maximum number of turns Dots and Boxes
4 replies. Last post: 2005-12-03
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4 replies. Last post: 2005-12-03
Reply to this topic Return to forummaybe is a well known question, but what is the maximum numbers of turns without making a complete square?
As I said in another thread:
I have not found any games here that lasted more than 42 moves. Maybe it is the maximum for “intelligent” play. The theoretical upper bound, assuming the players are not actually trying to win, seems to be 48 moves: There are 60 edges in total, and at least 13 of them must complete at least one box, giving a reduction of 12 in the number of moves. 13 comes from the fact that an edge can complete at most 2 boxes, and there are 25 boxes to be completed, so we get the smallest integer greater than or equal to 25/2.
Umm so the answer to your actual question is 47 (stake out 11 dominoes and one triomino).
Two games with 44 moves: <a href=‘http://www.littlegolem.net/jsp/game/game.jsp?gid=364998’>#364998
, <a href=‘http://www.littlegolem.net/jsp/game/game.jsp?gid=323023’>#323023