Answers.Body: <p>This is my best attempt thus far, which I believe attacks 236 (all but 20) squares. I used the staircase solution for 8 queens on the central 8x8 region in order to consequentially fully cover the 4 adjacent 8x4 side regions while putting many diagonals through the corner 4x4 regions. Then I placed the nightriders so as to not obstruct any of the queens' lines while also having each nightrider attack 1 unique queen each, by placing them towards the center of the long diagonals still within the corner 4x4 regions.</p>
  
  <p><a href="https://i.sstatic.net/SjLrM.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/SjLrM.png" alt="My personal best attempt at placing 8 queens and 8 nightriders on a 16x16 board so as to attack as many squares as possible"></a></p>
  
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Answers.CreationDate: 2019-11-09T17:57:00.050Z
Answers.Text: I looked at various queen placements and it seems that placing queens such that they don't attack each other produces worse results because it's impossible to cover main diagonals, and a pattern of 4 diagonal squares is not good for knightriders.
Answers.UserDisplayName: Sopel
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-11-09T13:51:20.513Z
Answers.LastActivityDate: 2019-11-09T13:51:20.513Z
Answers.UserDisplayName: RadiantDarkBlaze
Answers.Body: <p>It's possible to attack all squares.</p>
  
  <p>Q - queen</p>
  
  <p>N - nightrider</p>
  
  <p>Yellow background - attacked only by a queen</p>
  
  <p>Red background - attacked only by a nightrider</p>
  
  <p>Orange background - attacked by pieces of both types</p>
  
  <p><a href="https://i.sstatic.net/HBf2f.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/HBf2f.png" alt="enter image description here"></a></p>
  
  <p>Queens are placed such that 5 longest diagonals in each direction are attacked.</p>
  
  <p>This can be done with just 6 queens, so 2 are redundant and result in queens attacking queens by diagonals. So 4 queens are attacked by other queens, 4 are not. I added nightriders on the edge of the board such that the missing squares are also attacked. Placing nightriders on the edge doesn't block any of the queens' attacks.</p>
  
  <p>One can also see that the nightriders attacking queens could be placed in other ways, so there is more than one solution. An interesting question would be-how many?</p>
  
  <p>edit. now correct...</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-11-09T19:20:35.070Z
Answers.Text: I think I see 2 unattacked squares; the red squares at the upper part of the left edge and lower part of the right edge, the nightriders that seem to supposed to be watching them obstructed by the queens at the furthest corners of the central 8x8 region. However, that queen arrangement looks far superior to what I was previously using; and you're right on point with putting the nightriders along the edges. 254/256 is a massive improvement over 236/256, that's enough to make me believe all 256 squares might be possible; and 254/256 is still really impressive even if 256 is impossible after all.
Answers.UserDisplayName: RadiantDarkBlaze
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-11-09T19:49:29.963Z
Answers.Text: You're actually right! I'll look into it later if anything can be done about it. Right now im on mobile
Answers.UserDisplayName: Sopel
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-11-09T19:54:22.700Z
Answers.Text: I thing if you place the knightriders at top middle (one closer to middle) and bottom middle like if they were mirrored horizontally it fizes it
Answers.UserDisplayName: Sopel
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-11-09T17:53:10.523Z
Answers.LastActivityDate: 2019-11-09T22:13:28.830Z
Answers.LastEditDate: 2019-11-09T22:13:28.830Z
Answers.UserDisplayName: Sopel
Body: <p>Including but still obstructed by occupied squares, what is the maximum number of squares on a 16x16 board that 8 queens and 8 <a href="https://en.wikipedia.org/wiki/Nightrider_(chess)" rel="noreferrer">nightriders</a> can collectively attack at least once each? Even if attacking all 256 squares isn't possible, the maximum number still interests me.</p>
  
  <p>I'm unsure what tags to use for this, or if maybe I should've went to the mathematics SE for this one; please suggest additional tags and let me know if this question would better fit the mathematics SE.</p>
  
Tags: <chess-variants><mathematics><unorthodox-pieces>
Title: What is the maximum number of squares 8 queens and 8 nightriders can attack on a 16x16 board?
ThreadText: # What is the maximum number of squares 8 queens and 8 nightriders can attack on a 16x16 board?
  
  (Asked by: username_0 on 2019-11-09)
  
  Including but still obstructed by occupied squares, what is the maximum number of squares on a 16x16 board that 8 queens and 8 [nightriders](https://en.wikipedia.org/wiki/Nightrider_(chess)) can collectively attack at least once each? Even if attacking all 256 squares isn't possible, the maximum number still interests me.
  
  I'm unsure what tags to use for this, or if maybe I should've went to the mathematics SE for this one; please suggest additional tags and let me know if this question would better fit the mathematics SE.
  
  **Tags:** chess-variants, mathematics, unorthodox-pieces
  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_1 on 2019-11-09. Score: 4 | Accepted answer
  
  It's possible to attack all squares.
  
  Q - queen
  
  N - nightrider
  
  Yellow background - attacked only by a queen
  
  Red background - attacked only by a nightrider
  
  Orange background - attacked by pieces of both types
  
  [![enter image description here](https://i.sstatic.net/HBf2f.png)](https://i.sstatic.net/HBf2f.png)
  
  Queens are placed such that 5 longest diagonals in each direction are attacked.
  
  This can be done with just 6 queens, so 2 are redundant and result in queens attacking queens by diagonals. So 4 queens are attacked by other queens, 4 are not. I added nightriders on the edge of the board such that the missing squares are also attacked. Placing nightriders on the edge doesn't block any of the queens' attacks.
  
  One can also see that the nightriders attacking queens could be placed in other ways, so there is more than one solution. An interesting question would be-how many?
  
  edit. now correct...
  
  > **Comments:**
  > **username_0**: I think I see 2 unattacked squares; the red squares at the upper part of the left edge and lower part of the right edge, the nightriders that seem to supposed to be watching them obstructed by the queens at the furthest corners of the central 8x8 region. However, that queen arrangement looks far superior to what I was previously using; and you're right on point with putting the nightriders along the edges. 254/256 is a massive improvement over 236/256, that's enough to make me believe all 256 squares might be possible; and 254/256 is still really impressive even if 256 is impossible after all.  
  > **username_1**: You're actually right! I'll look into it later if anything can be done about it. Right now im on mobile  
  > **username_1**: I thing if you place the knightriders at top middle (one closer to middle) and bottom middle like if they were mirrored horizontally it fizes it  
  
  ---
  
  ### Answer by username_0 on 2019-11-09. Score: 2
  
  This is my best attempt thus far, which I believe attacks 236 (all but 20) squares. I used the staircase solution for 8 queens on the central 8x8 region in order to consequentially fully cover the 4 adjacent 8x4 side regions while putting many diagonals through the corner 4x4 regions. Then I placed the nightriders so as to not obstruct any of the queens' lines while also having each nightrider attack 1 unique queen each, by placing them towards the center of the long diagonals still within the corner 4x4 regions.
  
  [![My personal best attempt at placing 8 queens and 8 nightriders on a 16x16 board so as to attack as many squares as possible](https://i.sstatic.net/SjLrM.png)](https://i.sstatic.net/SjLrM.png)
  
  > **Comments:**
  > **username_1**: I looked at various queen placements and it seems that placing queens such that they don't attack each other produces worse results because it's impossible to cover main diagonals, and a pattern of 4 diagonal squares is not good for knightriders.  
  
  ---
  
  