7
$\begingroup$

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!

Improve this question
$\endgroup$

2 Answers 2

Reset to default
9
$\begingroup$

Can this be improved?

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

Improve this answer
$\endgroup$
4
  • 1
    $\begingroup$ 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. $\endgroup$
    – Dmitry Kamenetsky
    Nov 24, 2019 at 3:19
  • 1
    $\begingroup$ @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. $\endgroup$
    – Daniel Mathias
    Nov 24, 2019 at 3:32
  • 1
    $\begingroup$ Daniel that looks great, thanks for your efforts! $\endgroup$
    – Dmitry Kamenetsky
    Nov 24, 2019 at 3:37
  • $\begingroup$ I've searched for solutions with my own solver and I don't think this can be improved. Well done! $\endgroup$
    – Dmitry Kamenetsky
    Nov 24, 2019 at 9:13
3
$\begingroup$

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

enter image description here

Improve this answer
$\endgroup$
4
  • 1
    $\begingroup$ aha yes... i thought it should only be triples... $\endgroup$
    – Omega Krypton
    Nov 24, 2019 at 1:32
  • 2
    $\begingroup$ Now I see a way to get 10 of each by modifying your solution... I'll look for further improvements before posting. $\endgroup$
    – Daniel Mathias
    Nov 24, 2019 at 1:47
  • 1
    $\begingroup$ "Place an equal number of red, white and black bishops..." $\endgroup$
    – Quintec
    Nov 24, 2019 at 2:02
  • 1
    $\begingroup$ Feel free to add more bishops of one colour $\endgroup$
    – Dmitry Kamenetsky
    Nov 24, 2019 at 2:55

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.