ghabxph/nice-problem-042.md

## nice-problem-042.md

      
    Raw
  

              nice-problem-042.md
            
          
    The problem

682 - One digit is right and in its place
614 - One digit is right but in the wrong place
206 - Two digits are right, but both are in the wrong place
738 - All digits are wrong
380 - One digit is right, but in the wrong place

My conclusion: 042 How?

Statement #4 gives us nice eliminations.

Now, keep these numbers in mind. Lots of things are confirmed
right?
6 2 - One digit is right and in its place
614 - One digit is right but in the wrong place
206 - Two digits are right, but both are in the wrong place
    - All digits are wrong
  0 - One digit is right, but in the wrong place

Statement #1: (6 2) One digit is right and in its place


Statement 1.1. One digit is right (can be 6 or 2)
Statement 1.2. The right digit is in its place (6 on 1st place or 2 on 3rd position)

If 6 is our number, then 6 is key #1. If 2 is our number then 2 is key #3.
Let's move on.
Statement #2: (614) One digit is right but in the wrong place

Pick 6 as correct number, and go back to the rules.

Statement #1: (6  ) One digit is right and in its place
Statement #2: (6  ) One digit is right but in the wrong place (Contradiction)

Thus, 6 is eliminated by contradiction consequently giving us 2 as our key #3
(xx2).
At this point, either 1 or 4 is our possible key from statement #2.

If 1 is the right number, then 1 can only key #1, because key #3 is occupied by #2. (1x2)
If 4 is the right number, then 4 can be located either in 1st or 2nd position. (4x2, x42)

Let's move on.
Statement #3: (20 ) Two digits are right, but both are in the wrong place

0 can only be located in the 1st position, which consequently eliminates 1 in the process.
2 is known as key #3 (xx2), thus 0 can only be located at the first position (0x2), and
consequently eliminates 1 in the process. Thus 4 can only be located in 2nd position, giving
us a conclustion of 042 as our answer.
042 as our nice asnwer.


Statement #1 assures 2 in the 3rd position.
Statement #2 assures 4 in the 2nd position.
Statement #3 assures 0 in the first position.

EXTRA: Statement #5: (  0) - One digit is right, but in the wrong place

Statement #5 is merely just a supporting statement. We can even eliminate this 5th
statement and we still arrive to same conclusion that the answer is 042