Queens attacking exactly four queens

Question

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

score 11 · Accepted Answer · edited Mar 06 '20 at 19:28

11

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.

lichess

edited Mar 06 '20 at 19:28

JMP

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answered Mar 06 '20 at 07:26

daw

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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. – PuzzlesAndSolutionsYT Mar 06 '20 at 07:37
That is exactly the pretty solution I was looking for! Very well done. I wasn't sure that anyone would get it so quickly. – Dmitry Kamenetsky Mar 06 '20 at 08:03
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@Dmitry An alternative solution – Daniel Mathias Mar 06 '20 at 11:29
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Very nice Daniel! Please post it as an answer. – Dmitry Kamenetsky Mar 06 '20 at 13:39

Dmitry Kamenetsky · Answer 2 · 2020-03-10T06:56:26.030

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Interestingly there exist completely non-symmetric solutions:

And this one

edited Mar 10 '20 at 06:56

answered Mar 07 '20 at 09:04

Dmitry Kamenetsky

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How did you come up with this? – daw Mar 07 '20 at 15:20
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I used a computer program based on hill climbing – Dmitry Kamenetsky Mar 08 '20 at 00:49

Queens attacking exactly four queens

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