FA-5711 / Combinatorics / Open access
Tournament round robin games · case 01
Each game is counted from both participating teams.
ROOT CAUSE
Each game is counted from both participating teams.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return math.comb(teams,2)*meetings
Unsuccessful approach: Repeated meetings multiply the schedule rather than add a constant.
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. Tournament round robin games. Exact operational definition: math.comb(teams,2)*meetings
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(teams, meetings):
return teams*(teams-1)*meetings
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (4, 2)', solve(*(4, 2)), 12)
check('fixture 2: (1, 2)', solve(*(1, 2)), 0)
check('fixture 3: (3, 1)', solve(*(3, 1)), 3)
check('fixture 4: (5, 0)', solve(*(5, 0)), 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, 2) | 24 | 12 | Failed |
| fixture 2: (1, 2) | 0 | 0 | Passed |
| fixture 3: (3, 1) | 6 | 3 | Failed |
| fixture 4: (5, 0) | 0 | 0 | Passed |
SHA-256 / 6267a6e5f2d3ba02fe023b2113bf15fbda8f32f27e9f63353e4899e45219140e
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(teams, meetings):
return math.comb(teams,2)+meetings
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (4, 2)', solve(*(4, 2)), 12)
check('fixture 2: (1, 2)', solve(*(1, 2)), 0)
check('fixture 3: (3, 1)', solve(*(3, 1)), 3)
check('fixture 4: (5, 0)', solve(*(5, 0)), 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, 2) | 8 | 12 | Failed |
| fixture 2: (1, 2) | 2 | 0 | Failed |
| fixture 3: (3, 1) | 4 | 3 | Failed |
| fixture 4: (5, 0) | 10 | 0 | Failed |
SHA-256 / 3596a723b6ece8cf232b300d0e00e01b23a61e5a11f81abc67894d6d63514806
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(teams, meetings):
return math.comb(teams,2)*meetings
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: (4, 2)', solve(*(4, 2)), 12)
check('fixture 2: (1, 2)', solve(*(1, 2)), 0)
check('fixture 3: (3, 1)', solve(*(3, 1)), 3)
check('fixture 4: (5, 0)', solve(*(5, 0)), 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, 2) | 12 | 12 | Passed |
| fixture 2: (1, 2) | 0 | 0 | Passed |
| fixture 3: (3, 1) | 3 | 3 | Passed |
| fixture 4: (5, 0) | 0 | 0 | Passed |
SHA-256 / d3a74312943d0aec35f80ee4c70eac45a40ee847900efd749fabfe036c252c73
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 2026-09-29T14:37:52.779700+00:00.
Case digest / 6c0f8a8ff74cbb5bdc4ef7077407c0d288a92cc2c5f342f97ae85e9404f4a509