Can you paint the cells of a 5x5 grid in 5 colours such that for each cell its colour and the colour of its orthogonal (horizontal and vertical) neighbours are all different?
Someone had the right idea:
abcde cdeab eabcd bcdea deabc
Now in Technicolor, so you can see it for yourself:
Trivial Solution (similar to others')
And of course, it also grabs the bonus:
Let a, b, c, d, e be the colors. Then:
| a | b | c | d | e |
| d | e | a | b | c |
| b | c | d | e | a |
| e | a | b | c | d |
| c | d | e | a | b |
How I got there:
If you take
abcde, place it in the first row, and then right-shift it by three for each row, you get this system.