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?

(In reply to re(2): ...and going... by David Shin)

Well, maybe you are right David, maybe its better that Tristan doesn't post the targets.  On the other hand, if it wasn't for your proof on the 5x5 grid, I was still trying to improve it.

Here is the 6x6 solution, maybe on the left
there is improvement possible (Overkill)

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Posted by Hugo on 2005-02-09 16:14:50