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Mathematics-Online problems:

Interactive Problem 62: MasterMind

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
The object of the game ``MasterMind'' is to guess a combination of the colors Red (R), Green (G), and Blue (B). After each guess you will be informed about how many colors were chosen correctly and how many colors were in the correct position. A game may go like this:

        correct colors correct positions
1st guess: R G B 2 1
2nd guess: G B G 1 0

  a) Based upon the information of the first guess, how many combinations are still possible?


b) Which combination is the only one possible after both guesses?
  c) If, in addition, the color Yellow (Y) were given, how many combinations would be possible after the first two guesses?

Example: After the first guess the combination RBR, e.g., would be possible. In this case, the two colors R and B, and the position of R in the first guess would have been guessed correctly. On the other hand, the combination BGR is not possible, since otherwise in the first guess all colors would have been guessed correctly.


Answer:

  a) Number of combinations:


b) Possible Combination:
  c) Number of combinations:


   

(From: Day of Mathematics 1995)
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  automatically generated: 8/11/2017