{"abstract":"Only one factor of five per multiple is counted.","category":"Number theory","checks":4,"contract":"Integer inputs; n is positive unless a zero or negative fixture explicitly extends that operation. A modulus is greater than one; p is prime; exponent k may be signed when an inverse exists. n>=0. Return the number of trailing base-ten zero digits in n!. Exact operational definition: sum(n//(5**i) for i in range(1,n.bit_length()+1))","evaluation_group":"model-55c9e3a3f4294dcc","failed_approach":"Testing whether n itself is divisible ignores factors in preceding terms.","family":"xn-trailing-factorial-zeroes","id":"FA-5531","implementations":{"attempt":{"sha256":"648998c2a70f3a5515cb0b9746376e4fbad4ed0d7cca196bc120b462ad533a95","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):\n    return sum(n%(5**i)==0 for i in range(1,n.bit_length()+1))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0,)', solve(*(0,)), 0)\ncheck('fixture 2: (5,)', solve(*(5,)), 1)\ncheck('fixture 3: (25,)', solve(*(25,)), 6)\ncheck('fixture 4: (100,)', solve(*(100,)), 24)\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":"25b782e337165a7a028c80b4bf3ede28f08a7e26ff090ec3edb88919cb96bfa6","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):\n    return n//5\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0,)', solve(*(0,)), 0)\ncheck('fixture 2: (5,)', solve(*(5,)), 1)\ncheck('fixture 3: (25,)', solve(*(25,)), 6)\ncheck('fixture 4: (100,)', solve(*(100,)), 24)\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":"b97651b939d6bb1adaeeb0589b14cfc74ba8e6c6efc8c8e10ae2d0f21370f0f2","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):\n    return sum(n//(5**i) for i in range(1,n.bit_length()+1))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0,)', solve(*(0,)), 0)\ncheck('fixture 2: (5,)', solve(*(5,)), 1)\ncheck('fixture 3: (25,)', solve(*(25,)), 6)\ncheck('fixture 4: (100,)', solve(*(100,)), 24)\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-trailing-factorial-zeroes","generated_at":"2026-09-29T14:37:50.568561+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. Number theory results depend on the stated convention.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return sum(n//(5**i) for i in range(1,n.bit_length()+1))","root_cause":"Only one factor of five per multiple is counted.","sha256":"ec352940b74310803c05a820ae9b663c81d92af31c35342dd59bdf718bd6422b","title":"Trailing factorial zeroes · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":45.988,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":0,"passed":true},{"actual":1,"check":"fixture 2: (5,)","expected":1,"passed":true},{"actual":2,"check":"fixture 3: (25,)","expected":6,"passed":false},{"actual":2,"check":"fixture 4: (100,)","expected":24,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (5,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (25,)\", \"actual\": 2, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 4: (100,)\", \"actual\": 2, \"expected\": 24, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":49.95,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":0,"passed":true},{"actual":1,"check":"fixture 2: (5,)","expected":1,"passed":true},{"actual":5,"check":"fixture 3: (25,)","expected":6,"passed":false},{"actual":20,"check":"fixture 4: (100,)","expected":24,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (5,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (25,)\", \"actual\": 5, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 4: (100,)\", \"actual\": 20, \"expected\": 24, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":43.725,"exit_code":0,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":0,"passed":true},{"actual":1,"check":"fixture 2: (5,)","expected":1,"passed":true},{"actual":6,"check":"fixture 3: (25,)","expected":6,"passed":true},{"actual":24,"check":"fixture 4: (100,)","expected":24,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (5,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 3: (25,)\", \"actual\": 6, \"expected\": 6, \"passed\": true}, {\"check\": \"fixture 4: (100,)\", \"actual\": 24, \"expected\": 24, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}