My friend and I used to play a simple game. An abitrarily large array of dots was drawn on paper, and we took turns connecting adjacent dots vertically or horizontally. Whenever a box connecting four adjacent dots was made, the player who finished it got an extra turn and a point. When all possible lines were drawn, the game ended and the one with the most points won.

My friend and I were both horrible at this game; we both used the same ineffective strategy. On each of our turns, when possible, we would always make a move that would not allow the other player to make a box the next turn.

Using this strategy and 25 dots in a 5x5 grid, what is the fewest number of moves possible before someone has to let the other player score? What if we use 36 dots in a 6x6 grid? And 49 dots in a 7x7 grid?

Thanks Jer, I now understand what the fewest moves mean.

Then I have a solution  for the 6 x 6 grid at 22 moves:

_ | _ _ _ | _
  |   _   |
  |  |    | 
_ | _ _ _ | _
  |       |

The above solution is wrong, as Milind says 
in a further posting.  It indeed lacks 4 lines in
the perimeter. 

Edited on January 6, 2005, 8:29 am

Posted by Hugo on 2005-01-05 19:35:37