<PRE><B>Question 1208189</B>
&lt;pre&gt;
Here is my approach. In the diagram below, I have placed the number of
forbidden places for the second queen in the event that we choose to put the
first queen in that space. I will explain below, where I got them. 

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&lt;font color=&quot;red&quot;&gt;&lt;b&gt;21&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;green&quot;&gt;&lt;b&gt;23&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;green&quot;&gt;&lt;b&gt;23&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;green&quot;&gt;&lt;b&gt;23&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;green&quot;&gt;&lt;b&gt;23&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;green&quot;&gt;&lt;b&gt;23&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;green&quot;&gt;&lt;b&gt;23&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;21&lt;/b&gt;&lt;/font&gt;
&lt;font color=&quot;red&quot;&gt;&lt;b&gt;21&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;green&quot;&gt;&lt;b&gt;23&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;25&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;25&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;25&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;25&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;green&quot;&gt;&lt;b&gt;23&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;21&lt;/b&gt;&lt;/font&gt;
&lt;font color=&quot;red&quot;&gt;&lt;b&gt;21&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;green&quot;&gt;&lt;b&gt;23&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;25&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;green&quot;&gt;&lt;b&gt;27&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;green&quot;&gt;&lt;b&gt;27&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;25&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;green&quot;&gt;&lt;b&gt;23&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;21&lt;/b&gt;&lt;/font&gt;
&lt;font color=&quot;red&quot;&gt;&lt;b&gt;21&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;green&quot;&gt;&lt;b&gt;23&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;25&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;green&quot;&gt;&lt;b&gt;27&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;green&quot;&gt;&lt;b&gt;27&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;25&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;green&quot;&gt;&lt;b&gt;23&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;21&lt;/b&gt;&lt;/font&gt;
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&lt;font color=&quot;red&quot;&gt;&lt;b&gt;21&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;21&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;21&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;21&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;21&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;21&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;21&lt;/b&gt;&lt;/font&gt; &lt;font color=&quot;red&quot;&gt;&lt;b&gt;21&lt;/b&gt;&lt;/font&gt;

Case 1. We put a queen on the edge of the outer 8x8 square.

If we put a queen on the edge of the outer 8x8 square, there are 21 
forbidden places for the other queen, 7 on the same row, 7 on the same
column, and 7 on the same diagonal.  That&#39;s 21 forbidden places.  That&#39;s
why I put 21&#39;s around the outer edge of the 8x8 square and colored them
red. So for each of the 28 places we choose for one queen, there are 
63-21=42 safe places to put the other queen. That&#39;s (28)(42)=1176.

Case 2. We put a queen on the edge of the inner 6x6 square.

If we put a queen on the edge of the inner 6x6 square, there are 23 
forbidden places for the other queen, 7 on the same row, 7 on the same
column, and 9 on the same diagonal, since we pick up 2 more forbidden
places on the diagonals. That&#39;s 23 forbidden places.  That&#39;s
why I put 23&#39;s around the edge of the 6x6 square and colored them green.
So for each of the 20 places we choose for one queen, there are 63-23=40 
safe places to put the other queen. That&#39;s (20)(40)=800. 

Case 3. We put a queen on the edge of the inner 4x4 square.

If we put a queen on the edge of the inner 4x4 square, there are 25 
forbidden places for the other queen, 7 on the same row, 7 on the same
column, and 11 on the same diagonal, since we pick up 2 more forbidden
places on the diagonals. That&#39;s 25 forbidden places.  That&#39;s
why I put 25&#39;s around the edge of the 4x4 square and colored them red.
So for each of the 12 places we choose for one queen, there are 63-25=38 
safe places to put the other queen. That&#39;s (12)(38)=456. 

Case 4. We put a queen on the center 2x2 square.

If we put a queen on the edge of the center 2x2 square, there are 27 
forbidden places for the other queen, 7 on the same row, 7 on the same
column, and 13 on the same diagonal, since we pick up 2 more forbidden
places on the diagonals. That&#39;s 27 forbidden places.  That&#39;s
why I put 27&#39;s for the center 2x2 square and colored them green.
So for each of the 4 places we choose for one queen, there are 63-27=36 
safe places to put the other queen. That&#39;s (4)(36)=144.

Total for the 4 cases = 1176 + 800 + 456 + 144 = 2576.

Since we can swap the queens, we take half, and get 1288.

Edwin&lt;/pre&gt;</PRE>