# Peaceable Bishops on an 8x8 grid

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!

Can this be improved?

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

• 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 3:19
• @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 3:32
• Daniel that looks great, thanks for your efforts! – Dmitry Kamenetsky Nov 24 '19 at 3:37
• 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 9:13

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

• aha yes... i thought it should only be triples... – Omega Krypton Nov 24 '19 at 1:32
• 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 1:47
• "Place an equal number of red, white and black bishops..." – Quintec Nov 24 '19 at 2:02
• @Quintec thanks! rollbacked – Omega Krypton Nov 24 '19 at 2:03
• Feel free to add more bishops of one colour – Dmitry Kamenetsky Nov 24 '19 at 2:55