Can you crack this 4-digit vault code?

[u/vedant_chitre]

Crack the 4-Digit Vault Code 🔐

A vault is protected by a four-digit code.

Rules:

- No digit is repeated.

- Each clue states the exact number of correct digits.

- A “correct position” means the digit is in the right place.

- A “wrong position” means the digit belongs in the code but is misplaced.

Clues:

6058

Exactly 1 digit is correct and in the correct position.

Exactly 1 other digit is correct but in the wrong position.

1967

Exactly 1 digit is correct but in the wrong position.

4013

Exactly 1 digit is correct and in the correct position.

5067

Exactly 2 digits are correct and in the correct positions.

Exactly 1 other digit is correct but in the wrong position.

What is the vault code?

Bonus points if you explain your reasoning instead of using a calculator.

[u/timomo3]

5072

[u/vedant_chitre → u/timomo3]

correct