Discrete Peaceful Encampments: 9 queens on a chessboard












3












$begingroup$


Here's a discrete variation of yesterday's puzzle Peaceful Encampments.




You have 8 white queens and 8 black queens. Place all these pieces onto a normal 8x8 chessboard in such a way that no white queen threatens a black queen (nor vice versa).




Or, phrasing the puzzle in a way parallel to Black and white queens on an 8x8 chessboard — changing only one word from that puzzle — I would say:




What is the largest number of queens that can be placed on a regular 8×8 chessboard, if the following rules are met:




  1. A queen can be either black or white, and there can be unequal numbers of each type [but if so, we count the smaller population].

  2. A queen must not be threatened by other queens of a different color.

  3. Queens threaten all squares in the same row, column, or diagonal (as in chess). Also, threats are blocked by other queens [not that this matters].




Can you find a way to place more than 8 queens of each color "peacefully" on an 8x8 chessboard?






geometry chess checkerboard







share|improve this question











$endgroup$












  • $begingroup$
    Based on the rules, why couldn't one place 64 white queens or 64 black queens?
    $endgroup$
    – Jiminion
    4 hours ago






  • 1




    $begingroup$
    @Jiminion: Someone commented the same thing on puzzling.stackexchange.com/questions/28926/… ! :) I've edited that part of the question to reflect that if you place, e.g., 9 white queens and 7 black queens, your score is "7", not "9". And if you place 64 white queens and 0 black queens, your score is "0", not "64".
    $endgroup$
    – Quuxplusone
    3 hours ago


















3












$begingroup$


Here's a discrete variation of yesterday's puzzle Peaceful Encampments.




You have 8 white queens and 8 black queens. Place all these pieces onto a normal 8x8 chessboard in such a way that no white queen threatens a black queen (nor vice versa).




Or, phrasing the puzzle in a way parallel to Black and white queens on an 8x8 chessboard — changing only one word from that puzzle — I would say:




What is the largest number of queens that can be placed on a regular 8×8 chessboard, if the following rules are met:




  1. A queen can be either black or white, and there can be unequal numbers of each type [but if so, we count the smaller population].

  2. A queen must not be threatened by other queens of a different color.

  3. Queens threaten all squares in the same row, column, or diagonal (as in chess). Also, threats are blocked by other queens [not that this matters].




Can you find a way to place more than 8 queens of each color "peacefully" on an 8x8 chessboard?






geometry chess checkerboard







share|improve this question











$endgroup$












  • $begingroup$
    Based on the rules, why couldn't one place 64 white queens or 64 black queens?
    $endgroup$
    – Jiminion
    4 hours ago






  • 1




    $begingroup$
    @Jiminion: Someone commented the same thing on puzzling.stackexchange.com/questions/28926/… ! :) I've edited that part of the question to reflect that if you place, e.g., 9 white queens and 7 black queens, your score is "7", not "9". And if you place 64 white queens and 0 black queens, your score is "0", not "64".
    $endgroup$
    – Quuxplusone
    3 hours ago
















3












3








3





$begingroup$


Here's a discrete variation of yesterday's puzzle Peaceful Encampments.




You have 8 white queens and 8 black queens. Place all these pieces onto a normal 8x8 chessboard in such a way that no white queen threatens a black queen (nor vice versa).




Or, phrasing the puzzle in a way parallel to Black and white queens on an 8x8 chessboard — changing only one word from that puzzle — I would say:




What is the largest number of queens that can be placed on a regular 8×8 chessboard, if the following rules are met:




  1. A queen can be either black or white, and there can be unequal numbers of each type [but if so, we count the smaller population].

  2. A queen must not be threatened by other queens of a different color.

  3. Queens threaten all squares in the same row, column, or diagonal (as in chess). Also, threats are blocked by other queens [not that this matters].




Can you find a way to place more than 8 queens of each color "peacefully" on an 8x8 chessboard?






geometry chess checkerboard







share|improve this question











$endgroup$




Here's a discrete variation of yesterday's puzzle Peaceful Encampments.




You have 8 white queens and 8 black queens. Place all these pieces onto a normal 8x8 chessboard in such a way that no white queen threatens a black queen (nor vice versa).




Or, phrasing the puzzle in a way parallel to Black and white queens on an 8x8 chessboard — changing only one word from that puzzle — I would say:




What is the largest number of queens that can be placed on a regular 8×8 chessboard, if the following rules are met:




  1. A queen can be either black or white, and there can be unequal numbers of each type [but if so, we count the smaller population].

  2. A queen must not be threatened by other queens of a different color.

  3. Queens threaten all squares in the same row, column, or diagonal (as in chess). Also, threats are blocked by other queens [not that this matters].




Can you find a way to place more than 8 queens of each color "peacefully" on an 8x8 chessboard?






geometry chess checkerboard




geometry chess checkerboard






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 4 hours ago







Quuxplusone

















asked 4 hours ago









QuuxplusoneQuuxplusone

20815




20815












  • $begingroup$
    Based on the rules, why couldn't one place 64 white queens or 64 black queens?
    $endgroup$
    – Jiminion
    4 hours ago






  • 1




    $begingroup$
    @Jiminion: Someone commented the same thing on puzzling.stackexchange.com/questions/28926/… ! :) I've edited that part of the question to reflect that if you place, e.g., 9 white queens and 7 black queens, your score is "7", not "9". And if you place 64 white queens and 0 black queens, your score is "0", not "64".
    $endgroup$
    – Quuxplusone
    3 hours ago




















  • $begingroup$
    Based on the rules, why couldn't one place 64 white queens or 64 black queens?
    $endgroup$
    – Jiminion
    4 hours ago






  • 1




    $begingroup$
    @Jiminion: Someone commented the same thing on puzzling.stackexchange.com/questions/28926/… ! :) I've edited that part of the question to reflect that if you place, e.g., 9 white queens and 7 black queens, your score is "7", not "9". And if you place 64 white queens and 0 black queens, your score is "0", not "64".
    $endgroup$
    – Quuxplusone
    3 hours ago


















$begingroup$
Based on the rules, why couldn't one place 64 white queens or 64 black queens?
$endgroup$
– Jiminion
4 hours ago




$begingroup$
Based on the rules, why couldn't one place 64 white queens or 64 black queens?
$endgroup$
– Jiminion
4 hours ago




1




1




$begingroup$
@Jiminion: Someone commented the same thing on puzzling.stackexchange.com/questions/28926/… ! :) I've edited that part of the question to reflect that if you place, e.g., 9 white queens and 7 black queens, your score is "7", not "9". And if you place 64 white queens and 0 black queens, your score is "0", not "64".
$endgroup$
– Quuxplusone
3 hours ago






$begingroup$
@Jiminion: Someone commented the same thing on puzzling.stackexchange.com/questions/28926/… ! :) I've edited that part of the question to reflect that if you place, e.g., 9 white queens and 7 black queens, your score is "7", not "9". And if you place 64 white queens and 0 black queens, your score is "0", not "64".
$endgroup$
– Quuxplusone
3 hours ago












2 Answers
2






active

oldest

votes


















4












$begingroup$

Here's 8 peaceful queens of each color:




enter image description here




After a lot of messing around, I snuck in a 9th white queen (black still at 8)




enter image description here




I'll keep looking for a way to do 9 for each side, but it may not be possible.






share|improve this answer











$endgroup$





















    2












    $begingroup$

    Nine queens of each color. Some variation is possible.




    enter image description here







    share|improve this answer









    $endgroup$













    • $begingroup$
      Nice. Far more asymmetric than my "intended" solution!
      $endgroup$
      – Quuxplusone
      2 hours ago











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    2 Answers
    2






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    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    4












    $begingroup$

    Here's 8 peaceful queens of each color:




    enter image description here




    After a lot of messing around, I snuck in a 9th white queen (black still at 8)




    enter image description here




    I'll keep looking for a way to do 9 for each side, but it may not be possible.






    share|improve this answer











    $endgroup$


















      4












      $begingroup$

      Here's 8 peaceful queens of each color:




      enter image description here




      After a lot of messing around, I snuck in a 9th white queen (black still at 8)




      enter image description here




      I'll keep looking for a way to do 9 for each side, but it may not be possible.






      share|improve this answer











      $endgroup$
















        4












        4








        4





        $begingroup$

        Here's 8 peaceful queens of each color:




        enter image description here




        After a lot of messing around, I snuck in a 9th white queen (black still at 8)




        enter image description here




        I'll keep looking for a way to do 9 for each side, but it may not be possible.






        share|improve this answer











        $endgroup$



        Here's 8 peaceful queens of each color:




        enter image description here




        After a lot of messing around, I snuck in a 9th white queen (black still at 8)




        enter image description here




        I'll keep looking for a way to do 9 for each side, but it may not be possible.







        share|improve this answer














        share|improve this answer



        share|improve this answer








        edited 3 hours ago

























        answered 4 hours ago









        Excited RaichuExcited Raichu

        6,40021066




        6,40021066























            2












            $begingroup$

            Nine queens of each color. Some variation is possible.




            enter image description here







            share|improve this answer









            $endgroup$













            • $begingroup$
              Nice. Far more asymmetric than my "intended" solution!
              $endgroup$
              – Quuxplusone
              2 hours ago
















            2












            $begingroup$

            Nine queens of each color. Some variation is possible.




            enter image description here







            share|improve this answer









            $endgroup$













            • $begingroup$
              Nice. Far more asymmetric than my "intended" solution!
              $endgroup$
              – Quuxplusone
              2 hours ago














            2












            2








            2





            $begingroup$

            Nine queens of each color. Some variation is possible.




            enter image description here







            share|improve this answer









            $endgroup$



            Nine queens of each color. Some variation is possible.




            enter image description here








            share|improve this answer












            share|improve this answer



            share|improve this answer










            answered 2 hours ago









            Daniel MathiasDaniel Mathias

            5035




            5035












            • $begingroup$
              Nice. Far more asymmetric than my "intended" solution!
              $endgroup$
              – Quuxplusone
              2 hours ago


















            • $begingroup$
              Nice. Far more asymmetric than my "intended" solution!
              $endgroup$
              – Quuxplusone
              2 hours ago
















            $begingroup$
            Nice. Far more asymmetric than my "intended" solution!
            $endgroup$
            – Quuxplusone
            2 hours ago




            $begingroup$
            Nice. Far more asymmetric than my "intended" solution!
            $endgroup$
            – Quuxplusone
            2 hours ago


















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