{"abstract":"Each game is counted from both participating teams.","category":"Combinatorics","checks":4,"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","evaluation_group":"model-4a85da522b98a5c9","failed_approach":"Repeated meetings multiply the schedule rather than add a constant.","family":"xn-tournament-round-robin-games","id":"FA-5711","implementations":{"attempt":{"sha256":"3596a723b6ece8cf232b300d0e00e01b23a61e5a11f81abc67894d6d63514806","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(teams, meetings):\n    return math.comb(teams,2)+meetings\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (4, 2)', solve(*(4, 2)), 12)\ncheck('fixture 2: (1, 2)', solve(*(1, 2)), 0)\ncheck('fixture 3: (3, 1)', solve(*(3, 1)), 3)\ncheck('fixture 4: (5, 0)', solve(*(5, 0)), 0)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"6267a6e5f2d3ba02fe023b2113bf15fbda8f32f27e9f63353e4899e45219140e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(teams, meetings):\n    return teams*(teams-1)*meetings\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (4, 2)', solve(*(4, 2)), 12)\ncheck('fixture 2: (1, 2)', solve(*(1, 2)), 0)\ncheck('fixture 3: (3, 1)', solve(*(3, 1)), 3)\ncheck('fixture 4: (5, 0)', solve(*(5, 0)), 0)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"d3a74312943d0aec35f80ee4c70eac45a40ee847900efd749fabfe036c252c73","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(teams, meetings):\n    return math.comb(teams,2)*meetings\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (4, 2)', solve(*(4, 2)), 12)\ncheck('fixture 2: (1, 2)', solve(*(1, 2)), 0)\ncheck('fixture 3: (3, 1)', solve(*(3, 1)), 3)\ncheck('fixture 4: (5, 0)', solve(*(5, 0)), 0)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":" 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.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"xn-tournament-round-robin-games","generated_at":"2026-09-29T14:37:52.779700+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Combinatorics results depend on the stated convention.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return math.comb(teams,2)*meetings","root_cause":"Each game is counted from both participating teams.","sha256":"6c0f8a8ff74cbb5bdc4ef7077407c0d288a92cc2c5f342f97ae85e9404f4a509","title":"Tournament round robin games · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":54.233,"exit_code":1,"observations":[{"actual":8,"check":"fixture 1: (4, 2)","expected":12,"passed":false},{"actual":2,"check":"fixture 2: (1, 2)","expected":0,"passed":false},{"actual":4,"check":"fixture 3: (3, 1)","expected":3,"passed":false},{"actual":10,"check":"fixture 4: (5, 0)","expected":0,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (4, 2)\", \"actual\": 8, \"expected\": 12, \"passed\": false}, {\"check\": \"fixture 2: (1, 2)\", \"actual\": 2, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 3: (3, 1)\", \"actual\": 4, \"expected\": 3, \"passed\": false}, {\"check\": \"fixture 4: (5, 0)\", \"actual\": 10, \"expected\": 0, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":51.569,"exit_code":1,"observations":[{"actual":24,"check":"fixture 1: (4, 2)","expected":12,"passed":false},{"actual":0,"check":"fixture 2: (1, 2)","expected":0,"passed":true},{"actual":6,"check":"fixture 3: (3, 1)","expected":3,"passed":false},{"actual":0,"check":"fixture 4: (5, 0)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (4, 2)\", \"actual\": 24, \"expected\": 12, \"passed\": false}, {\"check\": \"fixture 2: (1, 2)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 3: (3, 1)\", \"actual\": 6, \"expected\": 3, \"passed\": false}, {\"check\": \"fixture 4: (5, 0)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.502,"exit_code":0,"observations":[{"actual":12,"check":"fixture 1: (4, 2)","expected":12,"passed":true},{"actual":0,"check":"fixture 2: (1, 2)","expected":0,"passed":true},{"actual":3,"check":"fixture 3: (3, 1)","expected":3,"passed":true},{"actual":0,"check":"fixture 4: (5, 0)","expected":0,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (4, 2)\", \"actual\": 12, \"expected\": 12, \"passed\": true}, {\"check\": \"fixture 2: (1, 2)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 3: (3, 1)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 4: (5, 0)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}