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?

Trying to improve my 32 moves solution, I always 
ended up in the same 32 move solution, so I 
started from scratch.  I hope that Tristan 
didn't do better then 31, because I feel that I 
am now one of the worlds leading experts in 
the box game.
Here's the solution:
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Posted by Hugo on 2005-03-24 17:09:42