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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: 2.6667 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): ...and going... | Comment 26 of 32 |
(In reply to re: ...and going... by Hugo)

I disagree with having Tristan tell us the number - let's try to find it ourselves.

By the way, Hugo, could you post your diagram for your latest 6x6 solution?  I'll try to prove optimality.


  Posted by David Shin on 2005-02-09 15:13:20
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