Implement Luhn-based card validation and inference

Q: Implement Luhn-based card validation and inference

This question evaluates understanding of the Luhn checksum, pattern recognition for card-brand inference, string manipulation with wildcards, combinatorial enumeration of valid combinations, and error-detection/correction models.

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Question

Implement utilities for credit-card validation and inference using the Luhn algorithm. Card brands and formats: VISA — 16 digits, starts with 4; MASTERCARD — 16 digits, starts with 51, 52, 53, 54, or 55; AMEX — 15 digits, starts with 34 or 37. Tasks:

Given a digit-only card number, return whether the checksum is valid and which brand it belongs to. Possible outputs: ["INVALID_CHECKSUM", "VISA", "MASTERCARD", "AMEX"].
Extend (
to also return "UNKNOWN" if the checksum is valid but the number does not match any known brand pattern.
Now allow '*' characters representing unknown digits (e.g., "****424242424242"). Return the number of possible valid cards per brand. Output as a list of "BRAND,count" pairs; multiple brands may be possible for the same pattern.
Given an observed string like "4333220284765319?", where the trailing '?' indicates that exactly one error occurred to the preceding digits, and the error is one of: changed digit, removed digit, added digit, or swapped two digits (transposition), output all possible original valid card numbers (and their brands) that could have produced the observed string.

Implement Luhn-based card validation and inference

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