FA-72341 / Check-digit algorithms / Open access

Luhn validation doubles the check digit position · case 01

Valid card numbers are reported invalid while some single-digit typos pass.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The doubling test uses i % 2 == 0, so the rightmost check digit is doubled instead of its left neighbour.

VERIFIED REPAIR

Double digits at odd offsets from the right (i % 2 == 1), leaving the check digit undoubled.

Unsuccessful approach: Counting the parity from the left only matches the rule for even-length numbers; odd lengths still fail.

Case contract

Input a card-style number that may contain spaces or hyphens as group separators. After removing them the text must be 2..19 ASCII digits, otherwise "malformed". Doubling applies to every second digit counting from the rightmost (check) digit, doubled values above 9 lose 9, and the number is "valid" when the sum is a multiple of 10, else "invalid".

Why this case matters

Payment-card, loyalty and account numbers are screened with the Luhn mod-10 check before any lookup.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(s):
    t = s.replace(' ', '').replace('-', '')
    if not t.isascii() or not t.isdigit() or len(t) < 2 or len(t) > 19:
        return 'malformed'
    total = 0
    for i, ch in enumerate(reversed(t)):
        d = ord(ch) - 48
        if i % 2 == 0:
            d *= 2
            if d > 9:
                d -= 9
        total += d
    return 'valid' if total % 10 == 0 else 'invalid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["59"]', ['59'], 'valid'], ['regression ["182"]', ['182'], 'valid'], ['partial-repair ["60866456"]', ['60866456'], 'valid'], ['control ["9207919074163"]', ['9207919074163'], 'valid'], ['control ["2300017738893848"]', ['2300017738893848'], 'valid'], ['control ["52"]', ['52'], 'invalid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid']], [['regression ["60866456"]', ['60866456'], 'valid'], ['regression ["49717735275"]', ['49717735275'], 'valid'], ['partial-repair ["067122965057139178"]', ['067122965057139178'], 'valid'], ['partial-repair ["3165356977"]', ['3165356977'], 'valid'], ['control ["60866459"]', ['60866459'], 'invalid'], ['control ["49717735278"]', ['49717735278'], 'invalid'], ['control ["9207919074166"]', ['9207919074166'], 'invalid'], ['control ["2300017738893841"]', ['2300017738893841'], 'invalid']], [['regression ["7985145013991721"]', ['7985145013991721'], 'valid'], ['regression ["067122965057139178"]', ['067122965057139178'], 'valid'], ['partial-repair ["5553"]', ['5553'], 'valid'], ['partial-repair ["77777779"]', ['77777779'], 'valid'], ['control ["0"]', ['0'], 'malformed'], ['control ["00"]', ['00'], 'valid'], ['control ["4111a1111"]', ['4111a1111'], 'malformed'], ['control ["12345678901234567890"]', ['12345678901234567890'], 'malformed']], [['regression ["9505094299844733505"]', ['9505094299844733505'], 'valid'], ['regression ["0906050370970"]', ['0906050370970'], 'valid'], ['partial-repair ["4111 1111 1111 1111"]', ['4111 1111 1111 1111'], 'valid'], ['partial-repair ["18"]', ['18'], 'valid'], ['control ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['control ["79927398710"]', ['79927398710'], 'invalid'], ['control ["-"]', ['-'], 'malformed'], ['control ["5555555555554444"]', ['5555555555554444'], 'valid']], [['regression ["91"]', ['91'], 'valid'], ['regression ["992"]', ['992'], 'valid'], ['partial-repair ["59"]', ['59'], 'valid'], ['partial-repair ["60866456"]', ['60866456'], 'valid'], ['control ["2300017738893848"]', ['2300017738893848'], 'valid'], ['control ["52"]', ['52'], 'invalid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid']]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
regression ["59"]	`invalid`	`valid`	Failed
regression ["182"]	`invalid`	`valid`	Failed
partial-repair ["60866456"]	`invalid`	`valid`	Failed
control ["9207919074163"]	`valid`	`valid`	Passed
control ["2300017738893848"]	`valid`	`valid`	Passed
control ["52"]	`invalid`	`invalid`	Passed
control ["185"]	`invalid`	`invalid`	Passed
control ["97959"]	`invalid`	`invalid`	Passed

SHA-256 / 89b6a12ba4914ed41a54a933abb240b76b483fedd806eff2e6853479f2fd8a0f

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(s):
    t = s.replace(' ', '').replace('-', '')
    if not t.isascii() or not t.isdigit() or len(t) < 2 or len(t) > 19:
        return 'malformed'
    total = 0
    for i, ch in enumerate(reversed(t)):
        d = ord(ch) - 48
        if (len(t) - 1 - i) % 2 == 1:
            d *= 2
            if d > 9:
                d -= 9
        total += d
    return 'valid' if total % 10 == 0 else 'invalid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["59"]', ['59'], 'valid'], ['regression ["182"]', ['182'], 'valid'], ['partial-repair ["60866456"]', ['60866456'], 'valid'], ['control ["9207919074163"]', ['9207919074163'], 'valid'], ['control ["2300017738893848"]', ['2300017738893848'], 'valid'], ['control ["52"]', ['52'], 'invalid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid']], [['regression ["60866456"]', ['60866456'], 'valid'], ['regression ["49717735275"]', ['49717735275'], 'valid'], ['partial-repair ["067122965057139178"]', ['067122965057139178'], 'valid'], ['partial-repair ["3165356977"]', ['3165356977'], 'valid'], ['control ["60866459"]', ['60866459'], 'invalid'], ['control ["49717735278"]', ['49717735278'], 'invalid'], ['control ["9207919074166"]', ['9207919074166'], 'invalid'], ['control ["2300017738893841"]', ['2300017738893841'], 'invalid']], [['regression ["7985145013991721"]', ['7985145013991721'], 'valid'], ['regression ["067122965057139178"]', ['067122965057139178'], 'valid'], ['partial-repair ["5553"]', ['5553'], 'valid'], ['partial-repair ["77777779"]', ['77777779'], 'valid'], ['control ["0"]', ['0'], 'malformed'], ['control ["00"]', ['00'], 'valid'], ['control ["4111a1111"]', ['4111a1111'], 'malformed'], ['control ["12345678901234567890"]', ['12345678901234567890'], 'malformed']], [['regression ["9505094299844733505"]', ['9505094299844733505'], 'valid'], ['regression ["0906050370970"]', ['0906050370970'], 'valid'], ['partial-repair ["4111 1111 1111 1111"]', ['4111 1111 1111 1111'], 'valid'], ['partial-repair ["18"]', ['18'], 'valid'], ['control ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['control ["79927398710"]', ['79927398710'], 'invalid'], ['control ["-"]', ['-'], 'malformed'], ['control ["5555555555554444"]', ['5555555555554444'], 'valid']], [['regression ["91"]', ['91'], 'valid'], ['regression ["992"]', ['992'], 'valid'], ['partial-repair ["59"]', ['59'], 'valid'], ['partial-repair ["60866456"]', ['60866456'], 'valid'], ['control ["2300017738893848"]', ['2300017738893848'], 'valid'], ['control ["52"]', ['52'], 'invalid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid']]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
regression ["59"]	`invalid`	`valid`	Failed
regression ["182"]	`valid`	`valid`	Passed
partial-repair ["60866456"]	`invalid`	`valid`	Failed
control ["9207919074163"]	`valid`	`valid`	Passed
control ["2300017738893848"]	`valid`	`valid`	Passed
control ["52"]	`invalid`	`invalid`	Passed
control ["185"]	`invalid`	`invalid`	Passed
control ["97959"]	`invalid`	`invalid`	Passed

SHA-256 / cb1608fc8f961eee1669ca0328390c3749766fc0c899bad9986a048d5fb9ecd5

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(s):
    t = s.replace(' ', '').replace('-', '')
    if not t.isascii() or not t.isdigit() or len(t) < 2 or len(t) > 19:
        return 'malformed'
    total = 0
    for i, ch in enumerate(reversed(t)):
        d = ord(ch) - 48
        if i % 2 == 1:
            d *= 2
            if d > 9:
                d -= 9
        total += d
    return 'valid' if total % 10 == 0 else 'invalid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["59"]', ['59'], 'valid'], ['regression ["182"]', ['182'], 'valid'], ['partial-repair ["60866456"]', ['60866456'], 'valid'], ['control ["9207919074163"]', ['9207919074163'], 'valid'], ['control ["2300017738893848"]', ['2300017738893848'], 'valid'], ['control ["52"]', ['52'], 'invalid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid']], [['regression ["60866456"]', ['60866456'], 'valid'], ['regression ["49717735275"]', ['49717735275'], 'valid'], ['partial-repair ["067122965057139178"]', ['067122965057139178'], 'valid'], ['partial-repair ["3165356977"]', ['3165356977'], 'valid'], ['control ["60866459"]', ['60866459'], 'invalid'], ['control ["49717735278"]', ['49717735278'], 'invalid'], ['control ["9207919074166"]', ['9207919074166'], 'invalid'], ['control ["2300017738893841"]', ['2300017738893841'], 'invalid']], [['regression ["7985145013991721"]', ['7985145013991721'], 'valid'], ['regression ["067122965057139178"]', ['067122965057139178'], 'valid'], ['partial-repair ["5553"]', ['5553'], 'valid'], ['partial-repair ["77777779"]', ['77777779'], 'valid'], ['control ["0"]', ['0'], 'malformed'], ['control ["00"]', ['00'], 'valid'], ['control ["4111a1111"]', ['4111a1111'], 'malformed'], ['control ["12345678901234567890"]', ['12345678901234567890'], 'malformed']], [['regression ["9505094299844733505"]', ['9505094299844733505'], 'valid'], ['regression ["0906050370970"]', ['0906050370970'], 'valid'], ['partial-repair ["4111 1111 1111 1111"]', ['4111 1111 1111 1111'], 'valid'], ['partial-repair ["18"]', ['18'], 'valid'], ['control ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['control ["79927398710"]', ['79927398710'], 'invalid'], ['control ["-"]', ['-'], 'malformed'], ['control ["5555555555554444"]', ['5555555555554444'], 'valid']], [['regression ["91"]', ['91'], 'valid'], ['regression ["992"]', ['992'], 'valid'], ['partial-repair ["59"]', ['59'], 'valid'], ['partial-repair ["60866456"]', ['60866456'], 'valid'], ['control ["2300017738893848"]', ['2300017738893848'], 'valid'], ['control ["52"]', ['52'], 'invalid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid']]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
regression ["59"]	`valid`	`valid`	Passed
regression ["182"]	`valid`	`valid`	Passed
partial-repair ["60866456"]	`valid`	`valid`	Passed
control ["9207919074163"]	`valid`	`valid`	Passed
control ["2300017738893848"]	`valid`	`valid`	Passed
control ["52"]	`invalid`	`invalid`	Passed
control ["185"]	`invalid`	`invalid`	Passed
control ["97959"]	`invalid`	`invalid`	Passed

SHA-256 / f5af44c26104a4069b314a0d49b7caab04d977329d005f79f97789736c84d8b8

Verification & scope

A deterministic, bounded teaching model of the named scheme under the stated contract; not a certified validator. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:48:37.720590+00:00.

Case digest / 63df08e782fd1749cee126d9686316a3c79a0e330e981bd219d6801c61519d63