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?
1) For 25 dots in a 5x5 grid, the fewest number of moves possible before someone has to let the other player score is 15.
2) For 36 dots in a 6x6 grid, the fewest number of moves possible before someone has to let the other player score is 23.
3) For 49 dots in a 7x7 grod, the fewest number of moves possible before someone has to let the other player score is 31.
Edited on August 4, 2023, 1:35 pm
Puzzle Thoughts
