Answers.Body: <p>If the two bishops travel on the same color squares, then all 64 squares can be covered by the eight pieces. However, if the bishops must travel on opposite colors, then the maximum number of squares that can be covered is 63. See <a href="http://tinyurl.com/3fh5k7rw" rel="noreferrer"><em>Eight Pieces Cannot Cover a Chess Board</em></a> for a complete discussion.</p>
  <p>Here is one of several possible 63 square solutions for opposite-color bishops:</p>
  <pre><code>[fen &quot;8/3nb2r/3n4/8/r7/1b6/2q2k2/8 w - - 1 1&quot;]
  </code></pre>
  <p>The d7 knight is not under attack.</p>
  <p>Here is one of the three solutions to covering all squares with same-color bishops:</p>
  <pre><code>[fen &quot;r7/8/2b2k2/3n4/4n3/2q2b2/8/7r w - - 1 1&quot;]
  </code></pre>
  <p>Citation:</p>
  <p>Robison, Arch D., Brian J. Hafner, and S. S. Skiena. &quot;Computer Games: Eight Pieces Cannot Cover a Chess Board.&quot; The Computer Journal 32, no. 6 (1989): 567-570.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-12-07T14:11:49.283Z
Answers.Text: In the same-color bishop solution, I like how the queen isn't any more useful than the king in providing coverage.
Answers.UserDisplayName: Engineer Toast
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-12-07T14:26:37.457Z
Answers.Text: @EngineerToast Almost. The queen covers the bishops and the king, the king doesn't.
Answers.UserDisplayName: Jens
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-12-07T14:27:34.497Z
Answers.Text: @Jens Ah! Of course. I completely neglected coverage of the occupied squares.
Answers.UserDisplayName: Engineer Toast
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-12-07T17:30:51.300Z
Answers.Text: The king is also covered by the knights, so that doesn't count. But yes, the queen is the only piece covering the bishops.
Answers.UserDisplayName: Deduplicator
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-12-07T01:12:36.720Z
Answers.LastActivityDate: 2021-12-07T12:43:41.080Z
Answers.LastEditDate: 2021-12-07T12:43:41.080Z
Answers.UserDisplayName: Pete Klimek
Body: <p>Can you place the eight (non-pawn) pieces of one color on an otherwise empty chess board, such that every square (including the squares that pieces are on), is attacked / defended?</p>
  <p>This is a problem that I wrestled with in high school and I'm not sure I've seen it discussed anywhere else.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-12-06T23:22:05.197Z
Comments.Text: If a piece is on a square, does that square count as being attacked? Or does another, separate piece, have to be attacking it?
Comments.UserDisplayName: odinchess.com
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-12-06T23:42:32.770Z
Comments.Text: It is impossible because before that happens it will be checkmate or stalemate.
Comments.UserDisplayName: Varun W.
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-12-06T23:49:14.877Z
Comments.Text: He's just asking if theoretically you can place the 8 pieces on the board to attack each square. Not a real chess game.
Comments.UserDisplayName: odinchess.com
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-12-07T08:23:20.157Z
Comments.Text: This might be better suited to puzzling.stackexchange.com than to chess.
Comments.UserDisplayName: Guntram Blohm
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-12-07T16:09:18.983Z
Comments.Text: This would be trivial with eight queens or eight rooks, no?
Comments.UserDisplayName: Hearth
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-12-07T18:57:33.553Z
Comments.Text: To be clear, you can use 8 queens if you wanted? Or is it just with the starting pieces (sans pawns)?
Comments.UserDisplayName: BruceWayne
Tags: <problems><pieces><chessboards>
Title: Can all 64 squares be attacked or defended by the eight pieces?
ThreadText: # Can all 64 squares be attacked or defended by the eight pieces?
  
  (Asked by: username_0 on 2021-12-06)
  
  Can you place the eight (non-pawn) pieces of one color on an otherwise empty chess board, such that every square (including the squares that pieces are on), is attacked / defended?
  
  This is a problem that I wrestled with in high school and I'm not sure I've seen it discussed anywhere else.
  
  **Tags:** problems, pieces, chessboards
  
  > **Comments:**
  > **username_1**: If a piece is on a square, does that square count as being attacked? Or does another, separate piece, have to be attacking it?  
  > **username_2**: It is impossible because before that happens it will be checkmate or stalemate.  
  > **username_1**: He's just asking if theoretically you can place the 8 pieces on the board to attack each square. Not a real chess game.  
  > **username_3**: This might be better suited to puzzling.stackexchange.com than to chess.  
  > **username_4**: This would be trivial with eight queens or eight rooks, no?  
  > **username_5**: To be clear, you can use 8 queens if you wanted? Or is it just with the starting pieces (sans pawns)?  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_6 on 2021-12-07. Score: 54
  
  If the two bishops travel on the same color squares, then all 64 squares can be covered by the eight pieces. However, if the bishops must travel on opposite colors, then the maximum number of squares that can be covered is 63. See Eight Pieces Cannot Cover a Chess Board for a complete discussion.
  Here is one of several possible 63 square solutions for opposite-color bishops:
  [fen "8/3nb2r/3n4/8/r7/1b6/2q2k2/8 w - - 1 1"]
  
  The d7 knight is not under attack.
  Here is one of the three solutions to covering all squares with same-color bishops:
  [fen "r7/8/2b2k2/3n4/4n3/2q2b2/8/7r w - - 1 1"]
  
  Citation:
  Robison, Arch D., Brian J. Hafner, and S. S. Skiena. "Computer Games: Eight Pieces Cannot Cover a Chess Board." The Computer Journal 32, no. 6 (1989): 567-570.
  
  > **Comments:**
  > **username_7**: In the same-color bishop solution, I like how the queen isn't any more useful than the king in providing coverage.  
  > **username_8**: @EngineerToast Almost. The queen covers the bishops and the king, the king doesn't.  
  > **username_7**: @username_8 Ah! Of course. I completely neglected coverage of the occupied squares.  
  > **username_9**: The king is also covered by the knights, so that doesn't count. But yes, the queen is the only piece covering the bishops.  
  
  ---
  
  