Why do this problem?
is one that requires working systematically. It is a good activity for promoting discussion between learners working together and also for giving encouragement to those whose spatial ability is better than their numerical achievements.
Which row and which column have none of that colour in them?
Have you checked the diagonals as well as the rows and columns?
Learners could try other-sized squares such as $4\times 4$ and $6\times 6$. With some squares it is possible to place one colour correctly but no more. Of which sized squares is this true?
You could suggest starting with just one colour, then fitting in the other colours, one at a time.