>>7813073
I have done a similar algorithm in the past.

I assigned a color for each digit (0,1,2,...,9)
(so it worked for up to 10 colors ...)

Tested all permutations (some optimization allowed to only test reasonable permutations).

In the case of a 2x2 matrix and 3 colors it worked like this
0000
Test: "fail, add one in base 3"
0001
Test "fail, add one in base 3"
0002
Test "fail, add one in base 3"
0010
Test "fail, add one in base 3"
....
2222
Test "fail"
end

I realized it would be much better if my test function would actually tell the algorithm what digit to increment.
0000
Test: "fail, at digit #2"
0100
Test "fail at digit #3"
0110
Test "win, increment count"
0111
...

There's probably better ways to do this (either with proper combinatorics or with a most efficient algorithm) but I was looking for a programming challenge for "beginners" at the time ...