Coloring a 3-player Chess board with 3 colors

Question

I'm referring to this type of chess:

https://en.m.wikipedia.org/wiki/Three-Man_Chess

It has $96$ "squares".

If $32$ of the "squares" are black, $32$ are white and $32$ are red, is it possible to arrange them such that no two squares which share a side/edge have the same color?

Answer 1

Here's one way to do it (I apologize in advance for using flood-fill in MSPaint):

In each color, there are two symmetrically-arranged "pieces" of $16$ squares joined at their corners. This setup also has the aesthetically pleasing property that nobody's starting squares share a color with their pieces.

Here is another such coloring found by a completely different approach. Here, we start with a checkerboard coloring with $48$ black and $48$ white squares, and change $16$ of each color to red. I've tried to do this somewhat symmetrically, but there are lots of ways to do this.