# Your mission is to break this mastermind code

Here is an altered mastermind puzzle which instead of colored pegs I used digits from 1 to 9 without any repetition. The picture below shows four guesses and their corresponding scores.The black pegs are for every correct digit and correct position and the white pegs are only for the correct digits and wrong position. Your mission is to break the code on the fifth guess and find what the hidden number is. Good luck. N.B. for those who are not familliar with mastermind game I suggest to visit this site: https://en.wikipedia.org/wiki/Mastermind_(board_game)

• this can't be solved. there is a black peg and a white peg for the same number and position first of all. Second, there is a black peg at the same spot even though the number is different. Commented Oct 22, 2017 at 1:06
• @9.0 the black and white pegs don't necessarily represent the same position Commented Oct 22, 2017 at 1:10
• @boboquack but OP says "black pegs are for every correct digit and correct position " ... ? Commented Oct 22, 2017 at 1:16
• For each correct digit in the correct position, you get a black peg on the left in some place. @9.0 Commented Oct 22, 2017 at 1:19
• @boboquack - oh. Commented Oct 22, 2017 at 1:48

The code is:

6741

Process:
Note: When I speak of a number being white or black, I mean that it is represented by a white or black peg respectively.

5 and 8 cannot be the black in row 4, otherwise there would be a black in row 2 or 3. So neither 5 or 8 are in the code, since there is no white in row 4.
Similarly, neither 1 nor 2 can be the black in row 1, since there would then be a black in row 2. So 6 must be the black in row 1, and the first digit of the code.
Now, 4 must be a white in row 2, because otherwise both 1 and 2 are whites, contradicting row 1. So 4 is also a white in row 3.
If 2 were the white in rows 1 and 2, 1 must not be in the code. So 3 would be in the code, but then we have 5 digits in the code - 6, 2, 3, 4 and the 7 or 9 from row 4. So 2 is not the white in row 1 or 2.
So 1 is the white in rows 1, 2 and 3. 1 cannot be the first digit in the code, since 6 is. By the positioning of the white 1 in rows 1, 2 and 3, the 1 can't be the second or third digit either. So 1 is the fourth digit.
Now, 9 can't be black in row 4, since it would be the fourth digit and we know 1 is the fourth digit. So the 7 is black in row 4, and the second digit of the code.
Then the 4 must be the third digit of the code, since we know it is white.

• excellent. Well done. Commented Oct 22, 2017 at 10:07

The solution is:

6741

Because:

From 1,2: In 1 the black dot is not the 1 or 2.
From 1,3: The black dot in 1 is not the 5.
Therefore the code starts with 6.
From 3,4: The 5 is not the black dot in 4.
Therefore 5 is not in the code.
From 1:Only 1 or 2 is part of the solution.
From 2:Only 4 or 8 is part of the solution.
From 2 and 4: 8 is not the black dot in 4.
Therefore 8 is not in the code.
So 4 is in the code.
From 4:Only 7 or 9 is part of the solution.
So the solution contains: (6), (7 or 9), (4), (1 or 2)
From 3:1 is part of the solution.
From 1,2,3: 1 is the last digit of the code.
From 4: 7 is the second digit of the code.
So 4 is the third digit of the code, making the code: 6741

• How is this fundamentally different to my solution? Commented Oct 22, 2017 at 1:27
• It is not, i think, i just started to work on a solution till i finished it, than posted it, after i posted it i saw yours. I enjoyed to find the solution, and happened to write it down as i advanced, in that way it has nothing to do with your solution. I do admit you were faster. Commented Oct 22, 2017 at 1:49
• Good work, well done. Commented Oct 22, 2017 at 10:08