FA-5601 / Combinatorics / Open access
Multiset selection count · case 01
Distinct-subset counting forbids permitted repeats.
ROOT CAUSE
Distinct-subset counting forbids permitted repeats.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return math.comb(n+k-1,k) if n else int(k==0)
Unsuccessful approach: Ordered tuples distinguish arrangements that represent the same multiset.
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. Multiset selection count. Exact operational definition: math.comb(n+k-1,k) if n else int(k==0)
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.comb(n,k)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (3, 2)', solve(*(3, 2)), 6)
check('fixture 2: (2, 3)', solve(*(2, 3)), 4)
check('fixture 3: (0, 0)', solve(*(0, 0)), 1)
check('fixture 4: (0, 2)', solve(*(0, 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: (3, 2) | 3 | 6 | Failed |
| fixture 2: (2, 3) | 0 | 4 | Failed |
| fixture 3: (0, 0) | 1 | 1 | Passed |
| fixture 4: (0, 2) | 0 | 0 | Passed |
SHA-256 / 4a39ea83b94b72d64a977dd239e200bc0e8f4378ef21b170ae545104b240b270
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 n**k
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (3, 2)', solve(*(3, 2)), 6)
check('fixture 2: (2, 3)', solve(*(2, 3)), 4)
check('fixture 3: (0, 0)', solve(*(0, 0)), 1)
check('fixture 4: (0, 2)', solve(*(0, 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: (3, 2) | 9 | 6 | Failed |
| fixture 2: (2, 3) | 8 | 4 | Failed |
| fixture 3: (0, 0) | 1 | 1 | Passed |
| fixture 4: (0, 2) | 0 | 0 | Passed |
SHA-256 / 311610e6694cf5157e5ebaa394128ad5c28f1ed428cb328fcf5e28f7c119da49
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-1,k) if n else int(k==0)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (3, 2)', solve(*(3, 2)), 6)
check('fixture 2: (2, 3)', solve(*(2, 3)), 4)
check('fixture 3: (0, 0)', solve(*(0, 0)), 1)
check('fixture 4: (0, 2)', solve(*(0, 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: (3, 2) | 6 | 6 | Passed |
| fixture 2: (2, 3) | 4 | 4 | Passed |
| fixture 3: (0, 0) | 1 | 1 | Passed |
| fixture 4: (0, 2) | 0 | 0 | Passed |
SHA-256 / dbf6dc92cf4a369f455255989629dbe143480d6fa4a81b2571ebcb179ab61f64
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 2026-09-29T14:37:51.270969+00:00.
Case digest / 625d76acee58033b7d0c75e5895f05c1304e66fee0e39fc6cf02a60f34418fe6