Discrete Peaceful Encampments: 9 queens on a chessboard












0












$begingroup$


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.

  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









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
















0












$begingroup$


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.

  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
    2 mins ago














0












0








0





$begingroup$


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.

  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.

  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










asked 10 mins ago









QuuxplusoneQuuxplusone

1935




1935












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


















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
















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




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










1 Answer
1






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1












$begingroup$

Here's 8 peaceful queens of each color:




enter image description here




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





share









$endgroup$













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    active

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    $begingroup$

    Here's 8 peaceful queens of each color:




    enter image description here




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





    share









    $endgroup$


















      1












      $begingroup$

      Here's 8 peaceful queens of each color:




      enter image description here




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





      share









      $endgroup$
















        1












        1








        1





        $begingroup$

        Here's 8 peaceful queens of each color:




        enter image description here




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





        share









        $endgroup$



        Here's 8 peaceful queens of each color:




        enter image description here




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






        share











        share


        share










        answered 3 mins ago









        Excited RaichuExcited Raichu

        6,37021065




        6,37021065






























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