This is the classic game of MasterMind, where the player tries to deduce the colors of 4 pegs. There are 6^4 = 1296 possible ways for the computer to have constructed the right answer. You have 10 guesses, and get feedback after each one on the number of pegs in the right holes and the number of pegs of the right color in the wrong holes.
Abe helped me some with the programming and design of the game.