>be you
>play game with me
>pic related
>we take (alternate) turns colouring the internal dots
>my colour = gray, yours = black
>before starting, a & c are coloured gray, b & d black
>i start
>if i manage to colour in gray a full path from a to c before you colour in black a full path from b to d, i win.
>if you can manage the opposite, you win.
>if one of us gets stuck with no node left to colour without the above two scenarios happening, the game ends in a draw.
Show that this can never end in a draw. Also, is there a way to force win?
>play game with me
>pic related
>we take (alternate) turns colouring the internal dots
>my colour = gray, yours = black
>before starting, a & c are coloured gray, b & d black
>i start
>if i manage to colour in gray a full path from a to c before you colour in black a full path from b to d, i win.
>if you can manage the opposite, you win.
>if one of us gets stuck with no node left to colour without the above two scenarios happening, the game ends in a draw.
Show that this can never end in a draw. Also, is there a way to force win?
