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Lock it up

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Step 1: Eliminate possibilities based on clue 4

Clue: 738: All digits are wrong.

This means that the digits 7, 3, and 8 are not part of the code. We can eliminate these from

all other clues.

Step 2: Use clue 1 and clue 5 to find a correct digit and its position

Clue: 682: One digit is right and in its place.

Clue: 380: One digit is right but in the wrong place. 

From Step 1, we know 8 is incorrect.


In 682, if 6 is right and in place, then 2 is wrong or in the wrong place. If 2 is right and in place, then 6 is wrong or in the wrong place.


In 380, we know 3 and 8 are wrong. This means 0 is the correct digit, but it's in the wrong place. So, the code has a 0, but it's not in the third position.

Step 3: Use clue 2 and clue 5 to narrow down possibilities

Clue: 614: One digit is right but in the wrong place. 

Clue: 380: One digit is right but in the wrong place. 

We know 0 is a correct digit but not in the third place.


If 0 is in the first place, then from 614, if 1 is the correct digit, it's not in the middle. If 4 is the correct digit, it's not in the last place.


If 0 is in the second place, then from 614, if 1 is the correct digit, it's not in the middle.

Step 4: Use clue 3 to confirm digits and positions

Clue: 206: Two digits are right but both are in the wrong place. 

We know 0 is a correct digit but not in the third place. If 0 is one of the two correct digits in 206, and it's in the wrong place (it's in the middle position here), then it must be in the first position of the final code.


Since 6 is incorrect (from clue 1 and 2), the other correct digit in 206 must be 2. Since it's in the wrong place (it's in the first position here), it must be in the second or third position of the final code.

Step 5: Combine information to find the solution

From Step 4, the first digit is 0.


From Clue 1 (682: One digit is right and in its place), since 8 is wrong and 6 is wrong (from clue 2 and 5), the correct digit must be 2, and it's in the correct place. So the third digit is 2.


From Clue 2 (614: One digit is right but in the wrong place), we know 6 is wrong. If 1 is the correct digit, it's not in the middle. If 4 is the correct digit, it's not in the last place.


Since we have 0 in the first place and 2 in the third place, the only remaining digit to find is the middle one.


From clue 2, if 4 is the correct digit, it's in the wrong place (it's in the third position in 614). So, 4 could be the middle digit. Let's check with all clues: 

  • 042:

    • 682: One digit (2) is right and in its place. (Correct)

    • 614: One digit (4) is right but in the wrong place. (Correct, 4 is in the middle, not last)

    • 206: Two digits (0 and 2) are right but both are in the wrong place. (Correct, 0 is in the first place, not middle; 2 is in the third place, not first)

    • 738: All digits are wrong. (Correct, 7, 3, 8 are not in 042)

    • 380: One digit (0) is right but in the wrong place. (Correct, 0 is in the first place, not third)

Answer:

The code to open the lock is 042.

 
 
 

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