The Factory's Secret Door puzzle involves finding a 4-digit code where each digit represents the count of a specific digit in the code itself. Specifically:

• The second digit is the number of 1s in the code.
• The third digit is the number of 2s in the code.
• The fourth digit is the number of 3s in the code.

After analyzing possible combinations, the only code that satisfies all conditions is 2020.

Verification:

• Code: 2020
  • First digit (2): Counts the number of 0s. There are two 0s (positions 2 and 4), so it matches.
  • Second digit (0): Counts the number of 1s. There are no 1s, so it matches.
  • Third digit (2): Counts the number of 2s. There are two 2s (positions 1 and 3), so it matches.
  • Fourth digit (0): Counts the number of 3s. There are no 3s, so it matches.

This code is self-descriptive and unique for a 4-digit sequence under the given rules. Entering 2020 will open the secret door.