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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 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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