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Assuming you have a board, and you attempt to play with your opponent such as that you try to avoid taking each other's pieces. Is there going to be a limit in the number of moves after which you can't avoid taking over another piece?

(Assuming of course that at least one player doesn't use a repetitive pattern movement that avoids contact from the enemy)

I was trying to find a solution myself but didn't know how to approach this problem.

iordanis
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You say that one player is not allowed to use a repetitive pattern.

In that case, since there are a finite number of moves to be made and a finite number of board configurations to achieve, if the board configuration must be new after each move (since otherwise, that would mean a repeat of a move the player already did), at some point, one player will have to lose a piece.

5xum
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  • so would the maximum number of moves be the number of configurations of the board? – iordanis Oct 01 '14 at 06:32
  • @μακακας Far from it, since most configurations of the board contain less than all of the pieces. The number would still be pretty big, if you ask me, but I don't think it is computable, since the space you need to search is enormous and I see no way to avoid an exhaustive search... – 5xum Oct 01 '14 at 06:34
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    Ok do you have an idea about the minimum number of moves after which you will be forced to eat another piece? – iordanis Oct 01 '14 at 06:45
  • @μακακας I already told you, I don't think this number is computable in reasonable time. – 5xum Oct 01 '14 at 06:47
  • It is certainly computable (in the technical meaning of that word), just not possible to compute in practice. – Robert Israel Oct 01 '14 at 06:49