Body: <p>Let White have the two bishops.  Given any setup, has the maximum number of moves to forced mate been calculated on an nxn board (for large enough n)?  If not, are there any bounds on this number?</p>
  <p>Of course, information on extensions of this problem to say any rectangular board, are also welcome.</p>
  <p>I should note that for a 2xn board checkmate isn't possible.  Also, for m &gt;= 3, with n &gt;= m without loss of generality,  I'm not certain whether forced mate is always possible.  I would say though that it is given m,n sufficiently large though.</p>
  <p>To update let the bishops be on opposite colored squares, of course.</p>
  <p>Update again:  I noticed someone edited the question out.  It isn't meant merely for the 8x8 board, but for any nxn board, where n is any sufficiently large natural number.  I know R&amp;K vs K has been solved in this way for any nxn board.  I'm wondering whether the same has been done for K BB vs. K on any nxn board.  Please watch what you edit next time.  Also, an answer has been accepted to the edited question, not my intended question.</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2016-07-27T12:49:03.397Z
Comments.Text: What do you mean by "without losing generality"?
Comments.UserDisplayName: hkBst
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2016-07-29T00:23:57.637Z
Comments.Text: In this case those words shouldn't have appeared.
Comments.UserDisplayName: Paul Burchett
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-08-30T12:00:14.207Z
Comments.Text: If you look at the edit history, you will see that nobody other than you has ever the edited the question, except for the tags. Since the question didn’t make it clear that you wanted an answer for general n×n, it’s not surprising that the existing answer got marked as accepted.
Comments.UserDisplayName: Stephen
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-08-30T12:49:46.310Z
Comments.Text: I don't remember editing the question out.  It certainly wasn't my intention to edit it out.  Also, it should've been clear that I was talking about a generalization, and not the standard 8x8 board.  I did have the variables m and n in the post, after all.
Comments.UserDisplayName: Paul Burchett
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-03-27T16:32:04.313Z
Comments.Text: It's been five years - so before I put time into this I'd like to know if you are still around and still interested in an answer ;).
Comments.UserDisplayName: Carlo Wood
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-03-27T16:42:38.783Z
Comments.Text: @CarloWood - The results would probably might make for a good math paper somewhere.  You can answer it here, but I'd probably try to publish it if I were you.
Comments.UserDisplayName: Paul Burchett
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-03-27T16:49:21.297Z
Comments.Text: I didn't spend time on it yet; I just thought it would be rather easy to write a program for it (since it only has a few pieces; and no doubt a very repetitive pattern). But if you think it is THAT difficult then I shouldn't waste my time on it ;). I am super busy writing a vulkan engine :/.
Comments.UserDisplayName: Carlo Wood
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-03-27T17:31:09.760Z
Comments.Text: The same problem for k and r versus lone king on a nxn board was published somewhere.  That's what led me to pose this question.  It seems like a fruitful extension.
Comments.UserDisplayName: Paul Burchett
Tags: <checkmate><bishops><mathematics>
Title: Checkmating with two bishops
ThreadText: # Checkmating with two bishops
  
  (Asked by: username_0 on 2016-07-26)
  
  Let White have the two bishops. Given any setup, has the maximum number of moves to forced mate been calculated on an nxn board (for large enough n)? If not, are there any bounds on this number?
  
  Of course, information on extensions of this problem to say any rectangular board, are also welcome.
  
  I should note that for a 2xn board checkmate isn't possible. Also, for m >= 3, with n >= m without loss of generality, I'm not certain whether forced mate is always possible. I would say though that it is given m,n sufficiently large though.
  
  To update let the bishops be on opposite colored squares, of course.
  
  Update again: I noticed someone edited the question out. It isn't meant merely for the 8x8 board, but for any nxn board, where n is any sufficiently large natural number. I know R&K vs K has been solved in this way for any nxn board. I'm wondering whether the same has been done for K BB vs. K on any nxn board. Please watch what you edit next time. Also, an answer has been accepted to the edited question, not my intended question.
  
  **Tags:** checkmate, bishops, mathematics
  
  > **Comments:**
  > **username_1**: What do you mean by "without losing generality"?  
  > **username_0**: In this case those words shouldn't have appeared.  
  > **username_2**: If you look at the edit history, you will see that nobody other than you has ever the edited the question, except for the tags. Since the question didn’t make it clear that you wanted an answer for general n×n, it’s not surprising that the existing answer got marked as accepted.  
  > **username_0**: I don't remember editing the question out.  It certainly wasn't my intention to edit it out.  Also, it should've been clear that I was talking about a generalization, and not the standard 8x8 board.  I did have the variables m and n in the post, after all.  
  > **username_3**: It's been five years - so before I put time into this I'd like to know if you are still around and still interested in an answer ;).  
  > **username_0**: @CarloWood - The results would probably might make for a good math paper somewhere.  You can answer it here, but I'd probably try to publish it if I were you.  
  > **username_3**: I didn't spend time on it yet; I just thought it would be rather easy to write a program for it (since it only has a few pieces; and no doubt a very repetitive pattern). But if you think it is THAT difficult then I shouldn't waste my time on it ;). I am super busy writing a vulkan engine :/.  
  > **username_0**: The same problem for k and r versus lone king on a nxn board was published somewhere.  That's what led me to pose this question.  It seems like a fruitful extension.  
  
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  ## 0 answers
  
  