FA-5596 / Combinatorics / Open access
Unordered samples without replacement · case 01
Ordered arrangements overcount each selected subset.
ROOT CAUSE
Ordered arrangements overcount each selected subset.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return math.comb(n,k)
Unsuccessful approach: The multiset coefficient permits repeated selections.
Case contract
Nonnegative integer counts. Permutation and combination counts are zero when a requested selection exceeds the available objects. Shape sizes satisfy the preconditions stated below. Unordered samples without replacement. Exact operational definition: math.comb(n,k)
Why this case matters
Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Combinatorics results depend on the stated convention.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(n, k):
return math.perm(n,k)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (5, 2)', solve(*(5, 2)), 10)
check('fixture 2: (3, 0)', solve(*(3, 0)), 1)
check('fixture 3: (3, 3)', solve(*(3, 3)), 1)
check('fixture 4: (2, 3)', solve(*(2, 3)), 0)
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 |
|---|---|---|---|
| fixture 1: (5, 2) | 20 | 10 | Failed |
| fixture 2: (3, 0) | 1 | 1 | Passed |
| fixture 3: (3, 3) | 6 | 1 | Failed |
| fixture 4: (2, 3) | 0 | 0 | Passed |
SHA-256 / f4912516abf93a03f8b748529bbe0cef4dbb3c1578d5853b2383eed5833fb377
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(n, k):
return math.comb(n+k-1,k)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (5, 2)', solve(*(5, 2)), 10)
check('fixture 2: (3, 0)', solve(*(3, 0)), 1)
check('fixture 3: (3, 3)', solve(*(3, 3)), 1)
check('fixture 4: (2, 3)', solve(*(2, 3)), 0)
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 |
|---|---|---|---|
| fixture 1: (5, 2) | 15 | 10 | Failed |
| fixture 2: (3, 0) | 1 | 1 | Passed |
| fixture 3: (3, 3) | 10 | 1 | Failed |
| fixture 4: (2, 3) | 4 | 0 | Failed |
SHA-256 / 14e6cf4e7c19d65d7bc36ba87dbc2bdd231dacd8550b9e07af1a680835814fad
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(n, k):
return math.comb(n,k)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (5, 2)', solve(*(5, 2)), 10)
check('fixture 2: (3, 0)', solve(*(3, 0)), 1)
check('fixture 3: (3, 3)', solve(*(3, 3)), 1)
check('fixture 4: (2, 3)', solve(*(2, 3)), 0)
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 |
|---|---|---|---|
| fixture 1: (5, 2) | 10 | 10 | Passed |
| fixture 2: (3, 0) | 1 | 1 | Passed |
| fixture 3: (3, 3) | 1 | 1 | Passed |
| fixture 4: (2, 3) | 0 | 0 | Passed |
SHA-256 / 02fcb7d6354aa7c9200a3979343476c271efa4fa23c22ba26f438dd11bb2f8cb
Verification & scope
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 2026-09-29T14:37:51.172721+00:00.
Case digest / fb7e7142ddd958ea66b5f08c37c586c54dab8eb554b3ee055aaa655a57784c6e