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Box game (Posted on 2005-01-04) Difficulty: 3 of 5
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)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
7 x 7 improvementHugo2005-03-24 17:09:42
re: I surrenderTristan2005-03-23 00:50:51
I surrenderHugo2005-03-22 17:02:11
Solutionthis many?Brandon2005-03-22 15:33:57
re(3): ...and going...Hugo2005-02-09 16:14:50
re(2): ...and going...David Shin2005-02-09 15:13:20
re: ...and going...Hugo2005-02-09 11:08:59
...and going...Tristan2005-02-09 00:00:56
re: Proof of optimality of 15 for 5x5Hugo2005-01-24 18:56:13
Proof of optimality of 15 for 5x5David Shin2005-01-15 18:24:57
Thoughts on the maximumDavid Shin2005-01-15 17:43:33
Towards a Grand Unifying Formula, HELP WANTEDHugo2005-01-14 18:42:22
Solution7 x 7 in 32 movesHugo2005-01-13 13:19:15
Solution7 x 7 in 34 movesHugo2005-01-13 10:02:26
Solution7 x 7 in 35 movesHugo2005-01-13 09:24:31
Solution5 x 5 in 15 movesHugo2005-01-12 13:35:25
Hints/TipsKeep on goingTristan2005-01-11 05:07:51
re: Solution 6x6 gridMilind2005-01-06 07:30:35
A probable solutionMilind2005-01-06 07:16:38
Solution 6x6 gridHugo2005-01-05 19:35:37
No SubjectJer2005-01-05 18:57:12
Question%$! Aahrg FEWEST!Hugo2005-01-05 09:06:27
re: In conclusionSteve Herman2005-01-05 04:59:12
Hints/TipsHow to draw in a commentTristan2005-01-05 01:42:57
Hints/TipsA goal to aim forTristan2005-01-05 01:18:17
In conclusionGamer2005-01-04 21:10:15
SolutionMilind2005-01-04 20:41:01
Some more movesHugo2005-01-04 20:25:18
I will attempt a pictureGamer2005-01-04 20:20:03
EfficiencyGamer2005-01-04 20:19:30
Possible SolutionEric2005-01-04 19:27:45
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