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?

I hate to comment too much on my own problem, but I'd also like to post the solution to this eventually.  The posted solutions for the 7x7 grid have not yet reached my solution.

Basically, what I'm saying, is that this puzzle currently belongs the category of "actually unsolved puzzles" rather than that much larger category of "solved puzzles without official solutions".

I haven't been able to prove my solution, perhaps someone might even improve upon my solution, though I think it unlikely.

But don't worry about solving this puzzle as soon as possible.  Puzzle on Perplexus are meant to be fun, not work!

Posted by Tristan on 2005-02-09 00:00:56