logical deduction - Coloring a 4 by 4 grid

I made this simple puzzle a couple of years ago. There are three colors which appear in every row and every column. Moreover, every color appears 5 or 6 times in total. Find the color of the square with the question mark.

Answer

I get:

Top right is fairly obvious, the 3rd row needs a red and green, and the red can't go in column 2.

Top row and last column now need red/green, and first column, last row need a blue, so the blues go.

Now we have 6 blues, and so we must have 5 reds and 5 greens. As top row/last column both need red/green, this gives us 5 reds, so ? is green.