I am trying to find the best strategy for a certain problem/game. Consider that there are 10 boxes. Inside each box, there is always one ball, and the color of the ball is of one of the following options: White, Red, Blue or Green. The goal of the game is to find the colors of the balls inside each box.
My only way to find the colors is to guess. I can give a possible combination and then I am given the total number of right guesses. For example, consider the case for 4 boxes: if the real combination is WGBR and I say RBGW. Then i would get as an answer "0", but if later I guessed WRRG, then I would be given "1" as an answer. Additionally, there is no known information on the number of balls of each color, they may be all blue, or none.
What I want is what is the strategy that minimizes the number of guesses I have to make for the 10 boxes (or ideally for n>0).
I have been trying to search for an answer but I can't seem to find this problem posed in a similar manner, so, in case you are aware of a similar problem or can give me some idea of where to start I'd be grateful.
Thanks in advance.