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Roberto: Thank you for explaining your mathematical excitement over the very interesting problem. I solved the problem in a matter of a minute or two. But I did not use math (at least not a a concious level). I had a strong hunch that a central pawn would be best to isolate 2 pawns on the rank, and then 2 on the file... I believed that the 'knight move' pattern optimized Queen placements for this problem... the Knight pattern is certainly abundant in the solution and I think that a mathematical solution should somehow incorporate the 'knight move' aspect of Queen placement. Best regards, Gary