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 Box game (Posted on 2005-01-04)
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?

 See The Solution Submitted by Tristan Rating: 3.5000 (4 votes)

 Subject Author Date 7 x 7 improvement Hugo 2005-03-24 17:09:42 re: I surrender Tristan 2005-03-23 00:50:51 I surrender Hugo 2005-03-22 17:02:11 this many? Brandon 2005-03-22 15:33:57 re(3): ...and going... Hugo 2005-02-09 16:14:50 re(2): ...and going... David Shin 2005-02-09 15:13:20 re: ...and going... Hugo 2005-02-09 11:08:59 ...and going... Tristan 2005-02-09 00:00:56 re: Proof of optimality of 15 for 5x5 Hugo 2005-01-24 18:56:13 Proof of optimality of 15 for 5x5 David Shin 2005-01-15 18:24:57 Thoughts on the maximum David Shin 2005-01-15 17:43:33 Towards a Grand Unifying Formula, HELP WANTED Hugo 2005-01-14 18:42:22 7 x 7 in 32 moves Hugo 2005-01-13 13:19:15 7 x 7 in 34 moves Hugo 2005-01-13 10:02:26 7 x 7 in 35 moves Hugo 2005-01-13 09:24:31 5 x 5 in 15 moves Hugo 2005-01-12 13:35:25 Keep on going Tristan 2005-01-11 05:07:51 re: Solution 6x6 grid Milind 2005-01-06 07:30:35 A probable solution Milind 2005-01-06 07:16:38 Solution 6x6 grid Hugo 2005-01-05 19:35:37 No Subject Jer 2005-01-05 18:57:12 %\$! Aahrg FEWEST! Hugo 2005-01-05 09:06:27 re: In conclusion Steve Herman 2005-01-05 04:59:12 How to draw in a comment Tristan 2005-01-05 01:42:57 A goal to aim for Tristan 2005-01-05 01:18:17 In conclusion Gamer 2005-01-04 21:10:15 Solution Milind 2005-01-04 20:41:01 Some more moves Hugo 2005-01-04 20:25:18 I will attempt a picture Gamer 2005-01-04 20:20:03 Efficiency Gamer 2005-01-04 20:19:30 Possible Solution Eric 2005-01-04 19:27:45

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