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?

The way to do this problem is realize that every possible box can only have 2 possible lines of that box. However, boxes share lines, so coordinating among boxes is important. The most efficient way would be to (if possible) save all the empty sides on the outside where they would only be used once. Since half of the possible lines must be empty lines (counting duplicates from two boxes as two lines) then the amount of time they are counted once is the most possible.

 

Posted by Gamer on 2005-01-04 20:19:30