{
  "software": "apple-numbers",
  "function": "PERMUTATIONA",
  "native_application_execution": false,
  "checked_date": "2026-10-12",
  "method": "Independent mathematical/text-processing models, not Apple Numbers or Zoho Sheet execution; random tests check documented bounds/transforms, not randomness.",
  "official_function_reference": "https://support.apple.com/guide/functions/permutationa-f4880b18fe/15.4/web/1.0",
  "passed": 5,
  "total": 5,
  "cases": [
    {
      "software": "apple-numbers",
      "function": "PERMUTATIONA",
      "expression": "=PERMUTATIONA(3,2)",
      "variables": {},
      "expected": 9,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "PERMUTATIONA",
      "expression": "=PERMUTATIONA(5,3)",
      "variables": {},
      "expected": 125,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "PERMUTATIONA",
      "expression": "=PERMUTATIONA(4,0)",
      "variables": {},
      "expected": 1,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "PERMUTATIONA",
      "expression": "=PERMUTATIONA(8,2)",
      "variables": {},
      "expected": 64,
      "numeric": true,
      "scope": "recovered worked example"
    },
    {
      "software": "apple-numbers",
      "function": "PERMUTATIONA",
      "expression": "=PERMUTATIONA(10,4)",
      "variables": {},
      "expected": 10000,
      "numeric": true,
      "scope": "recovered worked example"
    }
  ],
  "independent_results": [
    {
      "case": 244,
      "software": "apple-numbers",
      "function": "PERMUTATIONA",
      "expression": "=PERMUTATIONA(3,2)",
      "actual_independent_model": 9,
      "expected": 9,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 245,
      "software": "apple-numbers",
      "function": "PERMUTATIONA",
      "expression": "=PERMUTATIONA(5,3)",
      "actual_independent_model": 125,
      "expected": 125,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 246,
      "software": "apple-numbers",
      "function": "PERMUTATIONA",
      "expression": "=PERMUTATIONA(4,0)",
      "actual_independent_model": 1,
      "expected": 1,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 247,
      "software": "apple-numbers",
      "function": "PERMUTATIONA",
      "expression": "=PERMUTATIONA(8,2)",
      "actual_independent_model": 64,
      "expected": 64,
      "passed": true,
      "scope": "recovered worked example"
    },
    {
      "case": 248,
      "software": "apple-numbers",
      "function": "PERMUTATIONA",
      "expression": "=PERMUTATIONA(10,4)",
      "actual_independent_model": 10000,
      "expected": 10000,
      "passed": true,
      "scope": "recovered worked example"
    }
  ]
}