user16577: Including but still obstructed by occupied squares, what is the maximum number of squares on a 16x16 board that 8 queens and 8 nightriders 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.

user16577: 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.


user19415: 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

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...

16577: <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>
 16577: <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.stack.imgur.com/SjLrM.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/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>
 19415: <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.stack.imgur.com/HBf2f.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/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>
