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?

When forming 2 squares in the 5 dot grid, you can get up to 24 moves, for the 7 dot grid it would be 48 moves.  The 6 dot solution would be a 5 dot grid, with two  moves sticking out of each corner and one move in the mioddle of each side, giving 36 moves.

I believe there are better solutions possible.

Posted by Hugo on 2005-01-04 20:25:18