{"abstract":"Selections containing adjacent positions are not excluded.","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. Choose k positions among n linearly ordered positions with no adjacent selected pair. Exact operational definition: math.comb(n-k+1,k) if n-k+1>=k else 0","evaluation_group":"model-e946ec6de086c0fd","failed_approach":"The gap compression consumes one unnecessary trailing gap.","family":"xn-nonadjacent-subset-count-fixed-size","id":"FA-5726","implementations":{"attempt":{"sha256":"108d7004462be1e78688ad82907e519b7363c18949053096a4b537abb3e9d2ef","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(n, k):\n    return math.comb(n-k,k) if n-k>=k else 0\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (5, 2)', solve(*(5, 2)), 6)\ncheck('fixture 2: (3, 2)', solve(*(3, 2)), 1)\ncheck('fixture 3: (4, 3)', solve(*(4, 3)), 0)\ncheck('fixture 4: (6, 0)', solve(*(6, 0)), 1)\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":"3d858e3db838da710c277c8477f9d66628af652b65523c3ab410a0c3ed3fd72b","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(n, k):\n    return math.comb(n,k)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (5, 2)', solve(*(5, 2)), 6)\ncheck('fixture 2: (3, 2)', solve(*(3, 2)), 1)\ncheck('fixture 3: (4, 3)', solve(*(4, 3)), 0)\ncheck('fixture 4: (6, 0)', solve(*(6, 0)), 1)\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":"e70cd8e272d539013a0409067d2721e5fb3c419a93336a65cdaeb83b6a78a7df","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(n, k):\n    return math.comb(n-k+1,k) if n-k+1>=k else 0\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (5, 2)', solve(*(5, 2)), 6)\ncheck('fixture 2: (3, 2)', solve(*(3, 2)), 1)\ncheck('fixture 3: (4, 3)', solve(*(4, 3)), 0)\ncheck('fixture 4: (6, 0)', solve(*(6, 0)), 1)\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-nonadjacent-subset-count-fixed-size","generated_at":"2026-09-29T14:37:52.826696+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(n-k+1,k) if n-k+1>=k else 0","root_cause":"Selections containing adjacent positions are not excluded.","sha256":"99b4ad6c94e2aea534f3fe5c060720471b81303d4f722dda165a3515a75f59ed","title":"Nonadjacent subset count fixed size · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":44.521,"exit_code":1,"observations":[{"actual":3,"check":"fixture 1: (5, 2)","expected":6,"passed":false},{"actual":0,"check":"fixture 2: (3, 2)","expected":1,"passed":false},{"actual":0,"check":"fixture 3: (4, 3)","expected":0,"passed":true},{"actual":1,"check":"fixture 4: (6, 0)","expected":1,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (5, 2)\", \"actual\": 3, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 2: (3, 2)\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 3: (4, 3)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (6, 0)\", \"actual\": 1, \"expected\": 1, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":45.482,"exit_code":1,"observations":[{"actual":10,"check":"fixture 1: (5, 2)","expected":6,"passed":false},{"actual":3,"check":"fixture 2: (3, 2)","expected":1,"passed":false},{"actual":4,"check":"fixture 3: (4, 3)","expected":0,"passed":false},{"actual":1,"check":"fixture 4: (6, 0)","expected":1,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (5, 2)\", \"actual\": 10, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 2: (3, 2)\", \"actual\": 3, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 3: (4, 3)\", \"actual\": 4, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 4: (6, 0)\", \"actual\": 1, \"expected\": 1, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":44.894,"exit_code":0,"observations":[{"actual":6,"check":"fixture 1: (5, 2)","expected":6,"passed":true},{"actual":1,"check":"fixture 2: (3, 2)","expected":1,"passed":true},{"actual":0,"check":"fixture 3: (4, 3)","expected":0,"passed":true},{"actual":1,"check":"fixture 4: (6, 0)","expected":1,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (5, 2)\", \"actual\": 6, \"expected\": 6, \"passed\": true}, {\"check\": \"fixture 2: (3, 2)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (4, 3)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (6, 0)\", \"actual\": 1, \"expected\": 1, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}