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There are 4 pieces on the board, the white and black kings, as well as 2 white bishops (on differently colored squares).

The only way a stalemate occurs is if the black king is not in check, but cannot make a move. (No threefold repetition, timer, etc.) Remaining rules are same as chess.

Assuming perfect play by both players, give the position of the board where white wins, but requires the maximum possible moves to do a checkmate.

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    $\begingroup$ Wikipedia says "With the side with the bishops to move, checkmate can be forced in at most nineteen moves," so there's that $\endgroup$ – Lopsy Apr 9 '15 at 20:11
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    $\begingroup$ Although I answered it, it took only a couple of Google searches; plus this is not on-topic, given that humans cannot reasonably be expected to "solve it",i.e. demonstrate how a given number of moves is the best. Sorry, OP, but -1. $\endgroup$ – Aravind Apr 10 '15 at 6:42
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    $\begingroup$ I'm voting to close this question as off-topic because it might be more at home on Chess.SE. $\endgroup$ – A E Apr 10 '15 at 8:39
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    $\begingroup$ Questions should not be put on hold because they might be more on-topic elsewhere. If they are on-topic here, we should keep them. $\endgroup$ – Aza Apr 11 '15 at 19:30
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    $\begingroup$ @Emrakul The problem is that there is, as far as I can tell, nothing of a puzzle about this, especially given that answers suggest that OP's question in the comment above yours - 'is there a logical approach to achieving the minimal number of moves?' - has a negative answer. I think there are valid chess questions for this site, and valid optimization questions for this site, but this is neither of those. $\endgroup$ – Steven Stadnicki Apr 12 '15 at 3:48
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The answer is 19 moves. The first link in a search for "two bishops longest mate" shows this site: http://www.gilith.com/chess/endgames/kbb_k.html

Checking the Nalimov tablebase on this site: http://chessok.com/?page_id=361 shows that the position indeed requires 19 moves.

The position is: White: Ba4, Bd8, Ka1, Black: Kb4.

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