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Can you place 14 black and 14 white queens on a standard 8x8 chess board, such that each queen attacks exactly 4 opponent queens?

Good luck!

Here is a related question: Queens attacking exactly one queen

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2 Answers 2

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I hope this is correct. First, I noticed that these 8 queens close to the corners fulfill the conditions. Then I tried to add more queens while blocking already set queens to not increase their attacks.

enter image description here
lichess

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  • $\begingroup$ Seems right to me, i'm impressed. Tried to solve it for like 30 min without being able to, assumed it would have a 90 degree rotation symmetry but seems like it only needs to be a 180 degree symmetry. $\endgroup$
    – PuzzlesAndSolutionsYT
    Mar 6, 2020 at 7:37
  • $\begingroup$ That is exactly the pretty solution I was looking for! Very well done. I wasn't sure that anyone would get it so quickly. $\endgroup$
    – Dmitry Kamenetsky
    Mar 6, 2020 at 8:03
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    $\begingroup$ @Dmitry An alternative solution $\endgroup$
    – Daniel Mathias
    Mar 6, 2020 at 11:29
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    $\begingroup$ Very nice Daniel! Please post it as an answer. $\endgroup$
    – Dmitry Kamenetsky
    Mar 6, 2020 at 13:39
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Interestingly there exist completely non-symmetric solutions:

enter image description here

And this one

enter image description here

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  • $\begingroup$ How did you come up with this? $\endgroup$
    – daw
    Mar 7, 2020 at 15:20
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    $\begingroup$ I used a computer program based on hill climbing $\endgroup$
    – Dmitry Kamenetsky
    Mar 8, 2020 at 0:49

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