following game, red has won:

http://img141.imageshack.us/img141/1531/grid3te6.jpg

Firstly, this is a brilliant game and you will have fun playing it without knowing the solution.

Secondly, there is a 100% winning strategy for the first player. What is it? And can you prove it wins? Including winning on bigger boards?