user30479: 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.

user27379: 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.

30479: <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>
 27379: <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>
