On your first guess, just leave them all red. If you get any right, you know for a fact that you have that many red ones. If you don’t, you know for a fact that you don’t have any red ones.
Next, however many you get wrong, replace those with white. For example, if after your first turn, you had 2 right, next turn you should guess 2 red and 2 white.
Keep going like this, trying one color at a time for any you still have wrong. Since there are 6 different colors, you will know the correct colors at least by your 6th turn.
(more…)