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SOLUTION_EIGHT

                                             September 12, 2012
                                             September 13, 2013
                                                     
   The puzzle is described in                        
                                        SPOLIERS
        EIGHT_QUEENS 
                                                     
   Here I'm talking about the solutions.             
                                                     
                                                     
   Actually, there are multiple solutions,           
   I have no idea how many.  (In these days          
   drowning in computation, I expect that            
   someone must know, if only by exhausting          
   all permutations.)                                
                                                     
   This particular solution makes sense              
   after you've seen it: there's a way of            
   thinking about knights as "anti-queens":          
                                                                      
   They're the pieces that can move to the nearest                    
   locations that queens can't move to.  The knight is               
   the only piece that can attack a queen without also               
   being threatened by the queen; the knight has the                 
   ability to "sneak up" on even a queen, which is one               
   reason for the effectiveness of the "knight fork"                 
   (moving a knight into position where it attacks two               
   pieces simultaneously, making it impossible to just               
   "run away").                                                      
                                                                     
   The symmetric solution I found is like so:                        
                                                                     
   You arrange the queens in a square, but a square            
   with sides that aren't parallel to the board, so      
   that each queen is (at least) one knight move away    
   from the other.                                       
                                                         
                                                         
       +---+---+---+---+---+---+---+---+                 
       |   |   |   |   | Q |   |   |   |                 
       +---+---+---+---+---+---+---+---+             
       |   |   | Q |   |   |   |   |   |             
       +---+---+---+---+---+---+---+---+             
       | Q |   |   |   |   |   |   |   |             
       +---+---+---+---+---+---+---+---+             
       |   |   |   |   |   |   | q |   |             
       +---+---+---+---+---+---+---+---+             
       |   | Q |   |   |   |   |   |   |             
       +---+---+---+---+---+---+---+---+             
       |   |   |   |   |   |   |   | q |             
       +---+---+---+---+---+---+---+---+             
       |   |   |   |   |   | q |   |   |             
       +---+---+---+---+---+---+---+---+             
       |   |   |   | q |   |   |   |   |           This diagonally twisted
       +---+---+---+---+---+---+---+---+           square of queens can't
                                                   be a perfect square, or
Interestingly (to me) there are two                some would end up
groups of queens that are each placed a            sharing horizontals
night move apart within the group, but             and verticals.  By the
the nearest points of contact of the two           problem statement,
groups are a shifted further away than             each queen must have
that, one horizontal and one vertical.             it's own rank and file.
                                                     
And the two groups are themselves L-shaped,          
suggesting some sort of meta-knight move,          OVER_EIGHT
constructed of 3 knight moves.                       
                                                     
                                                     
                                                     
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