FA-5701 / Combinatorics / Open access
Hypergeometric numerator · case 01
Independent selection counts are added instead of multiplied.
ROOT CAUSE
Independent selection counts are added instead of multiplied.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return math.comb(good,successes)*math.comb(bad,draws-successes)
Unsuccessful approach: All draws are counted without the success constraint.
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. good,bad,draws,successes>=0 and successes<=draws. Count unlabelled draws with exactly successes good objects; impossible population selections return zero. Exact operational definition: math.comb(good,successes)*math.comb(bad,draws-successes)
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(good, bad, draws, successes):
return math.comb(good,successes)+math.comb(bad,draws-successes)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (4, 3, 3, 2)', solve(*(4, 3, 3, 2)), 18)
check('fixture 2: (2, 2, 2, 0)', solve(*(2, 2, 2, 0)), 1)
check('fixture 3: (3, 0, 2, 2)', solve(*(3, 0, 2, 2)), 3)
check('fixture 4: (1, 4, 2, 2)', solve(*(1, 4, 2, 2)), 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: (4, 3, 3, 2) | 9 | 18 | Failed |
| fixture 2: (2, 2, 2, 0) | 2 | 1 | Failed |
| fixture 3: (3, 0, 2, 2) | 4 | 3 | Failed |
| fixture 4: (1, 4, 2, 2) | 1 | 0 | Failed |
SHA-256 / 1d80965b8cffe0b86f786ee0dbdbfc1cd0726d8270c38607cff893f04dd77085
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(good, bad, draws, successes):
return math.comb(good+bad,draws)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (4, 3, 3, 2)', solve(*(4, 3, 3, 2)), 18)
check('fixture 2: (2, 2, 2, 0)', solve(*(2, 2, 2, 0)), 1)
check('fixture 3: (3, 0, 2, 2)', solve(*(3, 0, 2, 2)), 3)
check('fixture 4: (1, 4, 2, 2)', solve(*(1, 4, 2, 2)), 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: (4, 3, 3, 2) | 35 | 18 | Failed |
| fixture 2: (2, 2, 2, 0) | 6 | 1 | Failed |
| fixture 3: (3, 0, 2, 2) | 3 | 3 | Passed |
| fixture 4: (1, 4, 2, 2) | 10 | 0 | Failed |
SHA-256 / b88fb9d16b392e50b870b120315d397922b9d804ec8bec26b224561f4dde9c54
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(good, bad, draws, successes):
return math.comb(good,successes)*math.comb(bad,draws-successes)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (4, 3, 3, 2)', solve(*(4, 3, 3, 2)), 18)
check('fixture 2: (2, 2, 2, 0)', solve(*(2, 2, 2, 0)), 1)
check('fixture 3: (3, 0, 2, 2)', solve(*(3, 0, 2, 2)), 3)
check('fixture 4: (1, 4, 2, 2)', solve(*(1, 4, 2, 2)), 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: (4, 3, 3, 2) | 18 | 18 | Passed |
| fixture 2: (2, 2, 2, 0) | 1 | 1 | Passed |
| fixture 3: (3, 0, 2, 2) | 3 | 3 | Passed |
| fixture 4: (1, 4, 2, 2) | 0 | 0 | Passed |
SHA-256 / 917d6c55b7420a9613bc31220d536ff9529d203cecb5baf4b8ddd40fa055b5fb
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 2026-09-29T14:37:52.730035+00:00.
Case digest / 18f4ff0c8286f4419e62cdb587c2deba5f39d5f0ae261b0f36fab804e5e4ce77