Discrete Peaceful Encampments: Player 4 has entered the game!












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Here's a variation of Discrete Peaceful Encampments: Player 3 has entered the game! (which itself is a variation of Peaceful Encampments).




You have 3 white queens, 3 black queens, 3 red queens, and 3 green queens. Place all these pieces onto a normal 8x8 chessboard in such a way that no queen threatens a queen of a different color.




Okay, that was easier than the previous variations, right? You can probably use the pattern you found to solve these problems as well:




Place 5 queens of each of four different colors onto a 10x10 checkerboard so that no queen threatens a queen of a different color.



Place 7 queens of each of four different colors onto a 12x12 checkerboard so that no queen threatens a queen of a different color.




Which leads to the real puzzle:




At what point does it become possible to place more than $N-5$ queens of each of four different colors peacefully onto an $Ntimes N$ checkerboard?










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    0












    $begingroup$


    Here's a variation of Discrete Peaceful Encampments: Player 3 has entered the game! (which itself is a variation of Peaceful Encampments).




    You have 3 white queens, 3 black queens, 3 red queens, and 3 green queens. Place all these pieces onto a normal 8x8 chessboard in such a way that no queen threatens a queen of a different color.




    Okay, that was easier than the previous variations, right? You can probably use the pattern you found to solve these problems as well:




    Place 5 queens of each of four different colors onto a 10x10 checkerboard so that no queen threatens a queen of a different color.



    Place 7 queens of each of four different colors onto a 12x12 checkerboard so that no queen threatens a queen of a different color.




    Which leads to the real puzzle:




    At what point does it become possible to place more than $N-5$ queens of each of four different colors peacefully onto an $Ntimes N$ checkerboard?










    share









    $endgroup$















      0












      0








      0





      $begingroup$


      Here's a variation of Discrete Peaceful Encampments: Player 3 has entered the game! (which itself is a variation of Peaceful Encampments).




      You have 3 white queens, 3 black queens, 3 red queens, and 3 green queens. Place all these pieces onto a normal 8x8 chessboard in such a way that no queen threatens a queen of a different color.




      Okay, that was easier than the previous variations, right? You can probably use the pattern you found to solve these problems as well:




      Place 5 queens of each of four different colors onto a 10x10 checkerboard so that no queen threatens a queen of a different color.



      Place 7 queens of each of four different colors onto a 12x12 checkerboard so that no queen threatens a queen of a different color.




      Which leads to the real puzzle:




      At what point does it become possible to place more than $N-5$ queens of each of four different colors peacefully onto an $Ntimes N$ checkerboard?










      share









      $endgroup$




      Here's a variation of Discrete Peaceful Encampments: Player 3 has entered the game! (which itself is a variation of Peaceful Encampments).




      You have 3 white queens, 3 black queens, 3 red queens, and 3 green queens. Place all these pieces onto a normal 8x8 chessboard in such a way that no queen threatens a queen of a different color.




      Okay, that was easier than the previous variations, right? You can probably use the pattern you found to solve these problems as well:




      Place 5 queens of each of four different colors onto a 10x10 checkerboard so that no queen threatens a queen of a different color.



      Place 7 queens of each of four different colors onto a 12x12 checkerboard so that no queen threatens a queen of a different color.




      Which leads to the real puzzle:




      At what point does it become possible to place more than $N-5$ queens of each of four different colors peacefully onto an $Ntimes N$ checkerboard?








      mathematics geometry chess checkerboard





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