Most colour blinds are dichromats, they can actually see some colour, but typically lack either red or green receptors. If you make a set of colours where the red and the green values are the same and the colours are clearly differentiable to you they should be so for most colour blinds as well.
If you only have a few colours, different shades of grey can work well enough for full colour blinds, but 6 different shades is probably a bit over the top. So you will have to use shapes or patterns for these.
I think shapes could work really well for the problem at hand, make 6 simple yet clearly distinguishable shapes, draw them either black or different colours on the tiles and put a white number on top.
No matter what you choose to do, ask some colour blinds how they like it and be prepared to tweak your solutions accordingly.