{"abstract":"Only the unit-square placements are counted.","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. rows and cols are nonnegative cell counts; count all axis-aligned square placements of every positive integer side length. Exact operational definition: sum((rows-s+1)*(cols-s+1) for s in range(1,min(rows,cols)+1))","evaluation_group":"model-bfad958127b4b430","failed_approach":"The largest square size is excluded from the placement sum.","family":"xn-rectangular-grid-all-square-count","id":"FA-5646","implementations":{"attempt":{"sha256":"980a5bf6b74c97b6f3dce39256de220d25f2412fa6204ee4a08bfc86e6289b38","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(rows, cols):\n    return sum((rows-s+1)*(cols-s+1) for s in range(1,min(rows,cols)))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (2, 3)', solve(*(2, 3)), 8)\ncheck('fixture 2: (1, 4)', solve(*(1, 4)), 4)\ncheck('fixture 3: (0, 4)', solve(*(0, 4)), 0)\ncheck('fixture 4: (3, 3)', solve(*(3, 3)), 14)\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":"ef3aadbbabe179e3ada8702c03c071158b2a85ceee590cccb33d4eead2612577","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(rows, cols):\n    return rows*cols\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (2, 3)', solve(*(2, 3)), 8)\ncheck('fixture 2: (1, 4)', solve(*(1, 4)), 4)\ncheck('fixture 3: (0, 4)', solve(*(0, 4)), 0)\ncheck('fixture 4: (3, 3)', solve(*(3, 3)), 14)\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":"500ba89f6207bbc78085b7205e2fcbf2310fc2e6f75fcb25bd224f8c3c292597","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(rows, cols):\n    return sum((rows-s+1)*(cols-s+1) for s in range(1,min(rows,cols)+1))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (2, 3)', solve(*(2, 3)), 8)\ncheck('fixture 2: (1, 4)', solve(*(1, 4)), 4)\ncheck('fixture 3: (0, 4)', solve(*(0, 4)), 0)\ncheck('fixture 4: (3, 3)', solve(*(3, 3)), 14)\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-rectangular-grid-all-square-count","generated_at":"2026-09-29T14:37:51.864503+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 sum((rows-s+1)*(cols-s+1) for s in range(1,min(rows,cols)+1))","root_cause":"Only the unit-square placements are counted.","sha256":"5542dfbbf3732136e35bfaf948e1314b5755202ee6347c1307ddc32c9b16335c","title":"Rectangular grid all square count · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":43.948,"exit_code":1,"observations":[{"actual":6,"check":"fixture 1: (2, 3)","expected":8,"passed":false},{"actual":0,"check":"fixture 2: (1, 4)","expected":4,"passed":false},{"actual":0,"check":"fixture 3: (0, 4)","expected":0,"passed":true},{"actual":13,"check":"fixture 4: (3, 3)","expected":14,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 3)\", \"actual\": 6, \"expected\": 8, \"passed\": false}, {\"check\": \"fixture 2: (1, 4)\", \"actual\": 0, \"expected\": 4, \"passed\": false}, {\"check\": \"fixture 3: (0, 4)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (3, 3)\", \"actual\": 13, \"expected\": 14, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":136.714,"exit_code":1,"observations":[{"actual":6,"check":"fixture 1: (2, 3)","expected":8,"passed":false},{"actual":4,"check":"fixture 2: (1, 4)","expected":4,"passed":true},{"actual":0,"check":"fixture 3: (0, 4)","expected":0,"passed":true},{"actual":9,"check":"fixture 4: (3, 3)","expected":14,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 3)\", \"actual\": 6, \"expected\": 8, \"passed\": false}, {\"check\": \"fixture 2: (1, 4)\", \"actual\": 4, \"expected\": 4, \"passed\": true}, {\"check\": \"fixture 3: (0, 4)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (3, 3)\", \"actual\": 9, \"expected\": 14, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":43.759,"exit_code":0,"observations":[{"actual":8,"check":"fixture 1: (2, 3)","expected":8,"passed":true},{"actual":4,"check":"fixture 2: (1, 4)","expected":4,"passed":true},{"actual":0,"check":"fixture 3: (0, 4)","expected":0,"passed":true},{"actual":14,"check":"fixture 4: (3, 3)","expected":14,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 3)\", \"actual\": 8, \"expected\": 8, \"passed\": true}, {\"check\": \"fixture 2: (1, 4)\", \"actual\": 4, \"expected\": 4, \"passed\": true}, {\"check\": \"fixture 3: (0, 4)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (3, 3)\", \"actual\": 14, \"expected\": 14, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}