This puzzle has just one solution You must give a SHORT EXPL

 This puzzle has just one solution.  You must give a SHORT EXPLANATION of your reasoning in solving the puzzle.   R  G  W  Bu    Score: 1 white, 1 black           Bk R  Y  Bu    Score: 2 black Bk W  Y  W     Score: 2 black  Bk W  Bu Bu    Score: 1 white, 2 blacK 

Solution

Consider color red. Guess 3 with two reds and three scoring keys indicates thatthere must be at least one red peg in the secret code; but since the keys are white, thered(s) must be in position 3 or 4. However, guess 4 has only black keys and the redpegs are in positions 2 and 3. Since guess 3 indicates that there cannot be a red pegin position 2, we conclude that the secret code has exactly one red peg in position 3and no other red peg (or else the red peg in position 2 in Guess 1 would earn a whitekey). Note that the black key in guess 2 must also be due to the red in position 3.Guess 3 now implies that the green and yellow pegs must have earned two of thethree white keys (since one of the reds received no key). Since yellow is somewherein the secret code, then guess 4 tells us that yellow must be in position 1. So thesecret code is of the form Y R . Moreover, yellow cannot also occur in position 2 or 4, because it appears there in guesses 2 and 3, respectively, without earning a blackkey. So there is only one Y, as well as just one R, in the secret code. Since the keys
in guesses 2 and 4 are now known to be for yellow and red, the other colors in thesetwo guesses—black, blue, and white—cannot be in the secret code. Then the onlyremaining color that can appear in positions 2 and 4 is green, and the secret codeis Y G R G.