What is the largest number of knights that can be placed on an 8x8 chessboard such that no knight attacks any other knight?
Now add this condition: the number of knights occupying black squares is the same as the number of knights occupying white squares. Now what is the largest number of knights that can be placed?
Without the color restriction, you can place 32 knights on the same color. Since knights only attack opposite color squares none can attack another. I'm pretty sure this is optimum.
With the color restriction I cannot see how to do better than 24. There are many ways to do this. The simplest to explain is three strips along the first, fourth, and seventh rows. I'd be amazed to see a higher number.

Posted by Jer
on 20170705 09:33:58 