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
In conclusion by Gamer)
I think you are correct, Gamer, except for being a little dsylexic.
For n ODD, you can have the entire perimeter comprised of empty segments. So this
means you only use (n-1)(n-1) segments because half the outside isn't
used up with segments.
For n EVEN, the best you can do is (n)(n-1).
I'm sure that's what you meant, because you seem to have a great handle on this problem. Nicely done!
re: In conclusion
