Peaceable Bishops on an 8x8 grid

Question

Place an equal number of red, white and black bishops on a 8x8 chess grid, such that no two bishops of different colours attack each other. What is the largest number of bishops you can place? Bonus question: can you add more bishops of one colour?

Here is a similar question with queens: Discrete Peaceful Encampments: Player 3 has entered the game!

score 9 · Accepted Answer · edited Nov 24 '19 at 11:03

9

Can this be improved?

14,14,16
$$\begin{array}{|c|c|}\hline A&C&A&&&B&C&B\\ \hline C&A&C&A&B&C&B&C\\ \hline A&C&A&&&B&C&B\\ \hline &A&&&&&B&\\ \hline &B&&&&&A&\\ \hline B&C&B&&&A&C&A\\ \hline C&B&C&B&A&C&A&C\\ \hline B&C&B&&&A&C&A\\ \hline \end{array}$$

edited Nov 24 '19 at 11:03

JMP

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answered Nov 24 '19 at 03:14

Daniel Mathias

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1

That is a beautiful pattern! Could you add some grid lines, otherwise it is hard to see? Top left corner you can add another A. – Dmitry Kamenetsky Nov 24 '19 at 03:19
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@Dmitry Lacking vertical edge lines, but it is too much trouble to figure out the formatting on mobile. Also, the A was there in the top left, but MathJax ate it. – Daniel Mathias Nov 24 '19 at 03:32
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Daniel that looks great, thanks for your efforts! – Dmitry Kamenetsky Nov 24 '19 at 03:37
I've searched for solutions with my own solver and I don't think this can be improved. Well done! – Dmitry Kamenetsky Nov 24 '19 at 09:13

Omega Krypton · Answer 2 · 2019-11-24T02:02:48.013

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This should be optimal, but haven’t proved it...

edited Nov 24 '19 at 02:02

answered Nov 24 '19 at 00:59

Omega Krypton

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aha yes... i thought it should only be triples... – Omega Krypton Nov 24 '19 at 01:32
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Now I see a way to get 10 of each by modifying your solution... I'll look for further improvements before posting. – Daniel Mathias Nov 24 '19 at 01:47
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"Place an equal number of red, white and black bishops..." – Quintec Nov 24 '19 at 02:02
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Feel free to add more bishops of one colour – Dmitry Kamenetsky Nov 24 '19 at 02:55

Peaceable Bishops on an 8x8 grid

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