[
  {
    "family_id": "magnitude_estimation_000401",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10200 * 10100",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 10100?",
        "options": [
          "103019990",
          "103020020",
          "103020010",
          "103020000"
        ],
        "answer": "103020000",
        "correct_value": 103020000,
        "explanation": "Round to 10000: 10200≈10000, 10100≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10100 * 4937",
      "ns_shortcut": "Round 10100≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 4937?",
        "options": [
          "49863720",
          "49863710",
          "49863690",
          "49863700"
        ],
        "answer": "49863700",
        "correct_value": 49863700,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5835 * 6856",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5835 * 6856?",
        "options": [
          "40004770",
          "40004780",
          "40004760",
          "40004750"
        ],
        "answer": "40004760",
        "correct_value": 40004760,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000402",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10100 * 9900",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 9900?",
        "options": [
          "99990000",
          "99990020",
          "99990010",
          "99989990"
        ],
        "answer": "99990000",
        "correct_value": 99990000,
        "explanation": "Round to 10000: 10100≈10000, 9900≈10000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10100 * 4936",
      "ns_shortcut": "Round 10100≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 4936?",
        "options": [
          "49853600",
          "49853610",
          "49853590",
          "49853620"
        ],
        "answer": "49853600",
        "correct_value": 49853600,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6465 * 6928",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 6465 * 6928?",
        "options": [
          "44789540",
          "44789530",
          "44789520",
          "44789510"
        ],
        "answer": "44789520",
        "correct_value": 44789520,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000403",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10200 * 10200",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 10200?",
        "options": [
          "104039990",
          "104040000",
          "104040010",
          "104040020"
        ],
        "answer": "104040000",
        "correct_value": 104040000,
        "explanation": "Round to 10000: 10200≈10000, 10200≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10100 * 5043",
      "ns_shortcut": "Round 10100≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 5043?",
        "options": [
          "50934290",
          "50934310",
          "50934300",
          "50934320"
        ],
        "answer": "50934300",
        "correct_value": 50934300,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4527 * 4708",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4527 * 4708?",
        "options": [
          "21313136",
          "21313106",
          "21313116",
          "21313126"
        ],
        "answer": "21313116",
        "correct_value": 21313116,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000404",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9800 * 10200",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 10200?",
        "options": [
          "99960020",
          "99960000",
          "99960010",
          "99959990"
        ],
        "answer": "99960000",
        "correct_value": 99960000,
        "explanation": "Round to 10000: 9800≈10000, 10200≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 4950",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 4950?",
        "options": [
          "49005020",
          "49005010",
          "49004990",
          "49005000"
        ],
        "answer": "49005000",
        "correct_value": 49005000,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5067 * 5461",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5067 * 5461?",
        "options": [
          "27670877",
          "27670907",
          "27670887",
          "27670897"
        ],
        "answer": "27670887",
        "correct_value": 27670887,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000405",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9800 * 10100",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 10100?",
        "options": [
          "98980010",
          "98980020",
          "98980000",
          "98979990"
        ],
        "answer": "98980000",
        "correct_value": 98980000,
        "explanation": "Round to 10000: 9800≈10000, 10100≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 4892",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 4892?",
        "options": [
          "48430820",
          "48430800",
          "48430790",
          "48430810"
        ],
        "answer": "48430800",
        "correct_value": 48430800,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5392 * 5454",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5392 * 5454?",
        "options": [
          "29407958",
          "29407978",
          "29407988",
          "29407968"
        ],
        "answer": "29407968",
        "correct_value": 29407968,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000406",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9900 * 9800",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 9800?",
        "options": [
          "97019990",
          "97020020",
          "97020010",
          "97020000"
        ],
        "answer": "97020000",
        "correct_value": 97020000,
        "explanation": "Round to 10000: 9900≈10000, 9800≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 5002",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 5002?",
        "options": [
          "49519820",
          "49519800",
          "49519810",
          "49519790"
        ],
        "answer": "49519800",
        "correct_value": 49519800,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6302 * 4170",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 6302 * 4170?",
        "options": [
          "26279350",
          "26279360",
          "26279330",
          "26279340"
        ],
        "answer": "26279340",
        "correct_value": 26279340,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000407",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9900 * 10100",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 10100?",
        "options": [
          "99990000",
          "99989990",
          "99990020",
          "99990010"
        ],
        "answer": "99990000",
        "correct_value": 99990000,
        "explanation": "Round to 10000: 9900≈10000, 10100≈10000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9800 * 5164",
      "ns_shortcut": "Round 9800≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 5164?",
        "options": [
          "50607220",
          "50607210",
          "50607190",
          "50607200"
        ],
        "answer": "50607200",
        "correct_value": 50607200,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4630 * 6649",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4630 * 6649?",
        "options": [
          "30784860",
          "30784870",
          "30784880",
          "30784890"
        ],
        "answer": "30784870",
        "correct_value": 30784870,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000408",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9800 * 9900",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 9900?",
        "options": [
          "97020020",
          "97020000",
          "97020010",
          "97019990"
        ],
        "answer": "97020000",
        "correct_value": 97020000,
        "explanation": "Round to 10000: 9800≈10000, 9900≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 5003",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 5003?",
        "options": [
          "49529710",
          "49529690",
          "49529720",
          "49529700"
        ],
        "answer": "49529700",
        "correct_value": 49529700,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6067 * 4700",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 6067 * 4700?",
        "options": [
          "28514890",
          "28514920",
          "28514910",
          "28514900"
        ],
        "answer": "28514900",
        "correct_value": 28514900,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000409",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10200 * 10100",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 10100?",
        "options": [
          "103020020",
          "103019990",
          "103020000",
          "103020010"
        ],
        "answer": "103020000",
        "correct_value": 103020000,
        "explanation": "Round to 10000: 10200≈10000, 10100≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 4873",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 4873?",
        "options": [
          "48242700",
          "48242720",
          "48242690",
          "48242710"
        ],
        "answer": "48242700",
        "correct_value": 48242700,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5878 * 6113",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5878 * 6113?",
        "options": [
          "35932204",
          "35932224",
          "35932214",
          "35932234"
        ],
        "answer": "35932214",
        "correct_value": 35932214,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000410",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9900 * 9800",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 9800?",
        "options": [
          "97020020",
          "97020010",
          "97019990",
          "97020000"
        ],
        "answer": "97020000",
        "correct_value": 97020000,
        "explanation": "Round to 10000: 9900≈10000, 9800≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10200 * 4887",
      "ns_shortcut": "Round 10200≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 4887?",
        "options": [
          "49847410",
          "49847390",
          "49847420",
          "49847400"
        ],
        "answer": "49847400",
        "correct_value": 49847400,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5609 * 4150",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5609 * 4150?",
        "options": [
          "23277340",
          "23277350",
          "23277370",
          "23277360"
        ],
        "answer": "23277350",
        "correct_value": 23277350,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000411",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10100 * 10200",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 10200?",
        "options": [
          "103020000",
          "103020010",
          "103020020",
          "103019990"
        ],
        "answer": "103020000",
        "correct_value": 103020000,
        "explanation": "Round to 10000: 10100≈10000, 10200≈10000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10200 * 5157",
      "ns_shortcut": "Round 10200≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 5157?",
        "options": [
          "52601410",
          "52601420",
          "52601400",
          "52601390"
        ],
        "answer": "52601400",
        "correct_value": 52601400,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6160 * 6499",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 6160 * 6499?",
        "options": [
          "40033840",
          "40033830",
          "40033860",
          "40033850"
        ],
        "answer": "40033840",
        "correct_value": 40033840,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000412",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10200 * 9900",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 9900?",
        "options": [
          "100980000",
          "100980010",
          "100980020",
          "100979990"
        ],
        "answer": "100980000",
        "correct_value": 100980000,
        "explanation": "Round to 10000: 10200≈10000, 9900≈10000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10200 * 5039",
      "ns_shortcut": "Round 10200≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 5039?",
        "options": [
          "51397820",
          "51397810",
          "51397800",
          "51397790"
        ],
        "answer": "51397800",
        "correct_value": 51397800,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4150 * 6200",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4150 * 6200?",
        "options": [
          "25729990",
          "25730000",
          "25730010",
          "25730020"
        ],
        "answer": "25730000",
        "correct_value": 25730000,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000413",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10100 * 9900",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 9900?",
        "options": [
          "99989990",
          "99990010",
          "99990020",
          "99990000"
        ],
        "answer": "99990000",
        "correct_value": 99990000,
        "explanation": "Round to 10000: 10100≈10000, 9900≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 5056",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 5056?",
        "options": [
          "50054400",
          "50054390",
          "50054410",
          "50054420"
        ],
        "answer": "50054400",
        "correct_value": 50054400,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6210 * 6425",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 6210 * 6425?",
        "options": [
          "39899240",
          "39899260",
          "39899250",
          "39899270"
        ],
        "answer": "39899250",
        "correct_value": 39899250,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000414",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10200 * 9800",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 9800?",
        "options": [
          "99959990",
          "99960020",
          "99960010",
          "99960000"
        ],
        "answer": "99960000",
        "correct_value": 99960000,
        "explanation": "Round to 10000: 10200≈10000, 9800≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 4889",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 4889?",
        "options": [
          "48401090",
          "48401110",
          "48401100",
          "48401120"
        ],
        "answer": "48401100",
        "correct_value": 48401100,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5837 * 5219",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5837 * 5219?",
        "options": [
          "30463293",
          "30463323",
          "30463313",
          "30463303"
        ],
        "answer": "30463303",
        "correct_value": 30463303,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000415",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9900 * 9900",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 9900?",
        "options": [
          "98010000",
          "98009990",
          "98010010",
          "98010020"
        ],
        "answer": "98010000",
        "correct_value": 98010000,
        "explanation": "Round to 10000: 9900≈10000, 9900≈10000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9800 * 5115",
      "ns_shortcut": "Round 9800≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 5115?",
        "options": [
          "50127010",
          "50126990",
          "50127000",
          "50127020"
        ],
        "answer": "50127000",
        "correct_value": 50127000,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4430 * 5341",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4430 * 5341?",
        "options": [
          "23660630",
          "23660650",
          "23660620",
          "23660640"
        ],
        "answer": "23660630",
        "correct_value": 23660630,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000416",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9800 * 9900",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 9900?",
        "options": [
          "97020020",
          "97020000",
          "97020010",
          "97019990"
        ],
        "answer": "97020000",
        "correct_value": 97020000,
        "explanation": "Round to 10000: 9800≈10000, 9900≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 5127",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 5127?",
        "options": [
          "50757320",
          "50757300",
          "50757310",
          "50757290"
        ],
        "answer": "50757300",
        "correct_value": 50757300,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4878 * 5826",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4878 * 5826?",
        "options": [
          "28419218",
          "28419248",
          "28419238",
          "28419228"
        ],
        "answer": "28419228",
        "correct_value": 28419228,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000417",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10200 * 10100",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 10100?",
        "options": [
          "103020000",
          "103020010",
          "103020020",
          "103019990"
        ],
        "answer": "103020000",
        "correct_value": 103020000,
        "explanation": "Round to 10000: 10200≈10000, 10100≈10000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 5024",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 5024?",
        "options": [
          "49737620",
          "49737590",
          "49737610",
          "49737600"
        ],
        "answer": "49737600",
        "correct_value": 49737600,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4666 * 4590",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4666 * 4590?",
        "options": [
          "21416940",
          "21416960",
          "21416930",
          "21416950"
        ],
        "answer": "21416940",
        "correct_value": 21416940,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000418",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9900 * 9800",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 9800?",
        "options": [
          "97020000",
          "97020020",
          "97019990",
          "97020010"
        ],
        "answer": "97020000",
        "correct_value": 97020000,
        "explanation": "Round to 10000: 9900≈10000, 9800≈10000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10200 * 5030",
      "ns_shortcut": "Round 10200≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 5030?",
        "options": [
          "51305990",
          "51306020",
          "51306000",
          "51306010"
        ],
        "answer": "51306000",
        "correct_value": 51306000,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4485 * 6463",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4485 * 6463?",
        "options": [
          "28986565",
          "28986575",
          "28986555",
          "28986545"
        ],
        "answer": "28986555",
        "correct_value": 28986555,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000419",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10100 * 10100",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 10100?",
        "options": [
          "102010010",
          "102009990",
          "102010020",
          "102010000"
        ],
        "answer": "102010000",
        "correct_value": 102010000,
        "explanation": "Round to 10000: 10100≈10000, 10100≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9800 * 5093",
      "ns_shortcut": "Round 9800≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 5093?",
        "options": [
          "49911390",
          "49911410",
          "49911420",
          "49911400"
        ],
        "answer": "49911400",
        "correct_value": 49911400,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5203 * 5989",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5203 * 5989?",
        "options": [
          "31160777",
          "31160787",
          "31160757",
          "31160767"
        ],
        "answer": "31160767",
        "correct_value": 31160767,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000420",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10200 * 9800",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 9800?",
        "options": [
          "99959990",
          "99960000",
          "99960010",
          "99960020"
        ],
        "answer": "99960000",
        "correct_value": 99960000,
        "explanation": "Round to 10000: 10200≈10000, 9800≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10200 * 4932",
      "ns_shortcut": "Round 10200≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 4932?",
        "options": [
          "50306410",
          "50306390",
          "50306400",
          "50306420"
        ],
        "answer": "50306400",
        "correct_value": 50306400,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6241 * 5427",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 6241 * 5427?",
        "options": [
          "33869927",
          "33869917",
          "33869897",
          "33869907"
        ],
        "answer": "33869907",
        "correct_value": 33869907,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000421",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10200 * 10100",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 10100?",
        "options": [
          "103020000",
          "103020020",
          "103020010",
          "103019990"
        ],
        "answer": "103020000",
        "correct_value": 103020000,
        "explanation": "Round to 10000: 10200≈10000, 10100≈10000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 4808",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 4808?",
        "options": [
          "47599190",
          "47599210",
          "47599200",
          "47599220"
        ],
        "answer": "47599200",
        "correct_value": 47599200,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5841 * 6731",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5841 * 6731?",
        "options": [
          "39315791",
          "39315781",
          "39315771",
          "39315761"
        ],
        "answer": "39315771",
        "correct_value": 39315771,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000422",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9800 * 10200",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 10200?",
        "options": [
          "99960020",
          "99960010",
          "99960000",
          "99959990"
        ],
        "answer": "99960000",
        "correct_value": 99960000,
        "explanation": "Round to 10000: 9800≈10000, 10200≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 4800",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 4800?",
        "options": [
          "47520020",
          "47519990",
          "47520010",
          "47520000"
        ],
        "answer": "47520000",
        "correct_value": 47520000,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5135 * 6644",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5135 * 6644?",
        "options": [
          "34116950",
          "34116960",
          "34116930",
          "34116940"
        ],
        "answer": "34116940",
        "correct_value": 34116940,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000423",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10100 * 9800",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 9800?",
        "options": [
          "98980010",
          "98980020",
          "98979990",
          "98980000"
        ],
        "answer": "98980000",
        "correct_value": 98980000,
        "explanation": "Round to 10000: 10100≈10000, 9800≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9800 * 4976",
      "ns_shortcut": "Round 9800≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 4976?",
        "options": [
          "48764790",
          "48764810",
          "48764820",
          "48764800"
        ],
        "answer": "48764800",
        "correct_value": 48764800,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4491 * 6695",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4491 * 6695?",
        "options": [
          "30067265",
          "30067235",
          "30067245",
          "30067255"
        ],
        "answer": "30067245",
        "correct_value": 30067245,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000424",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9900 * 9900",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 9900?",
        "options": [
          "98010020",
          "98010010",
          "98010000",
          "98009990"
        ],
        "answer": "98010000",
        "correct_value": 98010000,
        "explanation": "Round to 10000: 9900≈10000, 9900≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9800 * 5030",
      "ns_shortcut": "Round 9800≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 5030?",
        "options": [
          "49294020",
          "49293990",
          "49294010",
          "49294000"
        ],
        "answer": "49294000",
        "correct_value": 49294000,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5391 * 5789",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5391 * 5789?",
        "options": [
          "31208519",
          "31208499",
          "31208489",
          "31208509"
        ],
        "answer": "31208499",
        "correct_value": 31208499,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000425",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10100 * 10200",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 10200?",
        "options": [
          "103020010",
          "103019990",
          "103020000",
          "103020020"
        ],
        "answer": "103020000",
        "correct_value": 103020000,
        "explanation": "Round to 10000: 10100≈10000, 10200≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 4899",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 4899?",
        "options": [
          "48500120",
          "48500090",
          "48500110",
          "48500100"
        ],
        "answer": "48500100",
        "correct_value": 48500100,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4747 * 5045",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4747 * 5045?",
        "options": [
          "23948635",
          "23948625",
          "23948605",
          "23948615"
        ],
        "answer": "23948615",
        "correct_value": 23948615,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000426",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10200 * 9900",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 9900?",
        "options": [
          "100979990",
          "100980010",
          "100980020",
          "100980000"
        ],
        "answer": "100980000",
        "correct_value": 100980000,
        "explanation": "Round to 10000: 10200≈10000, 9900≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 5179",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 5179?",
        "options": [
          "51272090",
          "51272110",
          "51272100",
          "51272120"
        ],
        "answer": "51272100",
        "correct_value": 51272100,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4403 * 5309",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4403 * 5309?",
        "options": [
          "23375527",
          "23375547",
          "23375517",
          "23375537"
        ],
        "answer": "23375527",
        "correct_value": 23375527,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000427",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10100 * 10200",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 10200?",
        "options": [
          "103020010",
          "103020020",
          "103019990",
          "103020000"
        ],
        "answer": "103020000",
        "correct_value": 103020000,
        "explanation": "Round to 10000: 10100≈10000, 10200≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10100 * 4800",
      "ns_shortcut": "Round 10100≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 4800?",
        "options": [
          "48480010",
          "48480000",
          "48480020",
          "48479990"
        ],
        "answer": "48480000",
        "correct_value": 48480000,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4470 * 5102",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4470 * 5102?",
        "options": [
          "22805930",
          "22805960",
          "22805950",
          "22805940"
        ],
        "answer": "22805940",
        "correct_value": 22805940,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000428",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10200 * 9800",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 9800?",
        "options": [
          "99960020",
          "99960010",
          "99960000",
          "99959990"
        ],
        "answer": "99960000",
        "correct_value": 99960000,
        "explanation": "Round to 10000: 10200≈10000, 9800≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10200 * 4808",
      "ns_shortcut": "Round 10200≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 4808?",
        "options": [
          "49041610",
          "49041600",
          "49041620",
          "49041590"
        ],
        "answer": "49041600",
        "correct_value": 49041600,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5007 * 6271",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5007 * 6271?",
        "options": [
          "31398897",
          "31398917",
          "31398887",
          "31398907"
        ],
        "answer": "31398897",
        "correct_value": 31398897,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000429",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10200 * 9800",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 9800?",
        "options": [
          "99960020",
          "99959990",
          "99960000",
          "99960010"
        ],
        "answer": "99960000",
        "correct_value": 99960000,
        "explanation": "Round to 10000: 10200≈10000, 9800≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10100 * 4829",
      "ns_shortcut": "Round 10100≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 4829?",
        "options": [
          "48772910",
          "48772890",
          "48772920",
          "48772900"
        ],
        "answer": "48772900",
        "correct_value": 48772900,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6272 * 5849",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 6272 * 5849?",
        "options": [
          "36684948",
          "36684938",
          "36684918",
          "36684928"
        ],
        "answer": "36684928",
        "correct_value": 36684928,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000430",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10100 * 9900",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 9900?",
        "options": [
          "99990020",
          "99990010",
          "99989990",
          "99990000"
        ],
        "answer": "99990000",
        "correct_value": 99990000,
        "explanation": "Round to 10000: 10100≈10000, 9900≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9800 * 5084",
      "ns_shortcut": "Round 9800≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 5084?",
        "options": [
          "49823210",
          "49823200",
          "49823220",
          "49823190"
        ],
        "answer": "49823200",
        "correct_value": 49823200,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5438 * 6588",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5438 * 6588?",
        "options": [
          "35825544",
          "35825534",
          "35825564",
          "35825554"
        ],
        "answer": "35825544",
        "correct_value": 35825544,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000431",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9800 * 9900",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 9900?",
        "options": [
          "97020020",
          "97019990",
          "97020010",
          "97020000"
        ],
        "answer": "97020000",
        "correct_value": 97020000,
        "explanation": "Round to 10000: 9800≈10000, 9900≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10100 * 4988",
      "ns_shortcut": "Round 10100≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 4988?",
        "options": [
          "50378820",
          "50378810",
          "50378790",
          "50378800"
        ],
        "answer": "50378800",
        "correct_value": 50378800,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5768 * 4862",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5768 * 4862?",
        "options": [
          "28044016",
          "28044026",
          "28044006",
          "28044036"
        ],
        "answer": "28044016",
        "correct_value": 28044016,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000432",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10100 * 10200",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 10200?",
        "options": [
          "103019990",
          "103020010",
          "103020000",
          "103020020"
        ],
        "answer": "103020000",
        "correct_value": 103020000,
        "explanation": "Round to 10000: 10100≈10000, 10200≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10200 * 5184",
      "ns_shortcut": "Round 10200≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 5184?",
        "options": [
          "52876790",
          "52876810",
          "52876820",
          "52876800"
        ],
        "answer": "52876800",
        "correct_value": 52876800,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4064 * 6832",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4064 * 6832?",
        "options": [
          "27765238",
          "27765248",
          "27765268",
          "27765258"
        ],
        "answer": "27765248",
        "correct_value": 27765248,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000433",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10200 * 9800",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 9800?",
        "options": [
          "99960010",
          "99959990",
          "99960020",
          "99960000"
        ],
        "answer": "99960000",
        "correct_value": 99960000,
        "explanation": "Round to 10000: 10200≈10000, 9800≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 4877",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 4877?",
        "options": [
          "48282310",
          "48282290",
          "48282320",
          "48282300"
        ],
        "answer": "48282300",
        "correct_value": 48282300,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6657 * 6666",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 6657 * 6666?",
        "options": [
          "44375572",
          "44375552",
          "44375582",
          "44375562"
        ],
        "answer": "44375562",
        "correct_value": 44375562,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000434",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10200 * 9800",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 9800?",
        "options": [
          "99960000",
          "99959990",
          "99960010",
          "99960020"
        ],
        "answer": "99960000",
        "correct_value": 99960000,
        "explanation": "Round to 10000: 10200≈10000, 9800≈10000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 4938",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 4938?",
        "options": [
          "48886190",
          "48886210",
          "48886220",
          "48886200"
        ],
        "answer": "48886200",
        "correct_value": 48886200,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5516 * 4789",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5516 * 4789?",
        "options": [
          "26416134",
          "26416144",
          "26416124",
          "26416114"
        ],
        "answer": "26416124",
        "correct_value": 26416124,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000435",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9800 * 10100",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 10100?",
        "options": [
          "98980010",
          "98979990",
          "98980000",
          "98980020"
        ],
        "answer": "98980000",
        "correct_value": 98980000,
        "explanation": "Round to 10000: 9800≈10000, 10100≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 5140",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 5140?",
        "options": [
          "50885990",
          "50886000",
          "50886020",
          "50886010"
        ],
        "answer": "50886000",
        "correct_value": 50886000,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5485 * 4149",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5485 * 4149?",
        "options": [
          "22757255",
          "22757265",
          "22757275",
          "22757285"
        ],
        "answer": "22757265",
        "correct_value": 22757265,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000436",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9800 * 9900",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 9900?",
        "options": [
          "97020020",
          "97020010",
          "97020000",
          "97019990"
        ],
        "answer": "97020000",
        "correct_value": 97020000,
        "explanation": "Round to 10000: 9800≈10000, 9900≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10200 * 5140",
      "ns_shortcut": "Round 10200≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 5140?",
        "options": [
          "52427990",
          "52428000",
          "52428010",
          "52428020"
        ],
        "answer": "52428000",
        "correct_value": 52428000,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4266 * 6408",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4266 * 6408?",
        "options": [
          "27336518",
          "27336528",
          "27336548",
          "27336538"
        ],
        "answer": "27336528",
        "correct_value": 27336528,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000437",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9900 * 10100",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 10100?",
        "options": [
          "99990000",
          "99989990",
          "99990020",
          "99990010"
        ],
        "answer": "99990000",
        "correct_value": 99990000,
        "explanation": "Round to 10000: 9900≈10000, 10100≈10000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10200 * 4900",
      "ns_shortcut": "Round 10200≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 4900?",
        "options": [
          "49979990",
          "49980000",
          "49980010",
          "49980020"
        ],
        "answer": "49980000",
        "correct_value": 49980000,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6787 * 6293",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 6787 * 6293?",
        "options": [
          "42710611",
          "42710601",
          "42710591",
          "42710581"
        ],
        "answer": "42710591",
        "correct_value": 42710591,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000438",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9800 * 10100",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 10100?",
        "options": [
          "98980000",
          "98980020",
          "98980010",
          "98979990"
        ],
        "answer": "98980000",
        "correct_value": 98980000,
        "explanation": "Round to 10000: 9800≈10000, 10100≈10000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9800 * 5007",
      "ns_shortcut": "Round 9800≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 5007?",
        "options": [
          "49068590",
          "49068600",
          "49068610",
          "49068620"
        ],
        "answer": "49068600",
        "correct_value": 49068600,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6117 * 4177",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 6117 * 4177?",
        "options": [
          "25550729",
          "25550699",
          "25550709",
          "25550719"
        ],
        "answer": "25550709",
        "correct_value": 25550709,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000439",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10200 * 10200",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 10200?",
        "options": [
          "104039990",
          "104040010",
          "104040000",
          "104040020"
        ],
        "answer": "104040000",
        "correct_value": 104040000,
        "explanation": "Round to 10000: 10200≈10000, 10200≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10200 * 5025",
      "ns_shortcut": "Round 10200≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 5025?",
        "options": [
          "51254990",
          "51255020",
          "51255010",
          "51255000"
        ],
        "answer": "51255000",
        "correct_value": 51255000,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4923 * 6823",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4923 * 6823?",
        "options": [
          "33589639",
          "33589649",
          "33589629",
          "33589619"
        ],
        "answer": "33589629",
        "correct_value": 33589629,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000440",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9900 * 9900",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 9900?",
        "options": [
          "98009990",
          "98010000",
          "98010010",
          "98010020"
        ],
        "answer": "98010000",
        "correct_value": 98010000,
        "explanation": "Round to 10000: 9900≈10000, 9900≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10200 * 5084",
      "ns_shortcut": "Round 10200≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 5084?",
        "options": [
          "51856800",
          "51856820",
          "51856810",
          "51856790"
        ],
        "answer": "51856800",
        "correct_value": 51856800,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6426 * 6564",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 6426 * 6564?",
        "options": [
          "42180254",
          "42180264",
          "42180274",
          "42180284"
        ],
        "answer": "42180264",
        "correct_value": 42180264,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000441",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9800 * 10200",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 10200?",
        "options": [
          "99960020",
          "99960000",
          "99959990",
          "99960010"
        ],
        "answer": "99960000",
        "correct_value": 99960000,
        "explanation": "Round to 10000: 9800≈10000, 10200≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10200 * 4948",
      "ns_shortcut": "Round 10200≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 4948?",
        "options": [
          "50469610",
          "50469620",
          "50469590",
          "50469600"
        ],
        "answer": "50469600",
        "correct_value": 50469600,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4390 * 6560",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4390 * 6560?",
        "options": [
          "28798410",
          "28798400",
          "28798420",
          "28798390"
        ],
        "answer": "28798400",
        "correct_value": 28798400,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000442",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9800 * 9800",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 9800?",
        "options": [
          "96039990",
          "96040020",
          "96040010",
          "96040000"
        ],
        "answer": "96040000",
        "correct_value": 96040000,
        "explanation": "Round to 10000: 9800≈10000, 9800≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10200 * 4812",
      "ns_shortcut": "Round 10200≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 4812?",
        "options": [
          "49082420",
          "49082400",
          "49082410",
          "49082390"
        ],
        "answer": "49082400",
        "correct_value": 49082400,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4223 * 5233",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4223 * 5233?",
        "options": [
          "22098969",
          "22098979",
          "22098959",
          "22098949"
        ],
        "answer": "22098959",
        "correct_value": 22098959,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000443",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9800 * 9800",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 9800?",
        "options": [
          "96040000",
          "96039990",
          "96040010",
          "96040020"
        ],
        "answer": "96040000",
        "correct_value": 96040000,
        "explanation": "Round to 10000: 9800≈10000, 9800≈10000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10200 * 5197",
      "ns_shortcut": "Round 10200≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 5197?",
        "options": [
          "53009410",
          "53009390",
          "53009400",
          "53009420"
        ],
        "answer": "53009400",
        "correct_value": 53009400,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5856 * 5571",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5856 * 5571?",
        "options": [
          "32623796",
          "32623776",
          "32623786",
          "32623766"
        ],
        "answer": "32623776",
        "correct_value": 32623776,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000444",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10100 * 9800",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 9800?",
        "options": [
          "98980000",
          "98980010",
          "98980020",
          "98979990"
        ],
        "answer": "98980000",
        "correct_value": 98980000,
        "explanation": "Round to 10000: 10100≈10000, 9800≈10000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10100 * 5021",
      "ns_shortcut": "Round 10100≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 5021?",
        "options": [
          "50712110",
          "50712100",
          "50712120",
          "50712090"
        ],
        "answer": "50712100",
        "correct_value": 50712100,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6427 * 4792",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 6427 * 4792?",
        "options": [
          "30798184",
          "30798174",
          "30798204",
          "30798194"
        ],
        "answer": "30798184",
        "correct_value": 30798184,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000445",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10100 * 10200",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 10200?",
        "options": [
          "103020000",
          "103020010",
          "103020020",
          "103019990"
        ],
        "answer": "103020000",
        "correct_value": 103020000,
        "explanation": "Round to 10000: 10100≈10000, 10200≈10000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 5136",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 5136?",
        "options": [
          "50846390",
          "50846420",
          "50846400",
          "50846410"
        ],
        "answer": "50846400",
        "correct_value": 50846400,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4521 * 5275",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4521 * 5275?",
        "options": [
          "23848275",
          "23848285",
          "23848295",
          "23848265"
        ],
        "answer": "23848275",
        "correct_value": 23848275,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000446",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10100 * 9900",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 9900?",
        "options": [
          "99990000",
          "99990020",
          "99989990",
          "99990010"
        ],
        "answer": "99990000",
        "correct_value": 99990000,
        "explanation": "Round to 10000: 10100≈10000, 9900≈10000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9900 * 5145",
      "ns_shortcut": "Round 9900≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 5145?",
        "options": [
          "50935520",
          "50935500",
          "50935490",
          "50935510"
        ],
        "answer": "50935500",
        "correct_value": 50935500,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4233 * 4971",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4233 * 4971?",
        "options": [
          "21042233",
          "21042263",
          "21042253",
          "21042243"
        ],
        "answer": "21042243",
        "correct_value": 21042243,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000447",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9900 * 9900",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9900 * 9900?",
        "options": [
          "98010020",
          "98009990",
          "98010000",
          "98010010"
        ],
        "answer": "98010000",
        "correct_value": 98010000,
        "explanation": "Round to 10000: 9900≈10000, 9900≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10200 * 4961",
      "ns_shortcut": "Round 10200≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 4961?",
        "options": [
          "50602210",
          "50602220",
          "50602190",
          "50602200"
        ],
        "answer": "50602200",
        "correct_value": 50602200,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6455 * 6835",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 6455 * 6835?",
        "options": [
          "44119925",
          "44119935",
          "44119915",
          "44119945"
        ],
        "answer": "44119925",
        "correct_value": 44119925,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000448",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10100 * 10200",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 10200?",
        "options": [
          "103020010",
          "103019990",
          "103020000",
          "103020020"
        ],
        "answer": "103020000",
        "correct_value": 103020000,
        "explanation": "Round to 10000: 10100≈10000, 10200≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9800 * 4874",
      "ns_shortcut": "Round 9800≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 4874?",
        "options": [
          "47765220",
          "47765200",
          "47765190",
          "47765210"
        ],
        "answer": "47765200",
        "correct_value": 47765200,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4014 * 6615",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 4014 * 6615?",
        "options": [
          "26552600",
          "26552610",
          "26552630",
          "26552620"
        ],
        "answer": "26552610",
        "correct_value": 26552610,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000449",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10200 * 9900",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10200 * 9900?",
        "options": [
          "100980000",
          "100980020",
          "100979990",
          "100980010"
        ],
        "answer": "100980000",
        "correct_value": 100980000,
        "explanation": "Round to 10000: 10200≈10000, 9900≈10000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10100 * 5179",
      "ns_shortcut": "Round 10100≈10000, then adjust.",
      "shortcut_strength": 0.7969999999999999,
      "pure_math": {
        "question": "Which of the following is the best estimate for 10100 * 5179?",
        "options": [
          "52307910",
          "52307900",
          "52307890",
          "52307920"
        ],
        "answer": "52307900",
        "correct_value": 52307900,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5485 * 4039",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5485 * 4039?",
        "options": [
          "22153935",
          "22153905",
          "22153925",
          "22153915"
        ],
        "answer": "22153915",
        "correct_value": 22153915,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "magnitude_estimation_000450",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9800 * 9900",
      "ns_shortcut": "Round both to 10000 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 9900?",
        "options": [
          "97019990",
          "97020000",
          "97020010",
          "97020020"
        ],
        "answer": "97020000",
        "correct_value": 97020000,
        "explanation": "Round to 10000: 9800≈10000, 9900≈10000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9800 * 4997",
      "ns_shortcut": "Round 9800≈10000, then adjust.",
      "shortcut_strength": 0.794,
      "pure_math": {
        "question": "Which of the following is the best estimate for 9800 * 4997?",
        "options": [
          "48970620",
          "48970610",
          "48970600",
          "48970590"
        ],
        "answer": "48970600",
        "correct_value": 48970600,
        "explanation": "One number rounds cleanly, the other less so."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5162 * 4712",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 5162 * 4712?",
        "options": [
          "24323364",
          "24323344",
          "24323334",
          "24323354"
        ],
        "answer": "24323344",
        "correct_value": 24323344,
        "explanation": "Both numbers far from any round target; no clean rounding shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000451",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10001 * 5029",
      "ns_shortcut": "Use (10000+1)*m = 10000*m + 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 10001 * 5029?",
        "options": [
          "50295019",
          "50295049",
          "50295029",
          "50295039"
        ],
        "answer": "50295029",
        "correct_value": 50295029,
        "explanation": "Distributive: (10000+1)*5029 = 10000*5029 + 1*5029."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9950 * 3967",
      "ns_shortcut": "Use (10000-50)*m, correction is 50*3967.",
      "shortcut_strength": 0.9,
      "pure_math": {
        "question": "What is 9950 * 3967?",
        "options": [
          "39471640",
          "39471670",
          "39471650",
          "39471660"
        ],
        "answer": "39471650",
        "correct_value": 39471650,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5551 * 6681",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5551 * 6681?",
        "options": [
          "37086251",
          "37086221",
          "37086241",
          "37086231"
        ],
        "answer": "37086231",
        "correct_value": 37086231,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000452",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10001 * 8474",
      "ns_shortcut": "Use (10000+1)*m = 10000*m + 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 10001 * 8474?",
        "options": [
          "84748474",
          "84748494",
          "84748464",
          "84748484"
        ],
        "answer": "84748474",
        "correct_value": 84748474,
        "explanation": "Distributive: (10000+1)*8474 = 10000*8474 + 1*8474."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10031 * 4852",
      "ns_shortcut": "Use (10000+31)*m, correction is 31*4852.",
      "shortcut_strength": 0.938,
      "pure_math": {
        "question": "What is 10031 * 4852?",
        "options": [
          "48670422",
          "48670412",
          "48670432",
          "48670402"
        ],
        "answer": "48670412",
        "correct_value": 48670412,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4484 * 4590",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 4484 * 4590?",
        "options": [
          "20581550",
          "20581580",
          "20581560",
          "20581570"
        ],
        "answer": "20581560",
        "correct_value": 20581560,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000453",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10002 * 7131",
      "ns_shortcut": "Use (10000+2)*m = 10000*m + 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 10002 * 7131?",
        "options": [
          "71324262",
          "71324272",
          "71324252",
          "71324282"
        ],
        "answer": "71324262",
        "correct_value": 71324262,
        "explanation": "Distributive: (10000+2)*7131 = 10000*7131 + 2*7131."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10024 * 3857",
      "ns_shortcut": "Use (10000+24)*m, correction is 24*3857.",
      "shortcut_strength": 0.952,
      "pure_math": {
        "question": "What is 10024 * 3857?",
        "options": [
          "38662578",
          "38662588",
          "38662568",
          "38662558"
        ],
        "answer": "38662568",
        "correct_value": 38662568,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6192 * 5203",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6192 * 5203?",
        "options": [
          "32216996",
          "32216976",
          "32216966",
          "32216986"
        ],
        "answer": "32216976",
        "correct_value": 32216976,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000454",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9998 * 5588",
      "ns_shortcut": "Use (10000-2)*m = 10000*m - 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 9998 * 5588?",
        "options": [
          "55868824",
          "55868814",
          "55868844",
          "55868834"
        ],
        "answer": "55868824",
        "correct_value": 55868824,
        "explanation": "Distributive: (10000-2)*5588 = 10000*5588 - 2*5588."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9969 * 1777",
      "ns_shortcut": "Use (10000-31)*m, correction is 31*1777.",
      "shortcut_strength": 0.938,
      "pure_math": {
        "question": "What is 9969 * 1777?",
        "options": [
          "17714923",
          "17714913",
          "17714933",
          "17714903"
        ],
        "answer": "17714913",
        "correct_value": 17714913,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4684 * 6082",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 4684 * 6082?",
        "options": [
          "28488088",
          "28488098",
          "28488108",
          "28488078"
        ],
        "answer": "28488088",
        "correct_value": 28488088,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000455",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10002 * 9501",
      "ns_shortcut": "Use (10000+2)*m = 10000*m + 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 10002 * 9501?",
        "options": [
          "95029022",
          "95029012",
          "95029002",
          "95028992"
        ],
        "answer": "95029002",
        "correct_value": 95029002,
        "explanation": "Distributive: (10000+2)*9501 = 10000*9501 + 2*9501."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9980 * 4023",
      "ns_shortcut": "Use (10000-20)*m, correction is 20*4023.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 9980 * 4023?",
        "options": [
          "40149550",
          "40149540",
          "40149530",
          "40149560"
        ],
        "answer": "40149540",
        "correct_value": 40149540,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5939 * 5098",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5939 * 5098?",
        "options": [
          "30277032",
          "30277022",
          "30277042",
          "30277012"
        ],
        "answer": "30277022",
        "correct_value": 30277022,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000456",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9999 * 4596",
      "ns_shortcut": "Use (10000-1)*m = 10000*m - 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 9999 * 4596?",
        "options": [
          "45955424",
          "45955404",
          "45955394",
          "45955414"
        ],
        "answer": "45955404",
        "correct_value": 45955404,
        "explanation": "Distributive: (10000-1)*4596 = 10000*4596 - 1*4596."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10016 * 2377",
      "ns_shortcut": "Use (10000+16)*m, correction is 16*2377.",
      "shortcut_strength": 0.968,
      "pure_math": {
        "question": "What is 10016 * 2377?",
        "options": [
          "23808032",
          "23808042",
          "23808022",
          "23808052"
        ],
        "answer": "23808032",
        "correct_value": 23808032,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6339 * 4642",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6339 * 4642?",
        "options": [
          "29425628",
          "29425638",
          "29425648",
          "29425658"
        ],
        "answer": "29425638",
        "correct_value": 29425638,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000457",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9999 * 2376",
      "ns_shortcut": "Use (10000-1)*m = 10000*m - 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 9999 * 2376?",
        "options": [
          "23757624",
          "23757614",
          "23757634",
          "23757644"
        ],
        "answer": "23757624",
        "correct_value": 23757624,
        "explanation": "Distributive: (10000-1)*2376 = 10000*2376 - 1*2376."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9950 * 7257",
      "ns_shortcut": "Use (10000-50)*m, correction is 50*7257.",
      "shortcut_strength": 0.9,
      "pure_math": {
        "question": "What is 9950 * 7257?",
        "options": [
          "72207140",
          "72207170",
          "72207150",
          "72207160"
        ],
        "answer": "72207150",
        "correct_value": 72207150,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5744 * 5846",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5744 * 5846?",
        "options": [
          "33579424",
          "33579444",
          "33579434",
          "33579414"
        ],
        "answer": "33579424",
        "correct_value": 33579424,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000458",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10001 * 9151",
      "ns_shortcut": "Use (10000+1)*m = 10000*m + 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 10001 * 9151?",
        "options": [
          "91519151",
          "91519141",
          "91519161",
          "91519171"
        ],
        "answer": "91519151",
        "correct_value": 91519151,
        "explanation": "Distributive: (10000+1)*9151 = 10000*9151 + 1*9151."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9979 * 5246",
      "ns_shortcut": "Use (10000-21)*m, correction is 21*5246.",
      "shortcut_strength": 0.958,
      "pure_math": {
        "question": "What is 9979 * 5246?",
        "options": [
          "52349844",
          "52349854",
          "52349834",
          "52349824"
        ],
        "answer": "52349834",
        "correct_value": 52349834,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6642 * 4309",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6642 * 4309?",
        "options": [
          "28620368",
          "28620388",
          "28620378",
          "28620398"
        ],
        "answer": "28620378",
        "correct_value": 28620378,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000459",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9998 * 5528",
      "ns_shortcut": "Use (10000-2)*m = 10000*m - 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 9998 * 5528?",
        "options": [
          "55268934",
          "55268964",
          "55268944",
          "55268954"
        ],
        "answer": "55268944",
        "correct_value": 55268944,
        "explanation": "Distributive: (10000-2)*5528 = 10000*5528 - 2*5528."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10022 * 2810",
      "ns_shortcut": "Use (10000+22)*m, correction is 22*2810.",
      "shortcut_strength": 0.956,
      "pure_math": {
        "question": "What is 10022 * 2810?",
        "options": [
          "28161840",
          "28161830",
          "28161820",
          "28161810"
        ],
        "answer": "28161820",
        "correct_value": 28161820,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5366 * 4804",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5366 * 4804?",
        "options": [
          "25778264",
          "25778254",
          "25778274",
          "25778284"
        ],
        "answer": "25778264",
        "correct_value": 25778264,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000460",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10001 * 4123",
      "ns_shortcut": "Use (10000+1)*m = 10000*m + 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 10001 * 4123?",
        "options": [
          "41234123",
          "41234113",
          "41234143",
          "41234133"
        ],
        "answer": "41234123",
        "correct_value": 41234123,
        "explanation": "Distributive: (10000+1)*4123 = 10000*4123 + 1*4123."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10039 * 5802",
      "ns_shortcut": "Use (10000+39)*m, correction is 39*5802.",
      "shortcut_strength": 0.922,
      "pure_math": {
        "question": "What is 10039 * 5802?",
        "options": [
          "58246288",
          "58246278",
          "58246298",
          "58246268"
        ],
        "answer": "58246278",
        "correct_value": 58246278,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5660 * 6374",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5660 * 6374?",
        "options": [
          "36076860",
          "36076830",
          "36076850",
          "36076840"
        ],
        "answer": "36076840",
        "correct_value": 36076840,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000461",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10002 * 4728",
      "ns_shortcut": "Use (10000+2)*m = 10000*m + 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 10002 * 4728?",
        "options": [
          "47289446",
          "47289456",
          "47289476",
          "47289466"
        ],
        "answer": "47289456",
        "correct_value": 47289456,
        "explanation": "Distributive: (10000+2)*4728 = 10000*4728 + 2*4728."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9957 * 4749",
      "ns_shortcut": "Use (10000-43)*m, correction is 43*4749.",
      "shortcut_strength": 0.914,
      "pure_math": {
        "question": "What is 9957 * 4749?",
        "options": [
          "47285813",
          "47285793",
          "47285803",
          "47285783"
        ],
        "answer": "47285793",
        "correct_value": 47285793,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5394 * 4350",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5394 * 4350?",
        "options": [
          "23463890",
          "23463910",
          "23463900",
          "23463920"
        ],
        "answer": "23463900",
        "correct_value": 23463900,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000462",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10002 * 4433",
      "ns_shortcut": "Use (10000+2)*m = 10000*m + 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 10002 * 4433?",
        "options": [
          "44338886",
          "44338866",
          "44338876",
          "44338856"
        ],
        "answer": "44338866",
        "correct_value": 44338866,
        "explanation": "Distributive: (10000+2)*4433 = 10000*4433 + 2*4433."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10025 * 6432",
      "ns_shortcut": "Use (10000+25)*m, correction is 25*6432.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "What is 10025 * 6432?",
        "options": [
          "64480800",
          "64480820",
          "64480810",
          "64480790"
        ],
        "answer": "64480800",
        "correct_value": 64480800,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6046 * 6697",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6046 * 6697?",
        "options": [
          "40490052",
          "40490062",
          "40490072",
          "40490082"
        ],
        "answer": "40490062",
        "correct_value": 40490062,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000463",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10002 * 7974",
      "ns_shortcut": "Use (10000+2)*m = 10000*m + 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 10002 * 7974?",
        "options": [
          "79755948",
          "79755958",
          "79755968",
          "79755938"
        ],
        "answer": "79755948",
        "correct_value": 79755948,
        "explanation": "Distributive: (10000+2)*7974 = 10000*7974 + 2*7974."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10029 * 1340",
      "ns_shortcut": "Use (10000+29)*m, correction is 29*1340.",
      "shortcut_strength": 0.942,
      "pure_math": {
        "question": "What is 10029 * 1340?",
        "options": [
          "13438870",
          "13438880",
          "13438850",
          "13438860"
        ],
        "answer": "13438860",
        "correct_value": 13438860,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5351 * 6326",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5351 * 6326?",
        "options": [
          "33850446",
          "33850426",
          "33850436",
          "33850416"
        ],
        "answer": "33850426",
        "correct_value": 33850426,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000464",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10002 * 2043",
      "ns_shortcut": "Use (10000+2)*m = 10000*m + 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 10002 * 2043?",
        "options": [
          "20434106",
          "20434096",
          "20434086",
          "20434076"
        ],
        "answer": "20434086",
        "correct_value": 20434086,
        "explanation": "Distributive: (10000+2)*2043 = 10000*2043 + 2*2043."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9962 * 4591",
      "ns_shortcut": "Use (10000-38)*m, correction is 38*4591.",
      "shortcut_strength": 0.924,
      "pure_math": {
        "question": "What is 9962 * 4591?",
        "options": [
          "45735532",
          "45735542",
          "45735552",
          "45735562"
        ],
        "answer": "45735542",
        "correct_value": 45735542,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4380 * 4701",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 4380 * 4701?",
        "options": [
          "20590390",
          "20590370",
          "20590400",
          "20590380"
        ],
        "answer": "20590380",
        "correct_value": 20590380,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000465",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9998 * 9005",
      "ns_shortcut": "Use (10000-2)*m = 10000*m - 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 9998 * 9005?",
        "options": [
          "90032000",
          "90032010",
          "90031980",
          "90031990"
        ],
        "answer": "90031990",
        "correct_value": 90031990,
        "explanation": "Distributive: (10000-2)*9005 = 10000*9005 - 2*9005."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10030 * 5162",
      "ns_shortcut": "Use (10000+30)*m, correction is 30*5162.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "What is 10030 * 5162?",
        "options": [
          "51774860",
          "51774870",
          "51774850",
          "51774880"
        ],
        "answer": "51774860",
        "correct_value": 51774860,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5191 * 6700",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5191 * 6700?",
        "options": [
          "34779720",
          "34779690",
          "34779710",
          "34779700"
        ],
        "answer": "34779700",
        "correct_value": 34779700,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000466",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10001 * 9495",
      "ns_shortcut": "Use (10000+1)*m = 10000*m + 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 10001 * 9495?",
        "options": [
          "94959515",
          "94959505",
          "94959485",
          "94959495"
        ],
        "answer": "94959495",
        "correct_value": 94959495,
        "explanation": "Distributive: (10000+1)*9495 = 10000*9495 + 1*9495."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10028 * 1577",
      "ns_shortcut": "Use (10000+28)*m, correction is 28*1577.",
      "shortcut_strength": 0.944,
      "pure_math": {
        "question": "What is 10028 * 1577?",
        "options": [
          "15814156",
          "15814146",
          "15814166",
          "15814176"
        ],
        "answer": "15814156",
        "correct_value": 15814156,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6196 * 5712",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6196 * 5712?",
        "options": [
          "35391562",
          "35391552",
          "35391572",
          "35391542"
        ],
        "answer": "35391552",
        "correct_value": 35391552,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000467",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10002 * 4382",
      "ns_shortcut": "Use (10000+2)*m = 10000*m + 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 10002 * 4382?",
        "options": [
          "43828784",
          "43828754",
          "43828764",
          "43828774"
        ],
        "answer": "43828764",
        "correct_value": 43828764,
        "explanation": "Distributive: (10000+2)*4382 = 10000*4382 + 2*4382."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9959 * 8574",
      "ns_shortcut": "Use (10000-41)*m, correction is 41*8574.",
      "shortcut_strength": 0.918,
      "pure_math": {
        "question": "What is 9959 * 8574?",
        "options": [
          "85388486",
          "85388476",
          "85388456",
          "85388466"
        ],
        "answer": "85388466",
        "correct_value": 85388466,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6405 * 4830",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6405 * 4830?",
        "options": [
          "30936170",
          "30936150",
          "30936160",
          "30936140"
        ],
        "answer": "30936150",
        "correct_value": 30936150,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000468",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9998 * 3337",
      "ns_shortcut": "Use (10000-2)*m = 10000*m - 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 9998 * 3337?",
        "options": [
          "33363346",
          "33363336",
          "33363326",
          "33363316"
        ],
        "answer": "33363326",
        "correct_value": 33363326,
        "explanation": "Distributive: (10000-2)*3337 = 10000*3337 - 2*3337."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9963 * 6793",
      "ns_shortcut": "Use (10000-37)*m, correction is 37*6793.",
      "shortcut_strength": 0.926,
      "pure_math": {
        "question": "What is 9963 * 6793?",
        "options": [
          "67678649",
          "67678679",
          "67678669",
          "67678659"
        ],
        "answer": "67678659",
        "correct_value": 67678659,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5883 * 5894",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5883 * 5894?",
        "options": [
          "34674412",
          "34674392",
          "34674422",
          "34674402"
        ],
        "answer": "34674402",
        "correct_value": 34674402,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000469",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10001 * 8476",
      "ns_shortcut": "Use (10000+1)*m = 10000*m + 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 10001 * 8476?",
        "options": [
          "84768476",
          "84768486",
          "84768466",
          "84768496"
        ],
        "answer": "84768476",
        "correct_value": 84768476,
        "explanation": "Distributive: (10000+1)*8476 = 10000*8476 + 1*8476."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10025 * 3109",
      "ns_shortcut": "Use (10000+25)*m, correction is 25*3109.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "What is 10025 * 3109?",
        "options": [
          "31167715",
          "31167725",
          "31167735",
          "31167745"
        ],
        "answer": "31167725",
        "correct_value": 31167725,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6529 * 5768",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6529 * 5768?",
        "options": [
          "37659292",
          "37659272",
          "37659282",
          "37659262"
        ],
        "answer": "37659272",
        "correct_value": 37659272,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000470",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9998 * 7447",
      "ns_shortcut": "Use (10000-2)*m = 10000*m - 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 9998 * 7447?",
        "options": [
          "74455116",
          "74455126",
          "74455096",
          "74455106"
        ],
        "answer": "74455106",
        "correct_value": 74455106,
        "explanation": "Distributive: (10000-2)*7447 = 10000*7447 - 2*7447."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10023 * 7922",
      "ns_shortcut": "Use (10000+23)*m, correction is 23*7922.",
      "shortcut_strength": 0.954,
      "pure_math": {
        "question": "What is 10023 * 7922?",
        "options": [
          "79402216",
          "79402206",
          "79402196",
          "79402226"
        ],
        "answer": "79402206",
        "correct_value": 79402206,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6858 * 6974",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6858 * 6974?",
        "options": [
          "47827692",
          "47827712",
          "47827682",
          "47827702"
        ],
        "answer": "47827692",
        "correct_value": 47827692,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000471",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9998 * 7041",
      "ns_shortcut": "Use (10000-2)*m = 10000*m - 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 9998 * 7041?",
        "options": [
          "70395938",
          "70395928",
          "70395908",
          "70395918"
        ],
        "answer": "70395918",
        "correct_value": 70395918,
        "explanation": "Distributive: (10000-2)*7041 = 10000*7041 - 2*7041."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9972 * 4868",
      "ns_shortcut": "Use (10000-28)*m, correction is 28*4868.",
      "shortcut_strength": 0.944,
      "pure_math": {
        "question": "What is 9972 * 4868?",
        "options": [
          "48543696",
          "48543716",
          "48543686",
          "48543706"
        ],
        "answer": "48543696",
        "correct_value": 48543696,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6071 * 4181",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6071 * 4181?",
        "options": [
          "25382861",
          "25382871",
          "25382851",
          "25382841"
        ],
        "answer": "25382851",
        "correct_value": 25382851,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000472",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10002 * 7244",
      "ns_shortcut": "Use (10000+2)*m = 10000*m + 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 10002 * 7244?",
        "options": [
          "72454488",
          "72454498",
          "72454478",
          "72454508"
        ],
        "answer": "72454488",
        "correct_value": 72454488,
        "explanation": "Distributive: (10000+2)*7244 = 10000*7244 + 2*7244."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9952 * 2636",
      "ns_shortcut": "Use (10000-48)*m, correction is 48*2636.",
      "shortcut_strength": 0.904,
      "pure_math": {
        "question": "What is 9952 * 2636?",
        "options": [
          "26233492",
          "26233482",
          "26233462",
          "26233472"
        ],
        "answer": "26233472",
        "correct_value": 26233472,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4468 * 6903",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 4468 * 6903?",
        "options": [
          "30842604",
          "30842624",
          "30842594",
          "30842614"
        ],
        "answer": "30842604",
        "correct_value": 30842604,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000473",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10002 * 8558",
      "ns_shortcut": "Use (10000+2)*m = 10000*m + 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 10002 * 8558?",
        "options": [
          "85597126",
          "85597136",
          "85597106",
          "85597116"
        ],
        "answer": "85597116",
        "correct_value": 85597116,
        "explanation": "Distributive: (10000+2)*8558 = 10000*8558 + 2*8558."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9982 * 2677",
      "ns_shortcut": "Use (10000-18)*m, correction is 18*2677.",
      "shortcut_strength": 0.964,
      "pure_math": {
        "question": "What is 9982 * 2677?",
        "options": [
          "26721814",
          "26721834",
          "26721824",
          "26721804"
        ],
        "answer": "26721814",
        "correct_value": 26721814,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4659 * 4697",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 4659 * 4697?",
        "options": [
          "21883333",
          "21883313",
          "21883343",
          "21883323"
        ],
        "answer": "21883323",
        "correct_value": 21883323,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000474",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9999 * 5819",
      "ns_shortcut": "Use (10000-1)*m = 10000*m - 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 9999 * 5819?",
        "options": [
          "58184171",
          "58184191",
          "58184201",
          "58184181"
        ],
        "answer": "58184181",
        "correct_value": 58184181,
        "explanation": "Distributive: (10000-1)*5819 = 10000*5819 - 1*5819."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10016 * 1853",
      "ns_shortcut": "Use (10000+16)*m, correction is 16*1853.",
      "shortcut_strength": 0.968,
      "pure_math": {
        "question": "What is 10016 * 1853?",
        "options": [
          "18559648",
          "18559638",
          "18559658",
          "18559668"
        ],
        "answer": "18559648",
        "correct_value": 18559648,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4627 * 5803",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 4627 * 5803?",
        "options": [
          "26850491",
          "26850471",
          "26850481",
          "26850501"
        ],
        "answer": "26850481",
        "correct_value": 26850481,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000475",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9998 * 9721",
      "ns_shortcut": "Use (10000-2)*m = 10000*m - 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 9998 * 9721?",
        "options": [
          "97190578",
          "97190558",
          "97190548",
          "97190568"
        ],
        "answer": "97190558",
        "correct_value": 97190558,
        "explanation": "Distributive: (10000-2)*9721 = 10000*9721 - 2*9721."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9983 * 4137",
      "ns_shortcut": "Use (10000-17)*m, correction is 17*4137.",
      "shortcut_strength": 0.966,
      "pure_math": {
        "question": "What is 9983 * 4137?",
        "options": [
          "41299691",
          "41299671",
          "41299661",
          "41299681"
        ],
        "answer": "41299671",
        "correct_value": 41299671,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5817 * 4213",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5817 * 4213?",
        "options": [
          "24507041",
          "24507031",
          "24507011",
          "24507021"
        ],
        "answer": "24507021",
        "correct_value": 24507021,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000476",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9999 * 5091",
      "ns_shortcut": "Use (10000-1)*m = 10000*m - 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 9999 * 5091?",
        "options": [
          "50904919",
          "50904899",
          "50904909",
          "50904929"
        ],
        "answer": "50904909",
        "correct_value": 50904909,
        "explanation": "Distributive: (10000-1)*5091 = 10000*5091 - 1*5091."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10046 * 8794",
      "ns_shortcut": "Use (10000+46)*m, correction is 46*8794.",
      "shortcut_strength": 0.908,
      "pure_math": {
        "question": "What is 10046 * 8794?",
        "options": [
          "88344534",
          "88344544",
          "88344524",
          "88344514"
        ],
        "answer": "88344524",
        "correct_value": 88344524,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5379 * 4786",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5379 * 4786?",
        "options": [
          "25743904",
          "25743914",
          "25743884",
          "25743894"
        ],
        "answer": "25743894",
        "correct_value": 25743894,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000477",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9999 * 3736",
      "ns_shortcut": "Use (10000-1)*m = 10000*m - 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 9999 * 3736?",
        "options": [
          "37356284",
          "37356254",
          "37356274",
          "37356264"
        ],
        "answer": "37356264",
        "correct_value": 37356264,
        "explanation": "Distributive: (10000-1)*3736 = 10000*3736 - 1*3736."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10018 * 8713",
      "ns_shortcut": "Use (10000+18)*m, correction is 18*8713.",
      "shortcut_strength": 0.964,
      "pure_math": {
        "question": "What is 10018 * 8713?",
        "options": [
          "87286844",
          "87286834",
          "87286824",
          "87286854"
        ],
        "answer": "87286834",
        "correct_value": 87286834,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6217 * 5617",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6217 * 5617?",
        "options": [
          "34920899",
          "34920909",
          "34920889",
          "34920879"
        ],
        "answer": "34920889",
        "correct_value": 34920889,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000478",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9999 * 2734",
      "ns_shortcut": "Use (10000-1)*m = 10000*m - 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 9999 * 2734?",
        "options": [
          "27337256",
          "27337266",
          "27337276",
          "27337286"
        ],
        "answer": "27337266",
        "correct_value": 27337266,
        "explanation": "Distributive: (10000-1)*2734 = 10000*2734 - 1*2734."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10047 * 3419",
      "ns_shortcut": "Use (10000+47)*m, correction is 47*3419.",
      "shortcut_strength": 0.906,
      "pure_math": {
        "question": "What is 10047 * 3419?",
        "options": [
          "34350713",
          "34350693",
          "34350683",
          "34350703"
        ],
        "answer": "34350693",
        "correct_value": 34350693,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4870 * 5878",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 4870 * 5878?",
        "options": [
          "28625880",
          "28625850",
          "28625860",
          "28625870"
        ],
        "answer": "28625860",
        "correct_value": 28625860,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000479",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10001 * 1719",
      "ns_shortcut": "Use (10000+1)*m = 10000*m + 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 10001 * 1719?",
        "options": [
          "17191739",
          "17191729",
          "17191709",
          "17191719"
        ],
        "answer": "17191719",
        "correct_value": 17191719,
        "explanation": "Distributive: (10000+1)*1719 = 10000*1719 + 1*1719."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9983 * 3235",
      "ns_shortcut": "Use (10000-17)*m, correction is 17*3235.",
      "shortcut_strength": 0.966,
      "pure_math": {
        "question": "What is 9983 * 3235?",
        "options": [
          "32294995",
          "32295025",
          "32295015",
          "32295005"
        ],
        "answer": "32295005",
        "correct_value": 32295005,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5030 * 4387",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5030 * 4387?",
        "options": [
          "22066610",
          "22066620",
          "22066600",
          "22066630"
        ],
        "answer": "22066610",
        "correct_value": 22066610,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000480",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9999 * 6440",
      "ns_shortcut": "Use (10000-1)*m = 10000*m - 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 9999 * 6440?",
        "options": [
          "64393560",
          "64393550",
          "64393580",
          "64393570"
        ],
        "answer": "64393560",
        "correct_value": 64393560,
        "explanation": "Distributive: (10000-1)*6440 = 10000*6440 - 1*6440."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9961 * 6005",
      "ns_shortcut": "Use (10000-39)*m, correction is 39*6005.",
      "shortcut_strength": 0.922,
      "pure_math": {
        "question": "What is 9961 * 6005?",
        "options": [
          "59815805",
          "59815795",
          "59815825",
          "59815815"
        ],
        "answer": "59815805",
        "correct_value": 59815805,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6491 * 6395",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6491 * 6395?",
        "options": [
          "41509965",
          "41509945",
          "41509955",
          "41509935"
        ],
        "answer": "41509945",
        "correct_value": 41509945,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000481",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9998 * 4811",
      "ns_shortcut": "Use (10000-2)*m = 10000*m - 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 9998 * 4811?",
        "options": [
          "48100388",
          "48100368",
          "48100398",
          "48100378"
        ],
        "answer": "48100378",
        "correct_value": 48100378,
        "explanation": "Distributive: (10000-2)*4811 = 10000*4811 - 2*4811."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9953 * 7657",
      "ns_shortcut": "Use (10000-47)*m, correction is 47*7657.",
      "shortcut_strength": 0.906,
      "pure_math": {
        "question": "What is 9953 * 7657?",
        "options": [
          "76210121",
          "76210141",
          "76210111",
          "76210131"
        ],
        "answer": "76210121",
        "correct_value": 76210121,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4244 * 4562",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 4244 * 4562?",
        "options": [
          "19361128",
          "19361118",
          "19361138",
          "19361148"
        ],
        "answer": "19361128",
        "correct_value": 19361128,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000482",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9999 * 3484",
      "ns_shortcut": "Use (10000-1)*m = 10000*m - 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 9999 * 3484?",
        "options": [
          "34836526",
          "34836536",
          "34836516",
          "34836506"
        ],
        "answer": "34836516",
        "correct_value": 34836516,
        "explanation": "Distributive: (10000-1)*3484 = 10000*3484 - 1*3484."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10042 * 2825",
      "ns_shortcut": "Use (10000+42)*m, correction is 42*2825.",
      "shortcut_strength": 0.916,
      "pure_math": {
        "question": "What is 10042 * 2825?",
        "options": [
          "28368650",
          "28368660",
          "28368640",
          "28368670"
        ],
        "answer": "28368650",
        "correct_value": 28368650,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5299 * 6635",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5299 * 6635?",
        "options": [
          "35158855",
          "35158875",
          "35158885",
          "35158865"
        ],
        "answer": "35158865",
        "correct_value": 35158865,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000483",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10001 * 1388",
      "ns_shortcut": "Use (10000+1)*m = 10000*m + 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 10001 * 1388?",
        "options": [
          "13881388",
          "13881378",
          "13881408",
          "13881398"
        ],
        "answer": "13881388",
        "correct_value": 13881388,
        "explanation": "Distributive: (10000+1)*1388 = 10000*1388 + 1*1388."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9974 * 5033",
      "ns_shortcut": "Use (10000-26)*m, correction is 26*5033.",
      "shortcut_strength": 0.948,
      "pure_math": {
        "question": "What is 9974 * 5033?",
        "options": [
          "50199132",
          "50199162",
          "50199152",
          "50199142"
        ],
        "answer": "50199142",
        "correct_value": 50199142,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6722 * 5016",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6722 * 5016?",
        "options": [
          "33717552",
          "33717542",
          "33717572",
          "33717562"
        ],
        "answer": "33717552",
        "correct_value": 33717552,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000484",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10001 * 4007",
      "ns_shortcut": "Use (10000+1)*m = 10000*m + 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 10001 * 4007?",
        "options": [
          "40074017",
          "40074007",
          "40074027",
          "40073997"
        ],
        "answer": "40074007",
        "correct_value": 40074007,
        "explanation": "Distributive: (10000+1)*4007 = 10000*4007 + 1*4007."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9974 * 1995",
      "ns_shortcut": "Use (10000-26)*m, correction is 26*1995.",
      "shortcut_strength": 0.948,
      "pure_math": {
        "question": "What is 9974 * 1995?",
        "options": [
          "19898140",
          "19898150",
          "19898130",
          "19898120"
        ],
        "answer": "19898130",
        "correct_value": 19898130,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6597 * 4578",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6597 * 4578?",
        "options": [
          "30201056",
          "30201086",
          "30201066",
          "30201076"
        ],
        "answer": "30201066",
        "correct_value": 30201066,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000485",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9999 * 9992",
      "ns_shortcut": "Use (10000-1)*m = 10000*m - 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 9999 * 9992?",
        "options": [
          "99909998",
          "99910028",
          "99910008",
          "99910018"
        ],
        "answer": "99910008",
        "correct_value": 99910008,
        "explanation": "Distributive: (10000-1)*9992 = 10000*9992 - 1*9992."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10026 * 2592",
      "ns_shortcut": "Use (10000+26)*m, correction is 26*2592.",
      "shortcut_strength": 0.948,
      "pure_math": {
        "question": "What is 10026 * 2592?",
        "options": [
          "25987412",
          "25987402",
          "25987392",
          "25987382"
        ],
        "answer": "25987392",
        "correct_value": 25987392,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5002 * 5735",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5002 * 5735?",
        "options": [
          "28686460",
          "28686470",
          "28686490",
          "28686480"
        ],
        "answer": "28686470",
        "correct_value": 28686470,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000486",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10001 * 5675",
      "ns_shortcut": "Use (10000+1)*m = 10000*m + 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 10001 * 5675?",
        "options": [
          "56755685",
          "56755675",
          "56755695",
          "56755665"
        ],
        "answer": "56755675",
        "correct_value": 56755675,
        "explanation": "Distributive: (10000+1)*5675 = 10000*5675 + 1*5675."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9980 * 1578",
      "ns_shortcut": "Use (10000-20)*m, correction is 20*1578.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 9980 * 1578?",
        "options": [
          "15748460",
          "15748430",
          "15748450",
          "15748440"
        ],
        "answer": "15748440",
        "correct_value": 15748440,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5546 * 4686",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5546 * 4686?",
        "options": [
          "25988556",
          "25988576",
          "25988566",
          "25988546"
        ],
        "answer": "25988556",
        "correct_value": 25988556,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000487",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10002 * 3553",
      "ns_shortcut": "Use (10000+2)*m = 10000*m + 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 10002 * 3553?",
        "options": [
          "35537126",
          "35537116",
          "35537106",
          "35537096"
        ],
        "answer": "35537106",
        "correct_value": 35537106,
        "explanation": "Distributive: (10000+2)*3553 = 10000*3553 + 2*3553."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9964 * 2612",
      "ns_shortcut": "Use (10000-36)*m, correction is 36*2612.",
      "shortcut_strength": 0.928,
      "pure_math": {
        "question": "What is 9964 * 2612?",
        "options": [
          "26025968",
          "26025988",
          "26025958",
          "26025978"
        ],
        "answer": "26025968",
        "correct_value": 26025968,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6263 * 6975",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6263 * 6975?",
        "options": [
          "43684425",
          "43684445",
          "43684415",
          "43684435"
        ],
        "answer": "43684425",
        "correct_value": 43684425,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000488",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10002 * 6011",
      "ns_shortcut": "Use (10000+2)*m = 10000*m + 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 10002 * 6011?",
        "options": [
          "60122022",
          "60122042",
          "60122032",
          "60122012"
        ],
        "answer": "60122022",
        "correct_value": 60122022,
        "explanation": "Distributive: (10000+2)*6011 = 10000*6011 + 2*6011."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9967 * 6423",
      "ns_shortcut": "Use (10000-33)*m, correction is 33*6423.",
      "shortcut_strength": 0.9339999999999999,
      "pure_math": {
        "question": "What is 9967 * 6423?",
        "options": [
          "64018061",
          "64018041",
          "64018031",
          "64018051"
        ],
        "answer": "64018041",
        "correct_value": 64018041,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6927 * 5921",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6927 * 5921?",
        "options": [
          "41014757",
          "41014787",
          "41014767",
          "41014777"
        ],
        "answer": "41014767",
        "correct_value": 41014767,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000489",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9998 * 1210",
      "ns_shortcut": "Use (10000-2)*m = 10000*m - 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 9998 * 1210?",
        "options": [
          "12097580",
          "12097570",
          "12097590",
          "12097600"
        ],
        "answer": "12097580",
        "correct_value": 12097580,
        "explanation": "Distributive: (10000-2)*1210 = 10000*1210 - 2*1210."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10017 * 2113",
      "ns_shortcut": "Use (10000+17)*m, correction is 17*2113.",
      "shortcut_strength": 0.966,
      "pure_math": {
        "question": "What is 10017 * 2113?",
        "options": [
          "21165941",
          "21165911",
          "21165921",
          "21165931"
        ],
        "answer": "21165921",
        "correct_value": 21165921,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5259 * 6624",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5259 * 6624?",
        "options": [
          "34835636",
          "34835606",
          "34835626",
          "34835616"
        ],
        "answer": "34835616",
        "correct_value": 34835616,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000490",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9998 * 7304",
      "ns_shortcut": "Use (10000-2)*m = 10000*m - 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 9998 * 7304?",
        "options": [
          "73025412",
          "73025382",
          "73025392",
          "73025402"
        ],
        "answer": "73025392",
        "correct_value": 73025392,
        "explanation": "Distributive: (10000-2)*7304 = 10000*7304 - 2*7304."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9960 * 8675",
      "ns_shortcut": "Use (10000-40)*m, correction is 40*8675.",
      "shortcut_strength": 0.92,
      "pure_math": {
        "question": "What is 9960 * 8675?",
        "options": [
          "86403000",
          "86403010",
          "86402990",
          "86403020"
        ],
        "answer": "86403000",
        "correct_value": 86403000,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6851 * 4235",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6851 * 4235?",
        "options": [
          "29014005",
          "29013985",
          "29013995",
          "29013975"
        ],
        "answer": "29013985",
        "correct_value": 29013985,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000491",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9999 * 8827",
      "ns_shortcut": "Use (10000-1)*m = 10000*m - 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 9999 * 8827?",
        "options": [
          "88261193",
          "88261163",
          "88261183",
          "88261173"
        ],
        "answer": "88261173",
        "correct_value": 88261173,
        "explanation": "Distributive: (10000-1)*8827 = 10000*8827 - 1*8827."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9983 * 9935",
      "ns_shortcut": "Use (10000-17)*m, correction is 17*9935.",
      "shortcut_strength": 0.966,
      "pure_math": {
        "question": "What is 9983 * 9935?",
        "options": [
          "99181115",
          "99181125",
          "99181105",
          "99181095"
        ],
        "answer": "99181105",
        "correct_value": 99181105,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6788 * 4602",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6788 * 4602?",
        "options": [
          "31238386",
          "31238366",
          "31238376",
          "31238396"
        ],
        "answer": "31238376",
        "correct_value": 31238376,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000492",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9998 * 2912",
      "ns_shortcut": "Use (10000-2)*m = 10000*m - 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 9998 * 2912?",
        "options": [
          "29114166",
          "29114186",
          "29114196",
          "29114176"
        ],
        "answer": "29114176",
        "correct_value": 29114176,
        "explanation": "Distributive: (10000-2)*2912 = 10000*2912 - 2*2912."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9971 * 3483",
      "ns_shortcut": "Use (10000-29)*m, correction is 29*3483.",
      "shortcut_strength": 0.942,
      "pure_math": {
        "question": "What is 9971 * 3483?",
        "options": [
          "34729003",
          "34729013",
          "34728993",
          "34728983"
        ],
        "answer": "34728993",
        "correct_value": 34728993,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5747 * 5034",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5747 * 5034?",
        "options": [
          "28930398",
          "28930408",
          "28930388",
          "28930418"
        ],
        "answer": "28930398",
        "correct_value": 28930398,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000493",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10001 * 7743",
      "ns_shortcut": "Use (10000+1)*m = 10000*m + 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 10001 * 7743?",
        "options": [
          "77437763",
          "77437753",
          "77437733",
          "77437743"
        ],
        "answer": "77437743",
        "correct_value": 77437743,
        "explanation": "Distributive: (10000+1)*7743 = 10000*7743 + 1*7743."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9982 * 6878",
      "ns_shortcut": "Use (10000-18)*m, correction is 18*6878.",
      "shortcut_strength": 0.964,
      "pure_math": {
        "question": "What is 9982 * 6878?",
        "options": [
          "68656186",
          "68656196",
          "68656206",
          "68656216"
        ],
        "answer": "68656196",
        "correct_value": 68656196,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6862 * 5260",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6862 * 5260?",
        "options": [
          "36094140",
          "36094130",
          "36094110",
          "36094120"
        ],
        "answer": "36094120",
        "correct_value": 36094120,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000494",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9998 * 2587",
      "ns_shortcut": "Use (10000-2)*m = 10000*m - 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 9998 * 2587?",
        "options": [
          "25864816",
          "25864836",
          "25864846",
          "25864826"
        ],
        "answer": "25864826",
        "correct_value": 25864826,
        "explanation": "Distributive: (10000-2)*2587 = 10000*2587 - 2*2587."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10029 * 1180",
      "ns_shortcut": "Use (10000+29)*m, correction is 29*1180.",
      "shortcut_strength": 0.942,
      "pure_math": {
        "question": "What is 10029 * 1180?",
        "options": [
          "11834210",
          "11834220",
          "11834230",
          "11834240"
        ],
        "answer": "11834220",
        "correct_value": 11834220,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4697 * 4721",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 4697 * 4721?",
        "options": [
          "22174547",
          "22174527",
          "22174537",
          "22174557"
        ],
        "answer": "22174537",
        "correct_value": 22174537,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000495",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9999 * 8970",
      "ns_shortcut": "Use (10000-1)*m = 10000*m - 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 9999 * 8970?",
        "options": [
          "89691020",
          "89691030",
          "89691050",
          "89691040"
        ],
        "answer": "89691030",
        "correct_value": 89691030,
        "explanation": "Distributive: (10000-1)*8970 = 10000*8970 - 1*8970."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10034 * 2729",
      "ns_shortcut": "Use (10000+34)*m, correction is 34*2729.",
      "shortcut_strength": 0.9319999999999999,
      "pure_math": {
        "question": "What is 10034 * 2729?",
        "options": [
          "27382786",
          "27382806",
          "27382796",
          "27382776"
        ],
        "answer": "27382786",
        "correct_value": 27382786,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4747 * 4784",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 4747 * 4784?",
        "options": [
          "22709648",
          "22709638",
          "22709658",
          "22709668"
        ],
        "answer": "22709648",
        "correct_value": 22709648,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000496",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9998 * 3721",
      "ns_shortcut": "Use (10000-2)*m = 10000*m - 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 9998 * 3721?",
        "options": [
          "37202578",
          "37202548",
          "37202568",
          "37202558"
        ],
        "answer": "37202558",
        "correct_value": 37202558,
        "explanation": "Distributive: (10000-2)*3721 = 10000*3721 - 2*3721."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10017 * 7017",
      "ns_shortcut": "Use (10000+17)*m, correction is 17*7017.",
      "shortcut_strength": 0.966,
      "pure_math": {
        "question": "What is 10017 * 7017?",
        "options": [
          "70289299",
          "70289289",
          "70289279",
          "70289309"
        ],
        "answer": "70289289",
        "correct_value": 70289289,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4120 * 6397",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 4120 * 6397?",
        "options": [
          "26355640",
          "26355660",
          "26355630",
          "26355650"
        ],
        "answer": "26355640",
        "correct_value": 26355640,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000497",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9998 * 1155",
      "ns_shortcut": "Use (10000-2)*m = 10000*m - 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 9998 * 1155?",
        "options": [
          "11547710",
          "11547680",
          "11547700",
          "11547690"
        ],
        "answer": "11547690",
        "correct_value": 11547690,
        "explanation": "Distributive: (10000-2)*1155 = 10000*1155 - 2*1155."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9954 * 7362",
      "ns_shortcut": "Use (10000-46)*m, correction is 46*7362.",
      "shortcut_strength": 0.908,
      "pure_math": {
        "question": "What is 9954 * 7362?",
        "options": [
          "73281358",
          "73281368",
          "73281338",
          "73281348"
        ],
        "answer": "73281348",
        "correct_value": 73281348,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5537 * 6468",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5537 * 6468?",
        "options": [
          "35813316",
          "35813306",
          "35813326",
          "35813336"
        ],
        "answer": "35813316",
        "correct_value": 35813316,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000498",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10001 * 8036",
      "ns_shortcut": "Use (10000+1)*m = 10000*m + 1*m.",
      "shortcut_strength": 0.9999,
      "pure_math": {
        "question": "What is 10001 * 8036?",
        "options": [
          "80368036",
          "80368026",
          "80368046",
          "80368056"
        ],
        "answer": "80368036",
        "correct_value": 80368036,
        "explanation": "Distributive: (10000+1)*8036 = 10000*8036 + 1*8036."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9962 * 8025",
      "ns_shortcut": "Use (10000-38)*m, correction is 38*8025.",
      "shortcut_strength": 0.924,
      "pure_math": {
        "question": "What is 9962 * 8025?",
        "options": [
          "79945040",
          "79945060",
          "79945050",
          "79945070"
        ],
        "answer": "79945050",
        "correct_value": 79945050,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5549 * 6500",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5549 * 6500?",
        "options": [
          "36068490",
          "36068520",
          "36068510",
          "36068500"
        ],
        "answer": "36068500",
        "correct_value": 36068500,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000499",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9998 * 1050",
      "ns_shortcut": "Use (10000-2)*m = 10000*m - 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 9998 * 1050?",
        "options": [
          "10497900",
          "10497910",
          "10497920",
          "10497890"
        ],
        "answer": "10497900",
        "correct_value": 10497900,
        "explanation": "Distributive: (10000-2)*1050 = 10000*1050 - 2*1050."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10016 * 7624",
      "ns_shortcut": "Use (10000+16)*m, correction is 16*7624.",
      "shortcut_strength": 0.968,
      "pure_math": {
        "question": "What is 10016 * 7624?",
        "options": [
          "76361974",
          "76361994",
          "76361984",
          "76362004"
        ],
        "answer": "76361984",
        "correct_value": 76361984,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6172 * 5143",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6172 * 5143?",
        "options": [
          "31742596",
          "31742616",
          "31742586",
          "31742606"
        ],
        "answer": "31742596",
        "correct_value": 31742596,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "structural_shortcuts_000500",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10002 * 9436",
      "ns_shortcut": "Use (10000+2)*m = 10000*m + 2*m.",
      "shortcut_strength": 0.9998,
      "pure_math": {
        "question": "What is 10002 * 9436?",
        "options": [
          "94378882",
          "94378872",
          "94378892",
          "94378862"
        ],
        "answer": "94378872",
        "correct_value": 94378872,
        "explanation": "Distributive: (10000+2)*9436 = 10000*9436 + 2*9436."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9962 * 8850",
      "ns_shortcut": "Use (10000-38)*m, correction is 38*8850.",
      "shortcut_strength": 0.924,
      "pure_math": {
        "question": "What is 9962 * 8850?",
        "options": [
          "88163690",
          "88163700",
          "88163720",
          "88163710"
        ],
        "answer": "88163700",
        "correct_value": 88163700,
        "explanation": "Distributive still works but correction term is larger."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4186 * 5332",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 4186 * 5332?",
        "options": [
          "22319772",
          "22319762",
          "22319752",
          "22319742"
        ],
        "answer": "22319752",
        "correct_value": 22319752,
        "explanation": "Neither factor near a power of 10; no clean decomposition."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "relative_distance_000501",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 720/1504 or 2500/4890?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.03252403950746202,
      "pure_math": {
        "question": "Which is larger: 720/1504 or 2500/4890?",
        "options": [
          "2500/4890",
          "3756/6378",
          "3249/5725",
          "720/1504"
        ],
        "answer": "2500/4890",
        "correct_value": 0.5112474437627812,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 2327/4686 or 2477/4858?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.013295035253877596,
      "pure_math": {
        "question": "Which is larger: 2327/4686 or 2477/4858?",
        "options": [
          "3848/7549",
          "2327/4686",
          "4665/8287",
          "2477/4858"
        ],
        "answer": "2477/4858",
        "correct_value": 0.5098806093042404,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 820/1490 or 4657/8028?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 820/1490 or 4657/8028?",
        "options": [
          "2501/4000",
          "4657/8028",
          "4142/7512",
          "820/1490"
        ],
        "answer": "4657/8028",
        "correct_value": 0.5800946686596911,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000502",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 1709/3501 or 2022/3864?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.035145681535532824,
      "pure_math": {
        "question": "Which is larger: 1709/3501 or 2022/3864?",
        "options": [
          "2022/3864",
          "4500/7823",
          "1709/3501",
          "1295/2503"
        ],
        "answer": "2022/3864",
        "correct_value": 0.5232919254658385,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 2117/4346 or 4715/9178?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.026613893023564095,
      "pure_math": {
        "question": "Which is larger: 2117/4346 or 4715/9178?",
        "options": [
          "2117/4346",
          "2312/4284",
          "4715/9178",
          "4199/8519"
        ],
        "answer": "4715/9178",
        "correct_value": 0.5137284811505775,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 2156/3919 or 3410/5879?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 2156/3919 or 3410/5879?",
        "options": [
          "3410/5879",
          "1023/1513",
          "3269/5076",
          "2156/3919"
        ],
        "answer": "3410/5879",
        "correct_value": 0.5800306174519476,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000503",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 3335/6848 or 2366/4567?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.0310608701902515,
      "pure_math": {
        "question": "Which is larger: 3335/6848 or 2366/4567?",
        "options": [
          "3335/6848",
          "2366/4567",
          "3053/6518",
          "3229/6375"
        ],
        "answer": "2366/4567",
        "correct_value": 0.5180643748631487,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 2714/5486 or 2660/5184?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.018403466961918802,
      "pure_math": {
        "question": "Which is larger: 2714/5486 or 2660/5184?",
        "options": [
          "2714/5486",
          "2377/4372",
          "2660/5184",
          "2683/5351"
        ],
        "answer": "2660/5184",
        "correct_value": 0.5131172839506173,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 1159/2107 or 5068/8737?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 1159/2107 or 5068/8737?",
        "options": [
          "1159/2107",
          "4785/9541",
          "5440/9912",
          "5068/8737"
        ],
        "answer": "5068/8737",
        "correct_value": 0.5800618061119377,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000504",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 937/1958 or 2145/4104?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.044111278366157136,
      "pure_math": {
        "question": "Which is larger: 937/1958 or 2145/4104?",
        "options": [
          "937/1958",
          "2965/6368",
          "2145/4104",
          "2325/3950"
        ],
        "answer": "2145/4104",
        "correct_value": 0.5226608187134503,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 1048/2147 or 710/1403?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.017935483913803674,
      "pure_math": {
        "question": "Which is larger: 1048/2147 or 710/1403?",
        "options": [
          "1048/2147",
          "1046/2292",
          "710/1403",
          "4143/8110"
        ],
        "answer": "710/1403",
        "correct_value": 0.5060584461867427,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 1592/2893 or 1853/3194?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 1592/2893 or 1853/3194?",
        "options": [
          "2835/5799",
          "1853/3194",
          "1592/2893",
          "1340/2595"
        ],
        "answer": "1853/3194",
        "correct_value": 0.5801502817783344,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000505",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 678/1397 or 2610/5068?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.029670355745963717,
      "pure_math": {
        "question": "Which is larger: 678/1397 or 2610/5068?",
        "options": [
          "1495/3298",
          "2610/5068",
          "678/1397",
          "2402/4466"
        ],
        "answer": "2610/5068",
        "correct_value": 0.5149960536700868,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 2627/5305 or 2524/4921?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.017710667375829325,
      "pure_math": {
        "question": "Which is larger: 2627/5305 or 2524/4921?",
        "options": [
          "650/1564",
          "2524/4921",
          "2627/5305",
          "4126/8872"
        ],
        "answer": "2524/4921",
        "correct_value": 0.5129038813249339,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 4726/8591 or 2077/3581?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 4726/8591 or 2077/3581?",
        "options": [
          "1895/3374",
          "4726/8591",
          "2197/3650",
          "2077/3581"
        ],
        "answer": "2077/3581",
        "correct_value": 0.580005585032114,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000506",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 4821/9880 or 611/1163?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.037409968634795565,
      "pure_math": {
        "question": "Which is larger: 4821/9880 or 611/1163?",
        "options": [
          "1007/2239",
          "4384/9102",
          "4821/9880",
          "611/1163"
        ],
        "answer": "611/1163",
        "correct_value": 0.5253654342218401,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 3770/7655 or 3515/6912?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.01604731006725213,
      "pure_math": {
        "question": "Which is larger: 3770/7655 or 3515/6912?",
        "options": [
          "3515/6912",
          "2243/4311",
          "3770/7655",
          "620/1217"
        ],
        "answer": "3515/6912",
        "correct_value": 0.5085358796296297,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 4621/8401 or 1568/2702?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 4621/8401 or 1568/2702?",
        "options": [
          "4633/6881",
          "4621/8401",
          "1568/2702",
          "2521/3974"
        ],
        "answer": "1568/2702",
        "correct_value": 0.5803108808290155,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000507",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 1761/3607 or 839/1585?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.04112018428939873,
      "pure_math": {
        "question": "Which is larger: 1761/3607 or 839/1585?",
        "options": [
          "2466/4706",
          "1761/3607",
          "839/1585",
          "1539/3361"
        ],
        "answer": "839/1585",
        "correct_value": 0.5293375394321767,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 3434/6901 or 579/1145?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.008067813727394735,
      "pure_math": {
        "question": "Which is larger: 3434/6901 or 579/1145?",
        "options": [
          "3434/6901",
          "4465/9420",
          "579/1145",
          "1790/3897"
        ],
        "answer": "579/1145",
        "correct_value": 0.5056768558951965,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 3367/6121 or 1402/2416?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 3367/6121 or 1402/2416?",
        "options": [
          "4071/8380",
          "1402/2416",
          "5253/8572",
          "3367/6121"
        ],
        "answer": "1402/2416",
        "correct_value": 0.5802980132450332,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000508",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 4574/9563 or 1066/2067?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.037421482298455044,
      "pure_math": {
        "question": "Which is larger: 4574/9563 or 1066/2067?",
        "options": [
          "1066/2067",
          "4574/9563",
          "4154/9609",
          "603/1396"
        ],
        "answer": "1066/2067",
        "correct_value": 0.5157232704402516,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 2831/5778 or 3246/6351?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.021138689535159627,
      "pure_math": {
        "question": "Which is larger: 2831/5778 or 3246/6351?",
        "options": [
          "3246/6351",
          "2647/5642",
          "2831/5778",
          "1235/2166"
        ],
        "answer": "3246/6351",
        "correct_value": 0.5111006140765234,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 5282/9603 or 5469/9428?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 5282/9603 or 5469/9428?",
        "options": [
          "5026/9626",
          "5282/9603",
          "5469/9428",
          "5102/7686"
        ],
        "answer": "5469/9428",
        "correct_value": 0.580080610946118,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000509",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 2291/4721 or 3587/6872?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.036694681998225065,
      "pure_math": {
        "question": "Which is larger: 2291/4721 or 3587/6872?",
        "options": [
          "4242/7771",
          "2210/5153",
          "2291/4721",
          "3587/6872"
        ],
        "answer": "3587/6872",
        "correct_value": 0.5219732246798603,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 4211/8613 or 1408/2790?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.01574738860612057,
      "pure_math": {
        "question": "Which is larger: 4211/8613 or 1408/2790?",
        "options": [
          "1408/2790",
          "1357/2398",
          "4881/9473",
          "4211/8613"
        ],
        "answer": "1408/2790",
        "correct_value": 0.5046594982078854,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 2742/4984 or 1384/2386?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 2742/4984 or 1384/2386?",
        "options": [
          "3570/7126",
          "2742/4984",
          "1384/2386",
          "4139/6960"
        ],
        "answer": "1384/2386",
        "correct_value": 0.5800502933780386,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000510",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 1151/2394 or 1112/2130?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.041280431124760264,
      "pure_math": {
        "question": "Which is larger: 1151/2394 or 1112/2130?",
        "options": [
          "3705/7774",
          "4009/7704",
          "1151/2394",
          "1112/2130"
        ],
        "answer": "1112/2130",
        "correct_value": 0.5220657276995305,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 3075/6212 or 4122/8130?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.012001411385652805,
      "pure_math": {
        "question": "Which is larger: 3075/6212 or 4122/8130?",
        "options": [
          "899/2130",
          "4122/8130",
          "3075/6212",
          "4451/8441"
        ],
        "answer": "4122/8130",
        "correct_value": 0.5070110701107011,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 5441/9891 or 3274/5644?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 5441/9891 or 3274/5644?",
        "options": [
          "1933/3100",
          "5441/9891",
          "3274/5644",
          "3421/6887"
        ],
        "answer": "3274/5644",
        "correct_value": 0.5800850460666194,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000511",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 1129/2359 or 2815/5467?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.036315003590466466,
      "pure_math": {
        "question": "Which is larger: 1129/2359 or 2815/5467?",
        "options": [
          "4617/7544",
          "1129/2359",
          "3097/7257",
          "2815/5467"
        ],
        "answer": "2815/5467",
        "correct_value": 0.5149076275836839,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 4439/9101 or 3283/6394?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.025701510422586338,
      "pure_math": {
        "question": "Which is larger: 4439/9101 or 3283/6394?",
        "options": [
          "4478/7448",
          "4439/9101",
          "2316/5539",
          "3283/6394"
        ],
        "answer": "3283/6394",
        "correct_value": 0.5134501094776353,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 4033/7331 or 1373/2367?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 4033/7331 or 1373/2367?",
        "options": [
          "3443/7076",
          "4033/7331",
          "2579/4224",
          "1373/2367"
        ],
        "answer": "1373/2367",
        "correct_value": 0.5800591465990705,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000512",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 876/1861 or 4150/8118?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.04049498801861151,
      "pure_math": {
        "question": "Which is larger: 876/1861 or 4150/8118?",
        "options": [
          "4150/8118",
          "876/1861",
          "848/1984",
          "5079/8348"
        ],
        "answer": "4150/8118",
        "correct_value": 0.5112096575511209,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 2038/4095 or 3201/6326?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.00832685774196995,
      "pure_math": {
        "question": "Which is larger: 2038/4095 or 3201/6326?",
        "options": [
          "3951/6710",
          "2038/4095",
          "3201/6326",
          "913/1833"
        ],
        "answer": "3201/6326",
        "correct_value": 0.5060069554220676,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 1169/2124 or 2782/4796?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 1169/2124 or 2782/4796?",
        "options": [
          "1508/2543",
          "3319/5369",
          "1169/2124",
          "2782/4796"
        ],
        "answer": "2782/4796",
        "correct_value": 0.5800667222685572,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000513",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 2115/4442 or 4220/8125?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.043247740103210586,
      "pure_math": {
        "question": "Which is larger: 2115/4442 or 4220/8125?",
        "options": [
          "2988/6396",
          "2115/4442",
          "4220/8125",
          "2510/5912"
        ],
        "answer": "4220/8125",
        "correct_value": 0.5193846153846153,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 4164/8518 or 1455/2846?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.022396703801317253,
      "pure_math": {
        "question": "Which is larger: 4164/8518 or 1455/2846?",
        "options": [
          "1455/2846",
          "4435/9722",
          "4164/8518",
          "1509/2827"
        ],
        "answer": "1455/2846",
        "correct_value": 0.511243851018974,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 1049/1907 or 3952/6813?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 1049/1907 or 3952/6813?",
        "options": [
          "3070/4539",
          "3952/6813",
          "1049/1907",
          "2244/4008"
        ],
        "answer": "3952/6813",
        "correct_value": 0.5800675179803317,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000514",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 3836/7863 or 1240/2380?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.03315389490401277,
      "pure_math": {
        "question": "Which is larger: 3836/7863 or 1240/2380?",
        "options": [
          "4761/7977",
          "1240/2380",
          "3836/7863",
          "2145/3881"
        ],
        "answer": "1240/2380",
        "correct_value": 0.5210084033613446,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 3773/7611 or 2090/4080?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.016525037291227063,
      "pure_math": {
        "question": "Which is larger: 3773/7611 or 2090/4080?",
        "options": [
          "2896/5449",
          "5960/9969",
          "2090/4080",
          "3773/7611"
        ],
        "answer": "2090/4080",
        "correct_value": 0.5122549019607843,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 4621/8401 or 1629/2807?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 4621/8401 or 1629/2807?",
        "options": [
          "4621/8401",
          "1629/2807",
          "2730/4365",
          "3336/4971"
        ],
        "answer": "1629/2807",
        "correct_value": 0.5803348770929818,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000515",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 1065/2258 or 930/1801?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.04472345596802091,
      "pure_math": {
        "question": "Which is larger: 1065/2258 or 930/1801?",
        "options": [
          "576/1110",
          "2301/5118",
          "930/1801",
          "1065/2258"
        ],
        "answer": "930/1801",
        "correct_value": 0.5163797890061077,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 4756/9664 or 3481/6855?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.01566876065713141,
      "pure_math": {
        "question": "Which is larger: 4756/9664 or 3481/6855?",
        "options": [
          "603/1004",
          "2578/6064",
          "4756/9664",
          "3481/6855"
        ],
        "answer": "3481/6855",
        "correct_value": 0.5078045222465354,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 1169/2124 or 5737/9891?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 1169/2124 or 5737/9891?",
        "options": [
          "1169/2124",
          "5737/9891",
          "6250/9795",
          "1903/3080"
        ],
        "answer": "5737/9891",
        "correct_value": 0.5800222424426246,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000516",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 3696/7723 or 5022/9842?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.031691638150813384,
      "pure_math": {
        "question": "Which is larger: 3696/7723 or 5022/9842?",
        "options": [
          "677/1587",
          "2788/5771",
          "5022/9842",
          "3696/7723"
        ],
        "answer": "5022/9842",
        "correct_value": 0.5102621418410892,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 2857/5805 or 3452/6799?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.015559794411677541,
      "pure_math": {
        "question": "Which is larger: 2857/5805 or 3452/6799?",
        "options": [
          "2761/6457",
          "930/1802",
          "2857/5805",
          "3452/6799"
        ],
        "answer": "3452/6799",
        "correct_value": 0.5077217237829093,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 5275/9590 or 1576/2717?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 5275/9590 or 1576/2717?",
        "options": [
          "1576/2717",
          "1560/2477",
          "1505/2342",
          "5275/9590"
        ],
        "answer": "1576/2717",
        "correct_value": 0.5800515274199485,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000517",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 2913/5963 or 1266/2469?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.024245707989874354,
      "pure_math": {
        "question": "Which is larger: 2913/5963 or 1266/2469?",
        "options": [
          "4031/9632",
          "1266/2469",
          "5397/9634",
          "2913/5963"
        ],
        "answer": "1266/2469",
        "correct_value": 0.5127582017010935,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 507/1030 or 651/1296?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.010081805106076924,
      "pure_math": {
        "question": "Which is larger: 507/1030 or 651/1296?",
        "options": [
          "1054/2234",
          "2969/7192",
          "651/1296",
          "507/1030"
        ],
        "answer": "651/1296",
        "correct_value": 0.5023148148148148,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 3090/5617 or 2526/4354?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 3090/5617 or 2526/4354?",
        "options": [
          "3090/5617",
          "1983/2979",
          "4702/8627",
          "2526/4354"
        ],
        "answer": "2526/4354",
        "correct_value": 0.5801561782269178,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000518",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 1224/2533 or 2082/4029?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.033532060347714,
      "pure_math": {
        "question": "Which is larger: 1224/2533 or 2082/4029?",
        "options": [
          "1224/2533",
          "2082/4029",
          "2039/4465",
          "4320/8790"
        ],
        "answer": "2082/4029",
        "correct_value": 0.5167535368577811,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 3858/7926 or 2451/4774?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.02665348863243905,
      "pure_math": {
        "question": "Which is larger: 3858/7926 or 2451/4774?",
        "options": [
          "3858/7926",
          "3615/8324",
          "2451/4774",
          "1021/1738"
        ],
        "answer": "2451/4774",
        "correct_value": 0.5134059488898198,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 1833/3332 or 1743/3005?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 1833/3332 or 1743/3005?",
        "options": [
          "708/1391",
          "4441/7620",
          "1743/3005",
          "1833/3332"
        ],
        "answer": "1743/3005",
        "correct_value": 0.5800332778702163,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000519",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 4192/8743 or 3885/7521?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.03708436006312599,
      "pure_math": {
        "question": "Which is larger: 4192/8743 or 3885/7521?",
        "options": [
          "4192/8743",
          "4112/6805",
          "3109/7250",
          "3885/7521"
        ],
        "answer": "3885/7521",
        "correct_value": 0.5165536497806142,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 2786/5607 or 823/1616?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.012403276844538347,
      "pure_math": {
        "question": "Which is larger: 2786/5607 or 823/1616?",
        "options": [
          "2786/5607",
          "2908/5704",
          "823/1616",
          "4675/8854"
        ],
        "answer": "823/1616",
        "correct_value": 0.5092821782178217,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 2598/4723 or 2121/3656?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 2598/4723 or 2121/3656?",
        "options": [
          "2121/3656",
          "647/1004",
          "4091/6563",
          "2598/4723"
        ],
        "answer": "2121/3656",
        "correct_value": 0.5801422319474836,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000520",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 4492/9276 or 3990/7700?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.033921361088243396,
      "pure_math": {
        "question": "Which is larger: 4492/9276 or 3990/7700?",
        "options": [
          "4492/9276",
          "4533/7570",
          "3990/7700",
          "1086/2564"
        ],
        "answer": "3990/7700",
        "correct_value": 0.5181818181818182,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 703/1440 or 3614/7049?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.02450239198625498,
      "pure_math": {
        "question": "Which is larger: 703/1440 or 3614/7049?",
        "options": [
          "1487/2679",
          "703/1440",
          "2909/4935",
          "3614/7049"
        ],
        "answer": "3614/7049",
        "correct_value": 0.5126968364306994,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 2122/3857 or 4363/7521?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 2122/3857 or 4363/7521?",
        "options": [
          "4363/7521",
          "1958/3581",
          "2122/3857",
          "1237/2406"
        ],
        "answer": "4363/7521",
        "correct_value": 0.5801090280547799,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000521",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 1636/3441 or 1135/2160?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.05001977784235845,
      "pure_math": {
        "question": "Which is larger: 1636/3441 or 1135/2160?",
        "options": [
          "1636/3441",
          "1135/2160",
          "2662/4824",
          "2364/4800"
        ],
        "answer": "1135/2160",
        "correct_value": 0.5254629629629629,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 1802/3676 or 4617/9102?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.017044407129069628,
      "pure_math": {
        "question": "Which is larger: 1802/3676 or 4617/9102?",
        "options": [
          "1802/3676",
          "1393/2811",
          "4617/9102",
          "4620/9621"
        ],
        "answer": "4617/9102",
        "correct_value": 0.507251153592617,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 570/1035 or 4022/6933?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 570/1035 or 4022/6933?",
        "options": [
          "2283/4147",
          "4022/6933",
          "4783/9783",
          "570/1035"
        ],
        "answer": "4022/6933",
        "correct_value": 0.5801240444252127,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000522",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 3196/6605 or 2062/3940?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.03947440217955178,
      "pure_math": {
        "question": "Which is larger: 3196/6605 or 2062/3940?",
        "options": [
          "4290/7361",
          "3196/6605",
          "2062/3940",
          "1719/3834"
        ],
        "answer": "2062/3940",
        "correct_value": 0.5233502538071066,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 4405/8957 or 4579/8994?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.0173230617392231,
      "pure_math": {
        "question": "Which is larger: 4405/8957 or 4579/8994?",
        "options": [
          "4405/8957",
          "885/1826",
          "3186/5270",
          "4579/8994"
        ],
        "answer": "4579/8994",
        "correct_value": 0.5091171892372693,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 3346/6082 or 3217/5545?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 3346/6082 or 3217/5545?",
        "options": [
          "1450/2374",
          "3550/6876",
          "3217/5545",
          "3346/6082"
        ],
        "answer": "3217/5545",
        "correct_value": 0.5801623083859333,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000523",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 3232/6723 or 1308/2502?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.042044008702007585,
      "pure_math": {
        "question": "Which is larger: 3232/6723 or 1308/2502?",
        "options": [
          "3232/6723",
          "2950/5214",
          "3599/8289",
          "1308/2502"
        ],
        "answer": "1308/2502",
        "correct_value": 0.5227817745803357,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 1472/3012 or 4739/9407?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.015061966089788492,
      "pure_math": {
        "question": "Which is larger: 1472/3012 or 4739/9407?",
        "options": [
          "3825/6790",
          "4739/9407",
          "1472/3012",
          "1331/3228"
        ],
        "answer": "4739/9407",
        "correct_value": 0.5037737854788987,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 1697/3085 or 2986/5147?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 1697/3085 or 2986/5147?",
        "options": [
          "1697/3085",
          "2986/5147",
          "3697/7243",
          "4936/9013"
        ],
        "answer": "2986/5147",
        "correct_value": 0.5801437730716923,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000524",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 3367/6924 or 4100/7968?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.02827862576823753,
      "pure_math": {
        "question": "Which is larger: 3367/6924 or 4100/7968?",
        "options": [
          "1602/2699",
          "2116/4792",
          "3367/6924",
          "4100/7968"
        ],
        "answer": "4100/7968",
        "correct_value": 0.5145582329317269,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 670/1355 or 1671/3275?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.01576406298414129,
      "pure_math": {
        "question": "Which is larger: 670/1355 or 1671/3275?",
        "options": [
          "2545/4545",
          "1671/3275",
          "670/1355",
          "477/1119"
        ],
        "answer": "1671/3275",
        "correct_value": 0.5102290076335878,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 4186/7610 or 5563/9591?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 4186/7610 or 5563/9591?",
        "options": [
          "4096/6903",
          "5563/9591",
          "5007/9062",
          "4186/7610"
        ],
        "answer": "5563/9591",
        "correct_value": 0.5800229381712022,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000525",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 4148/8645 or 1075/2070?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.039508749577399416,
      "pure_math": {
        "question": "Which is larger: 4148/8645 or 1075/2070?",
        "options": [
          "4218/7012",
          "1075/2070",
          "4148/8645",
          "846/1948"
        ],
        "answer": "1075/2070",
        "correct_value": 0.5193236714975845,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 999/2025 or 3938/7760?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.014140893470790339,
      "pure_math": {
        "question": "Which is larger: 999/2025 or 3938/7760?",
        "options": [
          "3938/7760",
          "999/2025",
          "874/2097",
          "3790/7857"
        ],
        "answer": "3938/7760",
        "correct_value": 0.5074742268041237,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 660/1199 or 2527/4356?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 660/1199 or 2527/4356?",
        "options": [
          "3858/5708",
          "2184/3258",
          "660/1199",
          "2527/4356"
        ],
        "answer": "2527/4356",
        "correct_value": 0.580119375573921,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000526",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 2433/5025 or 5002/9775?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.02753445050960035,
      "pure_math": {
        "question": "Which is larger: 2433/5025 or 5002/9775?",
        "options": [
          "4027/7545",
          "1529/2711",
          "5002/9775",
          "2433/5025"
        ],
        "answer": "5002/9775",
        "correct_value": 0.5117135549872123,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 2853/5863 or 3431/6764?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.0206332841553738,
      "pure_math": {
        "question": "Which is larger: 2853/5863 or 3431/6764?",
        "options": [
          "3431/6764",
          "1491/3514",
          "2853/5863",
          "4300/8556"
        ],
        "answer": "3431/6764",
        "correct_value": 0.507244234180958,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 2726/4955 or 1339/2308?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 2726/4955 or 1339/2308?",
        "options": [
          "2726/4955",
          "1339/2308",
          "3661/7122",
          "5819/8672"
        ],
        "answer": "1339/2308",
        "correct_value": 0.580155979202773,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000527",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 691/1467 or 3759/7322?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.04235500970360029,
      "pure_math": {
        "question": "Which is larger: 691/1467 or 3759/7322?",
        "options": [
          "3196/6626",
          "2609/4346",
          "691/1467",
          "3759/7322"
        ],
        "answer": "3759/7322",
        "correct_value": 0.5133843212237094,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 3413/6995 or 3178/6178?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.02648601380396809,
      "pure_math": {
        "question": "Which is larger: 3413/6995 or 3178/6178?",
        "options": [
          "3178/6178",
          "3413/6995",
          "3545/7770",
          "702/1686"
        ],
        "answer": "3178/6178",
        "correct_value": 0.5144059566202654,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 5134/9334 or 3584/6179?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 5134/9334 or 3584/6179?",
        "options": [
          "3584/6179",
          "2141/3978",
          "3798/5689",
          "5134/9334"
        ],
        "answer": "3584/6179",
        "correct_value": 0.5800291309273345,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000528",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 950/1988 or 3992/7689?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.04131604557766683,
      "pure_math": {
        "question": "Which is larger: 950/1988 or 3992/7689?",
        "options": [
          "950/1988",
          "525/1012",
          "3733/7602",
          "3992/7689"
        ],
        "answer": "3992/7689",
        "correct_value": 0.5191832487969827,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 2300/4668 or 4241/8395?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.01246528899511229,
      "pure_math": {
        "question": "Which is larger: 2300/4668 or 4241/8395?",
        "options": [
          "2300/4668",
          "770/1548",
          "4241/8395",
          "1911/3655"
        ],
        "answer": "4241/8395",
        "correct_value": 0.5051816557474688,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 4433/8060 or 4310/7430?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 4433/8060 or 4310/7430?",
        "options": [
          "4433/8060",
          "4310/7430",
          "2195/3231",
          "1333/2004"
        ],
        "answer": "4310/7430",
        "correct_value": 0.5800807537012113,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000529",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 2291/4734 or 1541/2985?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.03230198308823373,
      "pure_math": {
        "question": "Which is larger: 2291/4734 or 1541/2985?",
        "options": [
          "1541/2985",
          "2520/5980",
          "5037/8247",
          "2291/4734"
        ],
        "answer": "1541/2985",
        "correct_value": 0.5162479061976549,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 4263/8705 or 3604/7110?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.017173149272408428,
      "pure_math": {
        "question": "Which is larger: 4263/8705 or 3604/7110?",
        "options": [
          "4263/8705",
          "5029/8892",
          "3604/7110",
          "4703/9509"
        ],
        "answer": "3604/7110",
        "correct_value": 0.5068917018284107,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 3298/5995 or 4421/7622?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 3298/5995 or 4421/7622?",
        "options": [
          "3298/5995",
          "4421/7622",
          "1133/1724",
          "6379/9713"
        ],
        "answer": "4421/7622",
        "correct_value": 0.5800314877984781,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000530",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 4215/8704 or 4048/7805?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.03438178592625396,
      "pure_math": {
        "question": "Which is larger: 4215/8704 or 4048/7805?",
        "options": [
          "3622/8009",
          "4048/7805",
          "4215/8704",
          "830/1622"
        ],
        "answer": "4048/7805",
        "correct_value": 0.5186418962203716,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 3898/7908 or 522/1020?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.018846142402332677,
      "pure_math": {
        "question": "Which is larger: 3898/7908 or 522/1020?",
        "options": [
          "4921/9155",
          "522/1020",
          "3133/7077",
          "3898/7908"
        ],
        "answer": "522/1020",
        "correct_value": 0.5117647058823529,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 2328/4232 or 1511/2605?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 2328/4232 or 1511/2605?",
        "options": [
          "1727/3514",
          "1511/2605",
          "2328/4232",
          "3487/5972"
        ],
        "answer": "1511/2605",
        "correct_value": 0.5800383877159309,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000531",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 1413/2924 or 5003/9805?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.02700773845109594,
      "pure_math": {
        "question": "Which is larger: 1413/2924 or 5003/9805?",
        "options": [
          "5003/9805",
          "1413/2924",
          "2111/4594",
          "3981/8604"
        ],
        "answer": "5003/9805",
        "correct_value": 0.5102498725140234,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 3947/8037 or 2396/4719?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.01663104391395137,
      "pure_math": {
        "question": "Which is larger: 3947/8037 or 2396/4719?",
        "options": [
          "4878/9755",
          "2396/4719",
          "1425/2571",
          "3947/8037"
        ],
        "answer": "2396/4719",
        "correct_value": 0.5077346895528714,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 5331/9691 or 4663/8038?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 5331/9691 or 4663/8038?",
        "options": [
          "3604/5544",
          "4663/8038",
          "5331/9691",
          "2898/5850"
        ],
        "answer": "4663/8038",
        "correct_value": 0.5801194326947001,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000532",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 1577/3229 or 4499/8628?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.03305531997129052,
      "pure_math": {
        "question": "Which is larger: 1577/3229 or 4499/8628?",
        "options": [
          "863/1867",
          "2613/5444",
          "1577/3229",
          "4499/8628"
        ],
        "answer": "4499/8628",
        "correct_value": 0.5214418173388966,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 651/1321 or 4165/8224?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.013636074103747564,
      "pure_math": {
        "question": "Which is larger: 651/1321 or 4165/8224?",
        "options": [
          "651/1321",
          "1557/3547",
          "4165/8224",
          "1470/3174"
        ],
        "answer": "4165/8224",
        "correct_value": 0.5064445525291829,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 3126/5683 or 1149/1980?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 3126/5683 or 1149/1980?",
        "options": [
          "1149/1980",
          "3126/5683",
          "816/1677",
          "4221/7622"
        ],
        "answer": "1149/1980",
        "correct_value": 0.5803030303030303,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000533",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 4239/8731 or 676/1290?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.038519611577387536,
      "pure_math": {
        "question": "Which is larger: 4239/8731 or 676/1290?",
        "options": [
          "4239/8731",
          "676/1290",
          "1326/3086",
          "3768/8780"
        ],
        "answer": "676/1290",
        "correct_value": 0.524031007751938,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 2400/4862 or 1575/3123?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.010698743534817423,
      "pure_math": {
        "question": "Which is larger: 2400/4862 or 1575/3123?",
        "options": [
          "1575/3123",
          "781/1843",
          "513/1121",
          "2400/4862"
        ],
        "answer": "1575/3123",
        "correct_value": 0.5043227665706052,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 1909/3470 or 2046/3527?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 1909/3470 or 2046/3527?",
        "options": [
          "1855/3573",
          "1909/3470",
          "4561/7723",
          "2046/3527"
        ],
        "answer": "2046/3527",
        "correct_value": 0.5800963992061242,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000534",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 1687/3463 or 1082/2080?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.033042437637442024,
      "pure_math": {
        "question": "Which is larger: 1687/3463 or 1082/2080?",
        "options": [
          "4627/8310",
          "3697/6437",
          "1082/2080",
          "1687/3463"
        ],
        "answer": "1082/2080",
        "correct_value": 0.5201923076923077,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 3368/6863 or 5055/9916?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.019034683708002265,
      "pure_math": {
        "question": "Which is larger: 3368/6863 or 5055/9916?",
        "options": [
          "3368/6863",
          "5055/9916",
          "1449/2629",
          "1955/3580"
        ],
        "answer": "5055/9916",
        "correct_value": 0.5097821702299314,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 742/1349 or 3645/6284?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 742/1349 or 3645/6284?",
        "options": [
          "5006/8429",
          "3645/6284",
          "5631/9877",
          "742/1349"
        ],
        "answer": "3645/6284",
        "correct_value": 0.58004455760662,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000535",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 4806/9994 or 4838/9350?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.03654462196034203,
      "pure_math": {
        "question": "Which is larger: 4806/9994 or 4838/9350?",
        "options": [
          "4838/9350",
          "1125/2479",
          "4529/7452",
          "4806/9994"
        ],
        "answer": "4838/9350",
        "correct_value": 0.5174331550802139,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 2080/4249 or 1977/3874?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.020798297707511293,
      "pure_math": {
        "question": "Which is larger: 2080/4249 or 1977/3874?",
        "options": [
          "1765/3230",
          "2080/4249",
          "906/1744",
          "1977/3874"
        ],
        "answer": "1977/3874",
        "correct_value": 0.5103252452245741,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 921/1674 or 2861/4932?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 921/1674 or 2861/4932?",
        "options": [
          "1451/2137",
          "921/1674",
          "939/1743",
          "2861/4932"
        ],
        "answer": "2861/4932",
        "correct_value": 0.5800892133008921,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000536",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 4227/8715 or 2578/4974?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.03326931714450426,
      "pure_math": {
        "question": "Which is larger: 4227/8715 or 2578/4974?",
        "options": [
          "4227/8715",
          "2578/4974",
          "3195/6116",
          "3368/6660"
        ],
        "answer": "2578/4974",
        "correct_value": 0.5182951347004423,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 4531/9227 or 2577/5124?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.011868551438363406,
      "pure_math": {
        "question": "Which is larger: 4531/9227 or 2577/5124?",
        "options": [
          "4531/9227",
          "2479/4905",
          "2577/5124",
          "1395/2557"
        ],
        "answer": "2577/5124",
        "correct_value": 0.502927400468384,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 1803/3277 or 4410/7602?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 1803/3277 or 4410/7602?",
        "options": [
          "3354/5814",
          "3310/4913",
          "4410/7602",
          "1803/3277"
        ],
        "answer": "4410/7602",
        "correct_value": 0.580110497237569,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000537",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 589/1257 or 4520/8748?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.04811355449264637,
      "pure_math": {
        "question": "Which is larger: 589/1257 or 4520/8748?",
        "options": [
          "589/1257",
          "3858/7807",
          "3568/7877",
          "4520/8748"
        ],
        "answer": "4520/8748",
        "correct_value": 0.516689529035208,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 1302/2616 or 3160/6252?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.007731837738529201,
      "pure_math": {
        "question": "Which is larger: 1302/2616 or 3160/6252?",
        "options": [
          "4382/8072",
          "605/1031",
          "1302/2616",
          "3160/6252"
        ],
        "answer": "3160/6252",
        "correct_value": 0.5054382597568778,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 4091/7437 or 917/1581?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 4091/7437 or 917/1581?",
        "options": [
          "5253/8011",
          "4091/7437",
          "3997/5920",
          "917/1581"
        ],
        "answer": "917/1581",
        "correct_value": 0.5800126502213788,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000538",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 2070/4318 or 1903/3714?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.032996962284589426,
      "pure_math": {
        "question": "Which is larger: 2070/4318 or 1903/3714?",
        "options": [
          "5389/8922",
          "2070/4318",
          "1903/3714",
          "1294/2280"
        ],
        "answer": "1903/3714",
        "correct_value": 0.5123855681206246,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 1334/2702 or 2492/4911?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.013723930673614326,
      "pure_math": {
        "question": "Which is larger: 1334/2702 or 2492/4911?",
        "options": [
          "5626/9330",
          "3028/5443",
          "2492/4911",
          "1334/2702"
        ],
        "answer": "2492/4911",
        "correct_value": 0.5074322948482998,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 4519/8215 or 2258/3893?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 4519/8215 or 2258/3893?",
        "options": [
          "4519/8215",
          "4936/7619",
          "2017/3739",
          "2258/3893"
        ],
        "answer": "2258/3893",
        "correct_value": 0.5800154122784485,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000539",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 4708/9631 or 3885/7455?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.03228863368143653,
      "pure_math": {
        "question": "Which is larger: 4708/9631 or 3885/7455?",
        "options": [
          "3885/7455",
          "4708/9631",
          "3937/6491",
          "1966/3569"
        ],
        "answer": "3885/7455",
        "correct_value": 0.5211267605633803,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 1458/3000 or 4799/9337?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.02797665202955979,
      "pure_math": {
        "question": "Which is larger: 1458/3000 or 4799/9337?",
        "options": [
          "4663/9760",
          "4799/9337",
          "1458/3000",
          "1721/3980"
        ],
        "answer": "4799/9337",
        "correct_value": 0.5139766520295598,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 2251/4092 or 2314/3988?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 2251/4092 or 2314/3988?",
        "options": [
          "2574/3795",
          "2251/4092",
          "2314/3988",
          "3244/5317"
        ],
        "answer": "2314/3988",
        "correct_value": 0.5802407221664995,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000540",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 1357/2863 or 653/1232?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.05605412313847524,
      "pure_math": {
        "question": "Which is larger: 1357/2863 or 653/1232?",
        "options": [
          "4261/7084",
          "653/1232",
          "1357/2863",
          "3005/5434"
        ],
        "answer": "653/1232",
        "correct_value": 0.5300324675324676,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 2765/5666 or 1293/2574?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.01433241426181775,
      "pure_math": {
        "question": "Which is larger: 2765/5666 or 1293/2574?",
        "options": [
          "1378/3352",
          "2765/5666",
          "1293/2574",
          "3794/8013"
        ],
        "answer": "1293/2574",
        "correct_value": 0.5023310023310024,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 3249/5906 or 1086/1871?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 3249/5906 or 1086/1871?",
        "options": [
          "3499/6743",
          "1086/1871",
          "2366/4789",
          "3249/5906"
        ],
        "answer": "1086/1871",
        "correct_value": 0.5804382683057189,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000541",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 3455/7057 or 1296/2457?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.03788771806343011,
      "pure_math": {
        "question": "Which is larger: 3455/7057 or 1296/2457?",
        "options": [
          "1296/2457",
          "3455/7057",
          "1448/2762",
          "2582/4176"
        ],
        "answer": "1296/2457",
        "correct_value": 0.5274725274725275,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 4288/8738 or 4278/8346?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.021850732869101497,
      "pure_math": {
        "question": "Which is larger: 4288/8738 or 4278/8346?",
        "options": [
          "4288/8738",
          "3812/6978",
          "3244/6720",
          "4278/8346"
        ],
        "answer": "4278/8346",
        "correct_value": 0.5125808770668584,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 1762/3203 or 2041/3518?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 1762/3203 or 2041/3518?",
        "options": [
          "2041/3518",
          "1762/3203",
          "2626/5023",
          "5147/8264"
        ],
        "answer": "2041/3518",
        "correct_value": 0.5801591813530415,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000542",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 1738/3563 or 4691/9070?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.02940837178387079,
      "pure_math": {
        "question": "Which is larger: 1738/3563 or 4691/9070?",
        "options": [
          "1738/3563",
          "1308/2524",
          "3653/6715",
          "4691/9070"
        ],
        "answer": "4691/9070",
        "correct_value": 0.517199558985667,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 4477/9039 or 3111/6106?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.014200701136143745,
      "pure_math": {
        "question": "Which is larger: 4477/9039 or 3111/6106?",
        "options": [
          "4477/9039",
          "1527/2958",
          "3842/6686",
          "3111/6106"
        ],
        "answer": "3111/6106",
        "correct_value": 0.509498853586636,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 882/1603 or 3215/5543?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 882/1603 or 3215/5543?",
        "options": [
          "1650/3399",
          "3215/5543",
          "882/1603",
          "4741/7427"
        ],
        "answer": "3215/5543",
        "correct_value": 0.580010824463287,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000543",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 1740/3636 or 935/1782?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.04614350323921279,
      "pure_math": {
        "question": "Which is larger: 1740/3636 or 935/1782?",
        "options": [
          "1740/3636",
          "1028/1719",
          "566/1095",
          "935/1782"
        ],
        "answer": "935/1782",
        "correct_value": 0.5246913580246914,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 576/1163 or 1307/2579?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.011514724557799838,
      "pure_math": {
        "question": "Which is larger: 576/1163 or 1307/2579?",
        "options": [
          "3478/7986",
          "576/1163",
          "1307/2579",
          "4082/9615"
        ],
        "answer": "1307/2579",
        "correct_value": 0.5067855758045754,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 3640/6617 or 1284/2213?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 3640/6617 or 1284/2213?",
        "options": [
          "2211/3638",
          "4202/6334",
          "3640/6617",
          "1284/2213"
        ],
        "answer": "1284/2213",
        "correct_value": 0.5802078626299142,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000544",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 564/1193 or 2777/5354?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.04591987064375341,
      "pure_math": {
        "question": "Which is larger: 564/1193 or 2777/5354?",
        "options": [
          "2777/5354",
          "4021/6751",
          "2002/4605",
          "564/1193"
        ],
        "answer": "2777/5354",
        "correct_value": 0.518677624206201,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 3073/6182 or 2312/4534?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.01283669009605265,
      "pure_math": {
        "question": "Which is larger: 3073/6182 or 2312/4534?",
        "options": [
          "545/1164",
          "3073/6182",
          "4129/9426",
          "2312/4534"
        ],
        "answer": "2312/4534",
        "correct_value": 0.50992501102779,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 1836/3337 or 1582/2726?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 1836/3337 or 1582/2726?",
        "options": [
          "1836/3337",
          "3966/6408",
          "2258/4182",
          "1582/2726"
        ],
        "answer": "1582/2726",
        "correct_value": 0.5803374908290535,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000545",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 546/1163 or 4178/8181?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.04122001958483801,
      "pure_math": {
        "question": "Which is larger: 546/1163 or 4178/8181?",
        "options": [
          "3376/6472",
          "546/1163",
          "4178/8181",
          "1362/2256"
        ],
        "answer": "4178/8181",
        "correct_value": 0.510695513995844,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 1123/2272 or 4239/8365?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.012476164518491761,
      "pure_math": {
        "question": "Which is larger: 1123/2272 or 4239/8365?",
        "options": [
          "544/1169",
          "4239/8365",
          "1785/3232",
          "1123/2272"
        ],
        "answer": "4239/8365",
        "correct_value": 0.5067543335325763,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 4097/7449 or 5590/9637?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 4097/7449 or 5590/9637?",
        "options": [
          "1595/2643",
          "4097/7449",
          "5575/9833",
          "5590/9637"
        ],
        "answer": "5590/9637",
        "correct_value": 0.5800560340354882,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000546",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 2529/5242 or 3326/6478?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.03098062423353115,
      "pure_math": {
        "question": "Which is larger: 2529/5242 or 3326/6478?",
        "options": [
          "2061/4086",
          "3187/7258",
          "3326/6478",
          "2529/5242"
        ],
        "answer": "3326/6478",
        "correct_value": 0.5134300710095708,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 562/1151 or 1869/3717?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.01455379012109348,
      "pure_math": {
        "question": "Which is larger: 562/1151 or 1869/3717?",
        "options": [
          "1772/3473",
          "562/1151",
          "2516/4290",
          "1869/3717"
        ],
        "answer": "1869/3717",
        "correct_value": 0.5028248587570622,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 613/1114 or 5201/8966?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 613/1114 or 5201/8966?",
        "options": [
          "5201/8966",
          "4330/6880",
          "613/1114",
          "4958/9495"
        ],
        "answer": "5201/8966",
        "correct_value": 0.5800803033682802,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000547",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 3562/7384 or 4349/8510?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.028651462239949632,
      "pure_math": {
        "question": "Which is larger: 3562/7384 or 4349/8510?",
        "options": [
          "3562/7384",
          "875/1810",
          "2763/5571",
          "4349/8510"
        ],
        "answer": "4349/8510",
        "correct_value": 0.5110458284371328,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 1146/2321 or 2935/5835?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.009246450297145381,
      "pure_math": {
        "question": "Which is larger: 1146/2321 or 2935/5835?",
        "options": [
          "3371/6895",
          "2935/5835",
          "1146/2321",
          "1888/3457"
        ],
        "answer": "2935/5835",
        "correct_value": 0.5029991431019709,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 4914/8934 or 766/1320?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 4914/8934 or 766/1320?",
        "options": [
          "4914/8934",
          "2823/4203",
          "766/1320",
          "4605/9437"
        ],
        "answer": "766/1320",
        "correct_value": 0.5803030303030303,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000548",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 2084/4345 or 1083/2117?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.031941219988552316,
      "pure_math": {
        "question": "Which is larger: 2084/4345 or 1083/2117?",
        "options": [
          "803/1447",
          "1083/2117",
          "3159/6685",
          "2084/4345"
        ],
        "answer": "1083/2117",
        "correct_value": 0.5115729806329712,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 1462/2941 or 1754/3456?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.01041332155855279,
      "pure_math": {
        "question": "Which is larger: 1462/2941 or 1754/3456?",
        "options": [
          "696/1626",
          "1754/3456",
          "1462/2941",
          "3974/7902"
        ],
        "answer": "1754/3456",
        "correct_value": 0.5075231481481481,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 977/1775 or 1171/2018?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 977/1775 or 1171/2018?",
        "options": [
          "1167/2351",
          "4396/9082",
          "977/1775",
          "1171/2018"
        ],
        "answer": "1171/2018",
        "correct_value": 0.5802775024777007,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000549",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 561/1178 or 4700/9140?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.03799229491813816,
      "pure_math": {
        "question": "Which is larger: 561/1178 or 4700/9140?",
        "options": [
          "2950/5741",
          "4700/9140",
          "561/1178",
          "2881/5343"
        ],
        "answer": "4700/9140",
        "correct_value": 0.5142231947483589,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 4719/9712 or 3339/6557?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.023333040836421404,
      "pure_math": {
        "question": "Which is larger: 4719/9712 or 3339/6557?",
        "options": [
          "1473/3062",
          "564/1322",
          "4719/9712",
          "3339/6557"
        ],
        "answer": "3339/6557",
        "correct_value": 0.509226780539881,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 3431/6237 or 1152/1986?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 3431/6237 or 1152/1986?",
        "options": [
          "3431/6237",
          "4449/9055",
          "1152/1986",
          "4841/7443"
        ],
        "answer": "1152/1986",
        "correct_value": 0.5800604229607251,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000550",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 1790/3708 or 849/1603?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.04689191853731639,
      "pure_math": {
        "question": "Which is larger: 1790/3708 or 849/1603?",
        "options": [
          "1790/3708",
          "1339/2815",
          "1261/2367",
          "849/1603"
        ],
        "answer": "849/1603",
        "correct_value": 0.5296319401122894,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 2504/5149 or 1447/2829?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.025180137384897938,
      "pure_math": {
        "question": "Which is larger: 2504/5149 or 1447/2829?",
        "options": [
          "2932/6629",
          "2504/5149",
          "1447/2829",
          "1804/3893"
        ],
        "answer": "1447/2829",
        "correct_value": 0.5114881583598445,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 1599/2906 or 1151/1983?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 1599/2906 or 1151/1983?",
        "options": [
          "3013/5332",
          "1599/2906",
          "1151/1983",
          "4961/7600"
        ],
        "answer": "1151/1983",
        "correct_value": 0.5804336863338376,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "cancellation_identity_000551",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3639 + 3950 - 3949",
      "ns_shortcut": "Near-cancellation: 3950 - 3949 = 1, so answer ≈ 3639 + 1.",
      "shortcut_strength": 0.999746835443038,
      "pure_math": {
        "question": "Evaluate: 3639 + 3950 - 3949",
        "options": [
          "3650",
          "3660",
          "3630",
          "3640"
        ],
        "answer": "3640",
        "correct_value": 3640,
        "explanation": "B-C = 1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2974 + 6072 - 6239",
      "ns_shortcut": "Near-cancellation: 6072 - 6239 = -167, offset is manageable.",
      "shortcut_strength": 0.9724967061923584,
      "pure_math": {
        "question": "Evaluate: 2974 + 6072 - 6239",
        "options": [
          "2797",
          "2817",
          "2827",
          "2807"
        ],
        "answer": "2807",
        "correct_value": 2807,
        "explanation": "B-C = -167; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3639 + 3950 - 5459",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 3639 + 3950 - 5459",
        "options": [
          "2140",
          "2150",
          "2120",
          "2130"
        ],
        "answer": "2130",
        "correct_value": 2130,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000552",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9781 + 1382 - 1383",
      "ns_shortcut": "Near-cancellation: 1382 - 1383 = -1, so answer ≈ 9781 + -1.",
      "shortcut_strength": 0.9992764109985528,
      "pure_math": {
        "question": "Evaluate: 9781 + 1382 - 1383",
        "options": [
          "9800",
          "9780",
          "9770",
          "9790"
        ],
        "answer": "9780",
        "correct_value": 9780,
        "explanation": "B-C = -1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3778 + 6273 - 6422",
      "ns_shortcut": "Near-cancellation: 6273 - 6422 = -149, offset is manageable.",
      "shortcut_strength": 0.9762474095329189,
      "pure_math": {
        "question": "Evaluate: 3778 + 6273 - 6422",
        "options": [
          "3629",
          "3619",
          "3649",
          "3639"
        ],
        "answer": "3629",
        "correct_value": 3629,
        "explanation": "B-C = -149; still a moderate shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9781 + 1382 - 1838",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 9781 + 1382 - 1838",
        "options": [
          "9325",
          "9315",
          "9335",
          "9345"
        ],
        "answer": "9325",
        "correct_value": 9325,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000553",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4264 + 2511 - 2510",
      "ns_shortcut": "Near-cancellation: 2511 - 2510 = 1, so answer ≈ 4264 + 1.",
      "shortcut_strength": 0.9996017522899243,
      "pure_math": {
        "question": "Evaluate: 4264 + 2511 - 2510",
        "options": [
          "4265",
          "4255",
          "4275",
          "4285"
        ],
        "answer": "4265",
        "correct_value": 4265,
        "explanation": "B-C = 1; result ≈ A + offset."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1310 + 1194 - 1141",
      "ns_shortcut": "Near-cancellation: 1194 - 1141 = 53, offset is manageable.",
      "shortcut_strength": 0.9556113902847572,
      "pure_math": {
        "question": "Evaluate: 1310 + 1194 - 1141",
        "options": [
          "1383",
          "1373",
          "1353",
          "1363"
        ],
        "answer": "1363",
        "correct_value": 1363,
        "explanation": "B-C = 53; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4264 + 2511 - 1581",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 4264 + 2511 - 1581",
        "options": [
          "5184",
          "5194",
          "5204",
          "5214"
        ],
        "answer": "5194",
        "correct_value": 5194,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000554",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6105 + 3719 - 3720",
      "ns_shortcut": "Near-cancellation: 3719 - 3720 = -1, so answer ≈ 6105 + -1.",
      "shortcut_strength": 0.9997311105135789,
      "pure_math": {
        "question": "Evaluate: 6105 + 3719 - 3720",
        "options": [
          "6104",
          "6124",
          "6114",
          "6094"
        ],
        "answer": "6104",
        "correct_value": 6104,
        "explanation": "B-C = -1; result ≈ A + offset."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5249 + 8336 - 8124",
      "ns_shortcut": "Near-cancellation: 8336 - 8124 = 212, offset is manageable.",
      "shortcut_strength": 0.9745681381957774,
      "pure_math": {
        "question": "Evaluate: 5249 + 8336 - 8124",
        "options": [
          "5461",
          "5451",
          "5481",
          "5471"
        ],
        "answer": "5461",
        "correct_value": 5461,
        "explanation": "B-C = 212; still a moderate shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6105 + 3719 - 5618",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 6105 + 3719 - 5618",
        "options": [
          "4206",
          "4196",
          "4226",
          "4216"
        ],
        "answer": "4206",
        "correct_value": 4206,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000555",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "7126 + 2057 - 2055",
      "ns_shortcut": "Near-cancellation: 2057 - 2055 = 2, so answer ≈ 7126 + 2.",
      "shortcut_strength": 0.9990277102576568,
      "pure_math": {
        "question": "Evaluate: 7126 + 2057 - 2055",
        "options": [
          "7148",
          "7118",
          "7128",
          "7138"
        ],
        "answer": "7128",
        "correct_value": 7128,
        "explanation": "B-C = 2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5815 + 2681 - 2787",
      "ns_shortcut": "Near-cancellation: 2681 - 2787 = -106, offset is manageable.",
      "shortcut_strength": 0.9604625139873182,
      "pure_math": {
        "question": "Evaluate: 5815 + 2681 - 2787",
        "options": [
          "5729",
          "5699",
          "5719",
          "5709"
        ],
        "answer": "5709",
        "correct_value": 5709,
        "explanation": "B-C = -106; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7126 + 2057 - 1323",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 7126 + 2057 - 1323",
        "options": [
          "7850",
          "7860",
          "7870",
          "7880"
        ],
        "answer": "7860",
        "correct_value": 7860,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000556",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6861 + 5024 - 5026",
      "ns_shortcut": "Near-cancellation: 5024 - 5026 = -2, so answer ≈ 6861 + -2.",
      "shortcut_strength": 0.9996019108280255,
      "pure_math": {
        "question": "Evaluate: 6861 + 5024 - 5026",
        "options": [
          "6859",
          "6849",
          "6879",
          "6869"
        ],
        "answer": "6859",
        "correct_value": 6859,
        "explanation": "B-C = -2; result ≈ A + offset."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8817 + 7743 - 7445",
      "ns_shortcut": "Near-cancellation: 7743 - 7445 = 298, offset is manageable.",
      "shortcut_strength": 0.9615136252098669,
      "pure_math": {
        "question": "Evaluate: 8817 + 7743 - 7445",
        "options": [
          "9115",
          "9105",
          "9135",
          "9125"
        ],
        "answer": "9115",
        "correct_value": 9115,
        "explanation": "B-C = 298; still a moderate shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6861 + 5024 - 2865",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 6861 + 5024 - 2865",
        "options": [
          "9010",
          "9030",
          "9020",
          "9040"
        ],
        "answer": "9020",
        "correct_value": 9020,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000557",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6268 + 4816 - 4818",
      "ns_shortcut": "Near-cancellation: 4816 - 4818 = -2, so answer ≈ 6268 + -2.",
      "shortcut_strength": 0.9995847176079734,
      "pure_math": {
        "question": "Evaluate: 6268 + 4816 - 4818",
        "options": [
          "6286",
          "6266",
          "6276",
          "6256"
        ],
        "answer": "6266",
        "correct_value": 6266,
        "explanation": "B-C = -2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7349 + 4514 - 4628",
      "ns_shortcut": "Near-cancellation: 4514 - 4628 = -114, offset is manageable.",
      "shortcut_strength": 0.974745237040319,
      "pure_math": {
        "question": "Evaluate: 7349 + 4514 - 4628",
        "options": [
          "7255",
          "7245",
          "7225",
          "7235"
        ],
        "answer": "7235",
        "correct_value": 7235,
        "explanation": "B-C = -114; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6268 + 4816 - 7435",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 6268 + 4816 - 7435",
        "options": [
          "3649",
          "3669",
          "3659",
          "3639"
        ],
        "answer": "3649",
        "correct_value": 3649,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000558",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3344 + 1236 - 1234",
      "ns_shortcut": "Near-cancellation: 1236 - 1234 = 2, so answer ≈ 3344 + 2.",
      "shortcut_strength": 0.9983818770226537,
      "pure_math": {
        "question": "Evaluate: 3344 + 1236 - 1234",
        "options": [
          "3356",
          "3336",
          "3366",
          "3346"
        ],
        "answer": "3346",
        "correct_value": 3346,
        "explanation": "B-C = 2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3953 + 8998 - 9372",
      "ns_shortcut": "Near-cancellation: 8998 - 9372 = -374, offset is manageable.",
      "shortcut_strength": 0.9584352078239609,
      "pure_math": {
        "question": "Evaluate: 3953 + 8998 - 9372",
        "options": [
          "3589",
          "3579",
          "3569",
          "3599"
        ],
        "answer": "3579",
        "correct_value": 3579,
        "explanation": "B-C = -374; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3344 + 1236 - 1733",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 3344 + 1236 - 1733",
        "options": [
          "2867",
          "2847",
          "2837",
          "2857"
        ],
        "answer": "2847",
        "correct_value": 2847,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000559",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5670 + 1297 - 1299",
      "ns_shortcut": "Near-cancellation: 1297 - 1299 = -2, so answer ≈ 5670 + -2.",
      "shortcut_strength": 0.9984579799537394,
      "pure_math": {
        "question": "Evaluate: 5670 + 1297 - 1299",
        "options": [
          "5688",
          "5668",
          "5678",
          "5658"
        ],
        "answer": "5668",
        "correct_value": 5668,
        "explanation": "B-C = -2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5682 + 9549 - 9196",
      "ns_shortcut": "Near-cancellation: 9549 - 9196 = 353, offset is manageable.",
      "shortcut_strength": 0.9630327783013928,
      "pure_math": {
        "question": "Evaluate: 5682 + 9549 - 9196",
        "options": [
          "6035",
          "6045",
          "6025",
          "6055"
        ],
        "answer": "6035",
        "correct_value": 6035,
        "explanation": "B-C = 353; still a moderate shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5670 + 1297 - 1721",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 5670 + 1297 - 1721",
        "options": [
          "5236",
          "5266",
          "5256",
          "5246"
        ],
        "answer": "5246",
        "correct_value": 5246,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000560",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5500 + 6201 - 6200",
      "ns_shortcut": "Near-cancellation: 6201 - 6200 = 1, so answer ≈ 5500 + 1.",
      "shortcut_strength": 0.9998387356877922,
      "pure_math": {
        "question": "Evaluate: 5500 + 6201 - 6200",
        "options": [
          "5521",
          "5511",
          "5501",
          "5491"
        ],
        "answer": "5501",
        "correct_value": 5501,
        "explanation": "B-C = 1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8943 + 1428 - 1362",
      "ns_shortcut": "Near-cancellation: 1428 - 1362 = 66, offset is manageable.",
      "shortcut_strength": 0.953781512605042,
      "pure_math": {
        "question": "Evaluate: 8943 + 1428 - 1362",
        "options": [
          "9029",
          "9009",
          "8999",
          "9019"
        ],
        "answer": "9009",
        "correct_value": 9009,
        "explanation": "B-C = 66; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5500 + 6201 - 9922",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 5500 + 6201 - 9922",
        "options": [
          "1799",
          "1769",
          "1789",
          "1779"
        ],
        "answer": "1779",
        "correct_value": 1779,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000561",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1479 + 4675 - 4677",
      "ns_shortcut": "Near-cancellation: 4675 - 4677 = -2, so answer ≈ 1479 + -2.",
      "shortcut_strength": 0.9995721925133689,
      "pure_math": {
        "question": "Evaluate: 1479 + 4675 - 4677",
        "options": [
          "1487",
          "1497",
          "1467",
          "1477"
        ],
        "answer": "1477",
        "correct_value": 1477,
        "explanation": "B-C = -2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9037 + 3428 - 3342",
      "ns_shortcut": "Near-cancellation: 3428 - 3342 = 86, offset is manageable.",
      "shortcut_strength": 0.9749124854142357,
      "pure_math": {
        "question": "Evaluate: 9037 + 3428 - 3342",
        "options": [
          "9143",
          "9133",
          "9123",
          "9113"
        ],
        "answer": "9123",
        "correct_value": 9123,
        "explanation": "B-C = 86; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1479 + 4675 - 6468",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 1479 + 4675 - 6468",
        "options": [
          "-306",
          "-326",
          "-296",
          "-314"
        ],
        "answer": "-314",
        "correct_value": -314,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000562",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5254 + 1710 - 1712",
      "ns_shortcut": "Near-cancellation: 1710 - 1712 = -2, so answer ≈ 5254 + -2.",
      "shortcut_strength": 0.9988304093567252,
      "pure_math": {
        "question": "Evaluate: 5254 + 1710 - 1712",
        "options": [
          "5272",
          "5242",
          "5262",
          "5252"
        ],
        "answer": "5252",
        "correct_value": 5252,
        "explanation": "B-C = -2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6924 + 3845 - 3732",
      "ns_shortcut": "Near-cancellation: 3845 - 3732 = 113, offset is manageable.",
      "shortcut_strength": 0.9706111833550065,
      "pure_math": {
        "question": "Evaluate: 6924 + 3845 - 3732",
        "options": [
          "7057",
          "7027",
          "7037",
          "7047"
        ],
        "answer": "7037",
        "correct_value": 7037,
        "explanation": "B-C = 113; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5254 + 1710 - 2364",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 5254 + 1710 - 2364",
        "options": [
          "4620",
          "4610",
          "4590",
          "4600"
        ],
        "answer": "4600",
        "correct_value": 4600,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000563",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6144 + 3597 - 3599",
      "ns_shortcut": "Near-cancellation: 3597 - 3599 = -2, so answer ≈ 6144 + -2.",
      "shortcut_strength": 0.9994439810953573,
      "pure_math": {
        "question": "Evaluate: 6144 + 3597 - 3599",
        "options": [
          "6162",
          "6142",
          "6152",
          "6132"
        ],
        "answer": "6142",
        "correct_value": 6142,
        "explanation": "B-C = -2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8514 + 3606 - 3714",
      "ns_shortcut": "Near-cancellation: 3606 - 3714 = -108, offset is manageable.",
      "shortcut_strength": 0.9700499168053245,
      "pure_math": {
        "question": "Evaluate: 8514 + 3606 - 3714",
        "options": [
          "8416",
          "8406",
          "8396",
          "8426"
        ],
        "answer": "8406",
        "correct_value": 8406,
        "explanation": "B-C = -108; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6144 + 3597 - 5284",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 6144 + 3597 - 5284",
        "options": [
          "4457",
          "4447",
          "4477",
          "4467"
        ],
        "answer": "4457",
        "correct_value": 4457,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000564",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2356 + 6788 - 6789",
      "ns_shortcut": "Near-cancellation: 6788 - 6789 = -1, so answer ≈ 2356 + -1.",
      "shortcut_strength": 0.9998526812021213,
      "pure_math": {
        "question": "Evaluate: 2356 + 6788 - 6789",
        "options": [
          "2345",
          "2355",
          "2375",
          "2365"
        ],
        "answer": "2355",
        "correct_value": 2355,
        "explanation": "B-C = -1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3544 + 6192 - 6068",
      "ns_shortcut": "Near-cancellation: 6192 - 6068 = 124, offset is manageable.",
      "shortcut_strength": 0.9799741602067183,
      "pure_math": {
        "question": "Evaluate: 3544 + 6192 - 6068",
        "options": [
          "3678",
          "3688",
          "3668",
          "3658"
        ],
        "answer": "3668",
        "correct_value": 3668,
        "explanation": "B-C = 124; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2356 + 6788 - 9709",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 2356 + 6788 - 9709",
        "options": [
          "-545",
          "-555",
          "-565",
          "-575"
        ],
        "answer": "-565",
        "correct_value": -565,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000565",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2712 + 6582 - 6583",
      "ns_shortcut": "Near-cancellation: 6582 - 6583 = -1, so answer ≈ 2712 + -1.",
      "shortcut_strength": 0.9998480704952902,
      "pure_math": {
        "question": "Evaluate: 2712 + 6582 - 6583",
        "options": [
          "2711",
          "2701",
          "2721",
          "2731"
        ],
        "answer": "2711",
        "correct_value": 2711,
        "explanation": "B-C = -1; result ≈ A + offset."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1914 + 7864 - 7531",
      "ns_shortcut": "Near-cancellation: 7864 - 7531 = 333, offset is manageable.",
      "shortcut_strength": 0.9576551373346898,
      "pure_math": {
        "question": "Evaluate: 1914 + 7864 - 7531",
        "options": [
          "2237",
          "2267",
          "2247",
          "2257"
        ],
        "answer": "2247",
        "correct_value": 2247,
        "explanation": "B-C = 333; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2712 + 6582 - 10045",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 2712 + 6582 - 10045",
        "options": [
          "-749",
          "-751",
          "-739",
          "-769"
        ],
        "answer": "-751",
        "correct_value": -751,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000566",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "7556 + 4084 - 4086",
      "ns_shortcut": "Near-cancellation: 4084 - 4086 = -2, so answer ≈ 7556 + -2.",
      "shortcut_strength": 0.9995102840352595,
      "pure_math": {
        "question": "Evaluate: 7556 + 4084 - 4086",
        "options": [
          "7544",
          "7554",
          "7564",
          "7574"
        ],
        "answer": "7554",
        "correct_value": 7554,
        "explanation": "B-C = -2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5110 + 9694 - 9245",
      "ns_shortcut": "Near-cancellation: 9694 - 9245 = 449, offset is manageable.",
      "shortcut_strength": 0.9536826903239117,
      "pure_math": {
        "question": "Evaluate: 5110 + 9694 - 9245",
        "options": [
          "5549",
          "5569",
          "5559",
          "5579"
        ],
        "answer": "5559",
        "correct_value": 5559,
        "explanation": "B-C = 449; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7556 + 4084 - 2640",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 7556 + 4084 - 2640",
        "options": [
          "9020",
          "8990",
          "9000",
          "9010"
        ],
        "answer": "9000",
        "correct_value": 9000,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000567",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4064 + 5375 - 5377",
      "ns_shortcut": "Near-cancellation: 5375 - 5377 = -2, so answer ≈ 4064 + -2.",
      "shortcut_strength": 0.9996279069767442,
      "pure_math": {
        "question": "Evaluate: 4064 + 5375 - 5377",
        "options": [
          "4062",
          "4072",
          "4082",
          "4052"
        ],
        "answer": "4062",
        "correct_value": 4062,
        "explanation": "B-C = -2; result ≈ A + offset."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1735 + 1977 - 1923",
      "ns_shortcut": "Near-cancellation: 1977 - 1923 = 54, offset is manageable.",
      "shortcut_strength": 0.9726858877086495,
      "pure_math": {
        "question": "Evaluate: 1735 + 1977 - 1923",
        "options": [
          "1799",
          "1789",
          "1779",
          "1809"
        ],
        "answer": "1789",
        "correct_value": 1789,
        "explanation": "B-C = 54; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4064 + 5375 - 7712",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 4064 + 5375 - 7712",
        "options": [
          "1747",
          "1717",
          "1727",
          "1737"
        ],
        "answer": "1727",
        "correct_value": 1727,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000568",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9227 + 8064 - 8063",
      "ns_shortcut": "Near-cancellation: 8064 - 8063 = 1, so answer ≈ 9227 + 1.",
      "shortcut_strength": 0.9998759920634921,
      "pure_math": {
        "question": "Evaluate: 9227 + 8064 - 8063",
        "options": [
          "9218",
          "9248",
          "9238",
          "9228"
        ],
        "answer": "9228",
        "correct_value": 9228,
        "explanation": "B-C = 1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3573 + 6561 - 6822",
      "ns_shortcut": "Near-cancellation: 6561 - 6822 = -261, offset is manageable.",
      "shortcut_strength": 0.9602194787379973,
      "pure_math": {
        "question": "Evaluate: 3573 + 6561 - 6822",
        "options": [
          "3332",
          "3312",
          "3322",
          "3302"
        ],
        "answer": "3312",
        "correct_value": 3312,
        "explanation": "B-C = -261; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9227 + 8064 - 3915",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 9227 + 8064 - 3915",
        "options": [
          "13366",
          "13386",
          "13376",
          "13396"
        ],
        "answer": "13376",
        "correct_value": 13376,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000569",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3894 + 5525 - 5523",
      "ns_shortcut": "Near-cancellation: 5525 - 5523 = 2, so answer ≈ 3894 + 2.",
      "shortcut_strength": 0.9996380090497737,
      "pure_math": {
        "question": "Evaluate: 3894 + 5525 - 5523",
        "options": [
          "3906",
          "3916",
          "3896",
          "3886"
        ],
        "answer": "3896",
        "correct_value": 3896,
        "explanation": "B-C = 2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5760 + 6288 - 6442",
      "ns_shortcut": "Near-cancellation: 6288 - 6442 = -154, offset is manageable.",
      "shortcut_strength": 0.9755089058524173,
      "pure_math": {
        "question": "Evaluate: 5760 + 6288 - 6442",
        "options": [
          "5596",
          "5606",
          "5616",
          "5626"
        ],
        "answer": "5606",
        "correct_value": 5606,
        "explanation": "B-C = -154; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3894 + 5525 - 2035",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 3894 + 5525 - 2035",
        "options": [
          "7394",
          "7374",
          "7384",
          "7404"
        ],
        "answer": "7384",
        "correct_value": 7384,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000570",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9718 + 2660 - 2659",
      "ns_shortcut": "Near-cancellation: 2660 - 2659 = 1, so answer ≈ 9718 + 1.",
      "shortcut_strength": 0.999624060150376,
      "pure_math": {
        "question": "Evaluate: 9718 + 2660 - 2659",
        "options": [
          "9719",
          "9709",
          "9739",
          "9729"
        ],
        "answer": "9719",
        "correct_value": 9719,
        "explanation": "B-C = 1; result ≈ A + offset."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6763 + 3441 - 3518",
      "ns_shortcut": "Near-cancellation: 3441 - 3518 = -77, offset is manageable.",
      "shortcut_strength": 0.977622784074397,
      "pure_math": {
        "question": "Evaluate: 6763 + 3441 - 3518",
        "options": [
          "6706",
          "6686",
          "6676",
          "6696"
        ],
        "answer": "6686",
        "correct_value": 6686,
        "explanation": "B-C = -77; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9718 + 2660 - 1355",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 9718 + 2660 - 1355",
        "options": [
          "11043",
          "11013",
          "11023",
          "11033"
        ],
        "answer": "11023",
        "correct_value": 11023,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000571",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6789 + 9091 - 9092",
      "ns_shortcut": "Near-cancellation: 9091 - 9092 = -1, so answer ≈ 6789 + -1.",
      "shortcut_strength": 0.999890001099989,
      "pure_math": {
        "question": "Evaluate: 6789 + 9091 - 9092",
        "options": [
          "6808",
          "6778",
          "6798",
          "6788"
        ],
        "answer": "6788",
        "correct_value": 6788,
        "explanation": "B-C = -1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6226 + 4859 - 5059",
      "ns_shortcut": "Near-cancellation: 4859 - 5059 = -200, offset is manageable.",
      "shortcut_strength": 0.9588392673389586,
      "pure_math": {
        "question": "Evaluate: 6226 + 4859 - 5059",
        "options": [
          "6036",
          "6016",
          "6026",
          "6046"
        ],
        "answer": "6026",
        "correct_value": 6026,
        "explanation": "B-C = -200; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6789 + 9091 - 5916",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 6789 + 9091 - 5916",
        "options": [
          "9954",
          "9964",
          "9984",
          "9974"
        ],
        "answer": "9964",
        "correct_value": 9964,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000572",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1208 + 8780 - 8778",
      "ns_shortcut": "Near-cancellation: 8780 - 8778 = 2, so answer ≈ 1208 + 2.",
      "shortcut_strength": 0.9997722095671981,
      "pure_math": {
        "question": "Evaluate: 1208 + 8780 - 8778",
        "options": [
          "1220",
          "1200",
          "1210",
          "1230"
        ],
        "answer": "1210",
        "correct_value": 1210,
        "explanation": "B-C = 2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4456 + 5383 - 5218",
      "ns_shortcut": "Near-cancellation: 5383 - 5218 = 165, offset is manageable.",
      "shortcut_strength": 0.9693479472413152,
      "pure_math": {
        "question": "Evaluate: 4456 + 5383 - 5218",
        "options": [
          "4611",
          "4631",
          "4621",
          "4641"
        ],
        "answer": "4621",
        "correct_value": 4621,
        "explanation": "B-C = 165; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1208 + 8780 - 13847",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 1208 + 8780 - 13847",
        "options": [
          "-3851",
          "-3859",
          "-3841",
          "-3871"
        ],
        "answer": "-3859",
        "correct_value": -3859,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000573",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9000 + 5060 - 5058",
      "ns_shortcut": "Near-cancellation: 5060 - 5058 = 2, so answer ≈ 9000 + 2.",
      "shortcut_strength": 0.999604743083004,
      "pure_math": {
        "question": "Evaluate: 9000 + 5060 - 5058",
        "options": [
          "9012",
          "9022",
          "8992",
          "9002"
        ],
        "answer": "9002",
        "correct_value": 9002,
        "explanation": "B-C = 2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1199 + 5748 - 5541",
      "ns_shortcut": "Near-cancellation: 5748 - 5541 = 207, offset is manageable.",
      "shortcut_strength": 0.9639874739039666,
      "pure_math": {
        "question": "Evaluate: 1199 + 5748 - 5541",
        "options": [
          "1426",
          "1406",
          "1416",
          "1396"
        ],
        "answer": "1406",
        "correct_value": 1406,
        "explanation": "B-C = 207; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9000 + 5060 - 6782",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 9000 + 5060 - 6782",
        "options": [
          "7278",
          "7268",
          "7288",
          "7298"
        ],
        "answer": "7278",
        "correct_value": 7278,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000574",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6747 + 9945 - 9944",
      "ns_shortcut": "Near-cancellation: 9945 - 9944 = 1, so answer ≈ 6747 + 1.",
      "shortcut_strength": 0.9998994469582705,
      "pure_math": {
        "question": "Evaluate: 6747 + 9945 - 9944",
        "options": [
          "6748",
          "6768",
          "6758",
          "6738"
        ],
        "answer": "6748",
        "correct_value": 6748,
        "explanation": "B-C = 1; result ≈ A + offset."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7254 + 6211 - 5963",
      "ns_shortcut": "Near-cancellation: 6211 - 5963 = 248, offset is manageable.",
      "shortcut_strength": 0.9600708420544196,
      "pure_math": {
        "question": "Evaluate: 7254 + 6211 - 5963",
        "options": [
          "7512",
          "7502",
          "7522",
          "7492"
        ],
        "answer": "7502",
        "correct_value": 7502,
        "explanation": "B-C = 248; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6747 + 9945 - 15049",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 6747 + 9945 - 15049",
        "options": [
          "1663",
          "1633",
          "1653",
          "1643"
        ],
        "answer": "1643",
        "correct_value": 1643,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000575",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3423 + 7727 - 7728",
      "ns_shortcut": "Near-cancellation: 7727 - 7728 = -1, so answer ≈ 3423 + -1.",
      "shortcut_strength": 0.9998705836676589,
      "pure_math": {
        "question": "Evaluate: 3423 + 7727 - 7728",
        "options": [
          "3422",
          "3442",
          "3412",
          "3432"
        ],
        "answer": "3422",
        "correct_value": 3422,
        "explanation": "B-C = -1; result ≈ A + offset."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8125 + 7636 - 7301",
      "ns_shortcut": "Near-cancellation: 7636 - 7301 = 335, offset is manageable.",
      "shortcut_strength": 0.9561288632792038,
      "pure_math": {
        "question": "Evaluate: 8125 + 7636 - 7301",
        "options": [
          "8470",
          "8460",
          "8450",
          "8480"
        ],
        "answer": "8460",
        "correct_value": 8460,
        "explanation": "B-C = 335; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3423 + 7727 - 5044",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 3423 + 7727 - 5044",
        "options": [
          "6116",
          "6106",
          "6126",
          "6096"
        ],
        "answer": "6106",
        "correct_value": 6106,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000576",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5487 + 9932 - 9930",
      "ns_shortcut": "Near-cancellation: 9932 - 9930 = 2, so answer ≈ 5487 + 2.",
      "shortcut_strength": 0.999798630688683,
      "pure_math": {
        "question": "Evaluate: 5487 + 9932 - 9930",
        "options": [
          "5489",
          "5509",
          "5479",
          "5499"
        ],
        "answer": "5489",
        "correct_value": 5489,
        "explanation": "B-C = 2; result ≈ A + offset."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7897 + 1444 - 1480",
      "ns_shortcut": "Near-cancellation: 1444 - 1480 = -36, offset is manageable.",
      "shortcut_strength": 0.9750692520775623,
      "pure_math": {
        "question": "Evaluate: 7897 + 1444 - 1480",
        "options": [
          "7881",
          "7861",
          "7871",
          "7851"
        ],
        "answer": "7861",
        "correct_value": 7861,
        "explanation": "B-C = -36; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5487 + 9932 - 6173",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 5487 + 9932 - 6173",
        "options": [
          "9256",
          "9246",
          "9236",
          "9266"
        ],
        "answer": "9246",
        "correct_value": 9246,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000577",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8101 + 8460 - 8459",
      "ns_shortcut": "Near-cancellation: 8460 - 8459 = 1, so answer ≈ 8101 + 1.",
      "shortcut_strength": 0.9998817966903073,
      "pure_math": {
        "question": "Evaluate: 8101 + 8460 - 8459",
        "options": [
          "8112",
          "8092",
          "8102",
          "8122"
        ],
        "answer": "8102",
        "correct_value": 8102,
        "explanation": "B-C = 1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9745 + 4635 - 4420",
      "ns_shortcut": "Near-cancellation: 4635 - 4420 = 215, offset is manageable.",
      "shortcut_strength": 0.95361380798274,
      "pure_math": {
        "question": "Evaluate: 9745 + 4635 - 4420",
        "options": [
          "9950",
          "9970",
          "9960",
          "9980"
        ],
        "answer": "9960",
        "correct_value": 9960,
        "explanation": "B-C = 215; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8101 + 8460 - 13140",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 8101 + 8460 - 13140",
        "options": [
          "3421",
          "3441",
          "3411",
          "3431"
        ],
        "answer": "3421",
        "correct_value": 3421,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000578",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5722 + 2063 - 2062",
      "ns_shortcut": "Near-cancellation: 2063 - 2062 = 1, so answer ≈ 5722 + 1.",
      "shortcut_strength": 0.9995152690256908,
      "pure_math": {
        "question": "Evaluate: 5722 + 2063 - 2062",
        "options": [
          "5743",
          "5713",
          "5733",
          "5723"
        ],
        "answer": "5723",
        "correct_value": 5723,
        "explanation": "B-C = 1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2763 + 4914 - 5056",
      "ns_shortcut": "Near-cancellation: 4914 - 5056 = -142, offset is manageable.",
      "shortcut_strength": 0.9711029711029711,
      "pure_math": {
        "question": "Evaluate: 2763 + 4914 - 5056",
        "options": [
          "2611",
          "2621",
          "2641",
          "2631"
        ],
        "answer": "2621",
        "correct_value": 2621,
        "explanation": "B-C = -142; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5722 + 2063 - 1132",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 5722 + 2063 - 1132",
        "options": [
          "6673",
          "6653",
          "6663",
          "6643"
        ],
        "answer": "6653",
        "correct_value": 6653,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000579",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1817 + 5124 - 5125",
      "ns_shortcut": "Near-cancellation: 5124 - 5125 = -1, so answer ≈ 1817 + -1.",
      "shortcut_strength": 0.9998048399687745,
      "pure_math": {
        "question": "Evaluate: 1817 + 5124 - 5125",
        "options": [
          "1806",
          "1816",
          "1826",
          "1836"
        ],
        "answer": "1816",
        "correct_value": 1816,
        "explanation": "B-C = -1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2992 + 7169 - 6938",
      "ns_shortcut": "Near-cancellation: 7169 - 6938 = 231, offset is manageable.",
      "shortcut_strength": 0.9677779327660762,
      "pure_math": {
        "question": "Evaluate: 2992 + 7169 - 6938",
        "options": [
          "3233",
          "3243",
          "3223",
          "3213"
        ],
        "answer": "3223",
        "correct_value": 3223,
        "explanation": "B-C = 231; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1817 + 5124 - 2703",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 1817 + 5124 - 2703",
        "options": [
          "4248",
          "4228",
          "4238",
          "4258"
        ],
        "answer": "4238",
        "correct_value": 4238,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000580",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8752 + 6815 - 6816",
      "ns_shortcut": "Near-cancellation: 6815 - 6816 = -1, so answer ≈ 8752 + -1.",
      "shortcut_strength": 0.9998532648569333,
      "pure_math": {
        "question": "Evaluate: 8752 + 6815 - 6816",
        "options": [
          "8751",
          "8771",
          "8761",
          "8741"
        ],
        "answer": "8751",
        "correct_value": 8751,
        "explanation": "B-C = -1; result ≈ A + offset."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9730 + 2090 - 2170",
      "ns_shortcut": "Near-cancellation: 2090 - 2170 = -80, offset is manageable.",
      "shortcut_strength": 0.9617224880382775,
      "pure_math": {
        "question": "Evaluate: 9730 + 2090 - 2170",
        "options": [
          "9660",
          "9670",
          "9650",
          "9640"
        ],
        "answer": "9650",
        "correct_value": 9650,
        "explanation": "B-C = -80; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8752 + 6815 - 9568",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 8752 + 6815 - 9568",
        "options": [
          "6009",
          "5999",
          "5989",
          "6019"
        ],
        "answer": "5999",
        "correct_value": 5999,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000581",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4268 + 5101 - 5102",
      "ns_shortcut": "Near-cancellation: 5101 - 5102 = -1, so answer ≈ 4268 + -1.",
      "shortcut_strength": 0.9998039600078416,
      "pure_math": {
        "question": "Evaluate: 4268 + 5101 - 5102",
        "options": [
          "4277",
          "4267",
          "4287",
          "4257"
        ],
        "answer": "4267",
        "correct_value": 4267,
        "explanation": "B-C = -1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1511 + 7086 - 6939",
      "ns_shortcut": "Near-cancellation: 7086 - 6939 = 147, offset is manageable.",
      "shortcut_strength": 0.9792548687552921,
      "pure_math": {
        "question": "Evaluate: 1511 + 7086 - 6939",
        "options": [
          "1658",
          "1678",
          "1668",
          "1648"
        ],
        "answer": "1658",
        "correct_value": 1658,
        "explanation": "B-C = 147; still a moderate shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4268 + 5101 - 2454",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 4268 + 5101 - 2454",
        "options": [
          "6935",
          "6915",
          "6925",
          "6905"
        ],
        "answer": "6915",
        "correct_value": 6915,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000582",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3270 + 9632 - 9630",
      "ns_shortcut": "Near-cancellation: 9632 - 9630 = 2, so answer ≈ 3270 + 2.",
      "shortcut_strength": 0.9997923588039868,
      "pure_math": {
        "question": "Evaluate: 3270 + 9632 - 9630",
        "options": [
          "3272",
          "3282",
          "3262",
          "3292"
        ],
        "answer": "3272",
        "correct_value": 3272,
        "explanation": "B-C = 2; result ≈ A + offset."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3565 + 7213 - 7558",
      "ns_shortcut": "Near-cancellation: 7213 - 7558 = -345, offset is manageable.",
      "shortcut_strength": 0.9521696936087619,
      "pure_math": {
        "question": "Evaluate: 3565 + 7213 - 7558",
        "options": [
          "3210",
          "3240",
          "3220",
          "3230"
        ],
        "answer": "3220",
        "correct_value": 3220,
        "explanation": "B-C = -345; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3270 + 9632 - 14201",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 3270 + 9632 - 14201",
        "options": [
          "-1291",
          "-1311",
          "-1281",
          "-1299"
        ],
        "answer": "-1299",
        "correct_value": -1299,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000583",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "7896 + 2453 - 2454",
      "ns_shortcut": "Near-cancellation: 2453 - 2454 = -1, so answer ≈ 7896 + -1.",
      "shortcut_strength": 0.9995923359152059,
      "pure_math": {
        "question": "Evaluate: 7896 + 2453 - 2454",
        "options": [
          "7885",
          "7905",
          "7895",
          "7915"
        ],
        "answer": "7895",
        "correct_value": 7895,
        "explanation": "B-C = -1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7339 + 7247 - 7064",
      "ns_shortcut": "Near-cancellation: 7247 - 7064 = 183, offset is manageable.",
      "shortcut_strength": 0.9747481716572375,
      "pure_math": {
        "question": "Evaluate: 7339 + 7247 - 7064",
        "options": [
          "7532",
          "7522",
          "7542",
          "7512"
        ],
        "answer": "7522",
        "correct_value": 7522,
        "explanation": "B-C = 183; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7896 + 2453 - 3316",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 7896 + 2453 - 3316",
        "options": [
          "7023",
          "7053",
          "7043",
          "7033"
        ],
        "answer": "7033",
        "correct_value": 7033,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000584",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1890 + 2392 - 2394",
      "ns_shortcut": "Near-cancellation: 2392 - 2394 = -2, so answer ≈ 1890 + -2.",
      "shortcut_strength": 0.9991638795986622,
      "pure_math": {
        "question": "Evaluate: 1890 + 2392 - 2394",
        "options": [
          "1898",
          "1888",
          "1878",
          "1908"
        ],
        "answer": "1888",
        "correct_value": 1888,
        "explanation": "B-C = -2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5180 + 1094 - 1046",
      "ns_shortcut": "Near-cancellation: 1094 - 1046 = 48, offset is manageable.",
      "shortcut_strength": 0.9561243144424132,
      "pure_math": {
        "question": "Evaluate: 5180 + 1094 - 1046",
        "options": [
          "5228",
          "5248",
          "5218",
          "5238"
        ],
        "answer": "5228",
        "correct_value": 5228,
        "explanation": "B-C = 48; still a moderate shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1890 + 2392 - 3816",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 1890 + 2392 - 3816",
        "options": [
          "476",
          "486",
          "456",
          "466"
        ],
        "answer": "466",
        "correct_value": 466,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000585",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4359 + 9463 - 9464",
      "ns_shortcut": "Near-cancellation: 9463 - 9464 = -1, so answer ≈ 4359 + -1.",
      "shortcut_strength": 0.9998943252668288,
      "pure_math": {
        "question": "Evaluate: 4359 + 9463 - 9464",
        "options": [
          "4368",
          "4378",
          "4358",
          "4348"
        ],
        "answer": "4358",
        "correct_value": 4358,
        "explanation": "B-C = -1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8361 + 9361 - 8894",
      "ns_shortcut": "Near-cancellation: 9361 - 8894 = 467, offset is manageable.",
      "shortcut_strength": 0.9501121675034718,
      "pure_math": {
        "question": "Evaluate: 8361 + 9361 - 8894",
        "options": [
          "8818",
          "8828",
          "8848",
          "8838"
        ],
        "answer": "8828",
        "correct_value": 8828,
        "explanation": "B-C = 467; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4359 + 9463 - 4639",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 4359 + 9463 - 4639",
        "options": [
          "9193",
          "9203",
          "9173",
          "9183"
        ],
        "answer": "9183",
        "correct_value": 9183,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000586",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3507 + 2988 - 2990",
      "ns_shortcut": "Near-cancellation: 2988 - 2990 = -2, so answer ≈ 3507 + -2.",
      "shortcut_strength": 0.999330655957162,
      "pure_math": {
        "question": "Evaluate: 3507 + 2988 - 2990",
        "options": [
          "3495",
          "3525",
          "3505",
          "3515"
        ],
        "answer": "3505",
        "correct_value": 3505,
        "explanation": "B-C = -2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7739 + 4460 - 4580",
      "ns_shortcut": "Near-cancellation: 4460 - 4580 = -120, offset is manageable.",
      "shortcut_strength": 0.9730941704035875,
      "pure_math": {
        "question": "Evaluate: 7739 + 4460 - 4580",
        "options": [
          "7619",
          "7609",
          "7639",
          "7629"
        ],
        "answer": "7619",
        "correct_value": 7619,
        "explanation": "B-C = -120; still a moderate shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3507 + 2988 - 1144",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 3507 + 2988 - 1144",
        "options": [
          "5351",
          "5341",
          "5361",
          "5371"
        ],
        "answer": "5351",
        "correct_value": 5351,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000587",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4015 + 4854 - 4853",
      "ns_shortcut": "Near-cancellation: 4854 - 4853 = 1, so answer ≈ 4015 + 1.",
      "shortcut_strength": 0.9997939843428101,
      "pure_math": {
        "question": "Evaluate: 4015 + 4854 - 4853",
        "options": [
          "4026",
          "4016",
          "4036",
          "4006"
        ],
        "answer": "4016",
        "correct_value": 4016,
        "explanation": "B-C = 1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5324 + 9400 - 9137",
      "ns_shortcut": "Near-cancellation: 9400 - 9137 = 263, offset is manageable.",
      "shortcut_strength": 0.9720212765957447,
      "pure_math": {
        "question": "Evaluate: 5324 + 9400 - 9137",
        "options": [
          "5577",
          "5587",
          "5607",
          "5597"
        ],
        "answer": "5587",
        "correct_value": 5587,
        "explanation": "B-C = 263; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4015 + 4854 - 1874",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 4015 + 4854 - 1874",
        "options": [
          "6985",
          "6995",
          "7015",
          "7005"
        ],
        "answer": "6995",
        "correct_value": 6995,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000588",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9092 + 3990 - 3991",
      "ns_shortcut": "Near-cancellation: 3990 - 3991 = -1, so answer ≈ 9092 + -1.",
      "shortcut_strength": 0.9997493734335839,
      "pure_math": {
        "question": "Evaluate: 9092 + 3990 - 3991",
        "options": [
          "9111",
          "9101",
          "9081",
          "9091"
        ],
        "answer": "9091",
        "correct_value": 9091,
        "explanation": "B-C = -1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3999 + 1475 - 1546",
      "ns_shortcut": "Near-cancellation: 1475 - 1546 = -71, offset is manageable.",
      "shortcut_strength": 0.951864406779661,
      "pure_math": {
        "question": "Evaluate: 3999 + 1475 - 1546",
        "options": [
          "3938",
          "3918",
          "3928",
          "3948"
        ],
        "answer": "3928",
        "correct_value": 3928,
        "explanation": "B-C = -71; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9092 + 3990 - 6160",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 9092 + 3990 - 6160",
        "options": [
          "6922",
          "6912",
          "6942",
          "6932"
        ],
        "answer": "6922",
        "correct_value": 6922,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000589",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3427 + 1463 - 1462",
      "ns_shortcut": "Near-cancellation: 1463 - 1462 = 1, so answer ≈ 3427 + 1.",
      "shortcut_strength": 0.9993164730006835,
      "pure_math": {
        "question": "Evaluate: 3427 + 1463 - 1462",
        "options": [
          "3448",
          "3438",
          "3428",
          "3418"
        ],
        "answer": "3428",
        "correct_value": 3428,
        "explanation": "B-C = 1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1490 + 8682 - 8264",
      "ns_shortcut": "Near-cancellation: 8682 - 8264 = 418, offset is manageable.",
      "shortcut_strength": 0.9518544114259387,
      "pure_math": {
        "question": "Evaluate: 1490 + 8682 - 8264",
        "options": [
          "1898",
          "1918",
          "1928",
          "1908"
        ],
        "answer": "1908",
        "correct_value": 1908,
        "explanation": "B-C = 418; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3427 + 1463 - 1922",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 3427 + 1463 - 1922",
        "options": [
          "2968",
          "2988",
          "2958",
          "2978"
        ],
        "answer": "2968",
        "correct_value": 2968,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000590",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5536 + 1154 - 1155",
      "ns_shortcut": "Near-cancellation: 1154 - 1155 = -1, so answer ≈ 5536 + -1.",
      "shortcut_strength": 0.9991334488734835,
      "pure_math": {
        "question": "Evaluate: 5536 + 1154 - 1155",
        "options": [
          "5545",
          "5535",
          "5525",
          "5555"
        ],
        "answer": "5535",
        "correct_value": 5535,
        "explanation": "B-C = -1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8316 + 7043 - 6769",
      "ns_shortcut": "Near-cancellation: 7043 - 6769 = 274, offset is manageable.",
      "shortcut_strength": 0.9610961238108761,
      "pure_math": {
        "question": "Evaluate: 8316 + 7043 - 6769",
        "options": [
          "8590",
          "8580",
          "8610",
          "8600"
        ],
        "answer": "8590",
        "correct_value": 8590,
        "explanation": "B-C = 274; still a moderate shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5536 + 1154 - 1589",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 5536 + 1154 - 1589",
        "options": [
          "5101",
          "5111",
          "5091",
          "5121"
        ],
        "answer": "5101",
        "correct_value": 5101,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000591",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8528 + 3299 - 3298",
      "ns_shortcut": "Near-cancellation: 3299 - 3298 = 1, so answer ≈ 8528 + 1.",
      "shortcut_strength": 0.9996968778417702,
      "pure_math": {
        "question": "Evaluate: 8528 + 3299 - 3298",
        "options": [
          "8519",
          "8529",
          "8539",
          "8549"
        ],
        "answer": "8529",
        "correct_value": 8529,
        "explanation": "B-C = 1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8085 + 6684 - 6834",
      "ns_shortcut": "Near-cancellation: 6684 - 6834 = -150, offset is manageable.",
      "shortcut_strength": 0.9775583482944344,
      "pure_math": {
        "question": "Evaluate: 8085 + 6684 - 6834",
        "options": [
          "7955",
          "7935",
          "7925",
          "7945"
        ],
        "answer": "7935",
        "correct_value": 7935,
        "explanation": "B-C = -150; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8528 + 3299 - 5326",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 8528 + 3299 - 5326",
        "options": [
          "6501",
          "6491",
          "6521",
          "6511"
        ],
        "answer": "6501",
        "correct_value": 6501,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000592",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6703 + 7620 - 7622",
      "ns_shortcut": "Near-cancellation: 7620 - 7622 = -2, so answer ≈ 6703 + -2.",
      "shortcut_strength": 0.9997375328083989,
      "pure_math": {
        "question": "Evaluate: 6703 + 7620 - 7622",
        "options": [
          "6711",
          "6721",
          "6691",
          "6701"
        ],
        "answer": "6701",
        "correct_value": 6701,
        "explanation": "B-C = -2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4842 + 2423 - 2489",
      "ns_shortcut": "Near-cancellation: 2423 - 2489 = -66, offset is manageable.",
      "shortcut_strength": 0.9727610400330169,
      "pure_math": {
        "question": "Evaluate: 4842 + 2423 - 2489",
        "options": [
          "4776",
          "4766",
          "4796",
          "4786"
        ],
        "answer": "4776",
        "correct_value": 4776,
        "explanation": "B-C = -66; still a moderate shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6703 + 7620 - 4009",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 6703 + 7620 - 4009",
        "options": [
          "10304",
          "10334",
          "10314",
          "10324"
        ],
        "answer": "10314",
        "correct_value": 10314,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000593",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "7292 + 7887 - 7889",
      "ns_shortcut": "Near-cancellation: 7887 - 7889 = -2, so answer ≈ 7292 + -2.",
      "shortcut_strength": 0.99974641815646,
      "pure_math": {
        "question": "Evaluate: 7292 + 7887 - 7889",
        "options": [
          "7280",
          "7300",
          "7310",
          "7290"
        ],
        "answer": "7290",
        "correct_value": 7290,
        "explanation": "B-C = -2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5325 + 4060 - 4169",
      "ns_shortcut": "Near-cancellation: 4060 - 4169 = -109, offset is manageable.",
      "shortcut_strength": 0.973152709359606,
      "pure_math": {
        "question": "Evaluate: 5325 + 4060 - 4169",
        "options": [
          "5236",
          "5206",
          "5226",
          "5216"
        ],
        "answer": "5216",
        "correct_value": 5216,
        "explanation": "B-C = -109; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7292 + 7887 - 3037",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 7292 + 7887 - 3037",
        "options": [
          "12162",
          "12142",
          "12132",
          "12152"
        ],
        "answer": "12142",
        "correct_value": 12142,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000594",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8364 + 7192 - 7193",
      "ns_shortcut": "Near-cancellation: 7192 - 7193 = -1, so answer ≈ 8364 + -1.",
      "shortcut_strength": 0.999860956618465,
      "pure_math": {
        "question": "Evaluate: 8364 + 7192 - 7193",
        "options": [
          "8383",
          "8353",
          "8363",
          "8373"
        ],
        "answer": "8363",
        "correct_value": 8363,
        "explanation": "B-C = -1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8255 + 6767 - 6544",
      "ns_shortcut": "Near-cancellation: 6767 - 6544 = 223, offset is manageable.",
      "shortcut_strength": 0.967045958327176,
      "pure_math": {
        "question": "Evaluate: 8255 + 6767 - 6544",
        "options": [
          "8488",
          "8498",
          "8468",
          "8478"
        ],
        "answer": "8478",
        "correct_value": 8478,
        "explanation": "B-C = 223; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8364 + 7192 - 10012",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 8364 + 7192 - 10012",
        "options": [
          "5534",
          "5564",
          "5544",
          "5554"
        ],
        "answer": "5544",
        "correct_value": 5544,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000595",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2576 + 4339 - 4341",
      "ns_shortcut": "Near-cancellation: 4339 - 4341 = -2, so answer ≈ 2576 + -2.",
      "shortcut_strength": 0.9995390643005301,
      "pure_math": {
        "question": "Evaluate: 2576 + 4339 - 4341",
        "options": [
          "2594",
          "2564",
          "2574",
          "2584"
        ],
        "answer": "2574",
        "correct_value": 2574,
        "explanation": "B-C = -2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8238 + 6243 - 6371",
      "ns_shortcut": "Near-cancellation: 6243 - 6371 = -128, offset is manageable.",
      "shortcut_strength": 0.9794970366810828,
      "pure_math": {
        "question": "Evaluate: 8238 + 6243 - 6371",
        "options": [
          "8120",
          "8100",
          "8110",
          "8130"
        ],
        "answer": "8110",
        "correct_value": 8110,
        "explanation": "B-C = -128; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2576 + 4339 - 7037",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 2576 + 4339 - 7037",
        "options": [
          "-108",
          "-138",
          "-122",
          "-118"
        ],
        "answer": "-122",
        "correct_value": -122,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000596",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9205 + 6773 - 6772",
      "ns_shortcut": "Near-cancellation: 6773 - 6772 = 1, so answer ≈ 9205 + 1.",
      "shortcut_strength": 0.9998523549387273,
      "pure_math": {
        "question": "Evaluate: 9205 + 6773 - 6772",
        "options": [
          "9226",
          "9196",
          "9206",
          "9216"
        ],
        "answer": "9206",
        "correct_value": 9206,
        "explanation": "B-C = 1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8386 + 6423 - 6198",
      "ns_shortcut": "Near-cancellation: 6423 - 6198 = 225, offset is manageable.",
      "shortcut_strength": 0.9649696403549743,
      "pure_math": {
        "question": "Evaluate: 8386 + 6423 - 6198",
        "options": [
          "8611",
          "8631",
          "8601",
          "8621"
        ],
        "answer": "8611",
        "correct_value": 8611,
        "explanation": "B-C = 225; still a moderate shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9205 + 6773 - 9324",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 9205 + 6773 - 9324",
        "options": [
          "6674",
          "6664",
          "6644",
          "6654"
        ],
        "answer": "6654",
        "correct_value": 6654,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000597",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4777 + 1848 - 1847",
      "ns_shortcut": "Near-cancellation: 1848 - 1847 = 1, so answer ≈ 4777 + 1.",
      "shortcut_strength": 0.9994588744588745,
      "pure_math": {
        "question": "Evaluate: 4777 + 1848 - 1847",
        "options": [
          "4798",
          "4788",
          "4768",
          "4778"
        ],
        "answer": "4778",
        "correct_value": 4778,
        "explanation": "B-C = 1; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4607 + 4868 - 4673",
      "ns_shortcut": "Near-cancellation: 4868 - 4673 = 195, offset is manageable.",
      "shortcut_strength": 0.9599424815119145,
      "pure_math": {
        "question": "Evaluate: 4607 + 4868 - 4673",
        "options": [
          "4792",
          "4802",
          "4812",
          "4822"
        ],
        "answer": "4802",
        "correct_value": 4802,
        "explanation": "B-C = 195; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4777 + 1848 - 1000",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 4777 + 1848 - 1000",
        "options": [
          "5625",
          "5615",
          "5645",
          "5635"
        ],
        "answer": "5625",
        "correct_value": 5625,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000598",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "7540 + 1933 - 1935",
      "ns_shortcut": "Near-cancellation: 1933 - 1935 = -2, so answer ≈ 7540 + -2.",
      "shortcut_strength": 0.9989653388515262,
      "pure_math": {
        "question": "Evaluate: 7540 + 1933 - 1935",
        "options": [
          "7558",
          "7538",
          "7548",
          "7528"
        ],
        "answer": "7538",
        "correct_value": 7538,
        "explanation": "B-C = -2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7167 + 4130 - 4255",
      "ns_shortcut": "Near-cancellation: 4130 - 4255 = -125, offset is manageable.",
      "shortcut_strength": 0.9697336561743342,
      "pure_math": {
        "question": "Evaluate: 7167 + 4130 - 4255",
        "options": [
          "7032",
          "7062",
          "7042",
          "7052"
        ],
        "answer": "7042",
        "correct_value": 7042,
        "explanation": "B-C = -125; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7540 + 1933 - 1012",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 7540 + 1933 - 1012",
        "options": [
          "8481",
          "8451",
          "8461",
          "8471"
        ],
        "answer": "8461",
        "correct_value": 8461,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000599",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2021 + 4865 - 4863",
      "ns_shortcut": "Near-cancellation: 4865 - 4863 = 2, so answer ≈ 2021 + 2.",
      "shortcut_strength": 0.9995889003083248,
      "pure_math": {
        "question": "Evaluate: 2021 + 4865 - 4863",
        "options": [
          "2033",
          "2013",
          "2043",
          "2023"
        ],
        "answer": "2023",
        "correct_value": 2023,
        "explanation": "B-C = 2; result ≈ A + offset."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7016 + 6649 - 6426",
      "ns_shortcut": "Near-cancellation: 6649 - 6426 = 223, offset is manageable.",
      "shortcut_strength": 0.9664611219732291,
      "pure_math": {
        "question": "Evaluate: 7016 + 6649 - 6426",
        "options": [
          "7249",
          "7259",
          "7229",
          "7239"
        ],
        "answer": "7239",
        "correct_value": 7239,
        "explanation": "B-C = 223; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2021 + 4865 - 7453",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 2021 + 4865 - 7453",
        "options": [
          "-553",
          "-567",
          "-583",
          "-563"
        ],
        "answer": "-567",
        "correct_value": -567,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "cancellation_identity_000600",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2704 + 1588 - 1586",
      "ns_shortcut": "Near-cancellation: 1588 - 1586 = 2, so answer ≈ 2704 + 2.",
      "shortcut_strength": 0.9987405541561712,
      "pure_math": {
        "question": "Evaluate: 2704 + 1588 - 1586",
        "options": [
          "2706",
          "2696",
          "2726",
          "2716"
        ],
        "answer": "2706",
        "correct_value": 2706,
        "explanation": "B-C = 2; result ≈ A + offset."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7101 + 8902 - 9105",
      "ns_shortcut": "Near-cancellation: 8902 - 9105 = -203, offset is manageable.",
      "shortcut_strength": 0.9771961356998428,
      "pure_math": {
        "question": "Evaluate: 7101 + 8902 - 9105",
        "options": [
          "6908",
          "6898",
          "6888",
          "6918"
        ],
        "answer": "6898",
        "correct_value": 6898,
        "explanation": "B-C = -203; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2704 + 1588 - 1056",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 2704 + 1588 - 1056",
        "options": [
          "3236",
          "3226",
          "3256",
          "3246"
        ],
        "answer": "3236",
        "correct_value": 3236,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000602",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2520 * 3783",
      "ns_shortcut": "Round to 2500×4000 for easy mental computation.",
      "shortcut_strength": 0.968875,
      "pure_math": {
        "question": "Estimate 2520 × 3783.",
        "options": [
          "9533170",
          "9533150",
          "9533180",
          "9533160"
        ],
        "answer": "9533160",
        "correct_value": 9533160,
        "explanation": "Round to compatible pair 2500×4000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2497 * 3111",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.888275,
      "pure_math": {
        "question": "Estimate 2497 × 3111.",
        "options": [
          "7768177",
          "7768167",
          "7768157",
          "7768187"
        ],
        "answer": "7768167",
        "correct_value": 7768167,
        "explanation": "One number rounds to 2500, other is farther from 4000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9467 * 3526",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 9467 × 3526.",
        "options": [
          "33380642",
          "33380662",
          "33380652",
          "33380632"
        ],
        "answer": "33380642",
        "correct_value": 33380642,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000603",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2520 * 3783",
      "ns_shortcut": "Round to 2500×4000 for easy mental computation.",
      "shortcut_strength": 0.968875,
      "pure_math": {
        "question": "Estimate 2520 × 3783.",
        "options": [
          "9533170",
          "9533150",
          "9533180",
          "9533160"
        ],
        "answer": "9533160",
        "correct_value": 9533160,
        "explanation": "Round to compatible pair 2500×4000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2497 * 3111",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.888275,
      "pure_math": {
        "question": "Estimate 2497 × 3111.",
        "options": [
          "7768177",
          "7768167",
          "7768157",
          "7768187"
        ],
        "answer": "7768167",
        "correct_value": 7768167,
        "explanation": "One number rounds to 2500, other is farther from 4000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9467 * 3526",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 9467 × 3526.",
        "options": [
          "33380642",
          "33380662",
          "33380652",
          "33380632"
        ],
        "answer": "33380642",
        "correct_value": 33380642,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000604",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5081 * 2047",
      "ns_shortcut": "Round to 5000×2000 for easy mental computation.",
      "shortcut_strength": 0.98015,
      "pure_math": {
        "question": "Estimate 5081 × 2047.",
        "options": [
          "10400807",
          "10400817",
          "10400827",
          "10400797"
        ],
        "answer": "10400807",
        "correct_value": 10400807,
        "explanation": "Round to compatible pair 5000×2000 = 10000000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5087 * 1499",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.86605,
      "pure_math": {
        "question": "Estimate 5087 × 1499.",
        "options": [
          "7625403",
          "7625433",
          "7625423",
          "7625413"
        ],
        "answer": "7625413",
        "correct_value": 7625413,
        "explanation": "One number rounds to 5000, other is farther from 2000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5858 * 5856",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 5858 × 5856.",
        "options": [
          "34304448",
          "34304438",
          "34304458",
          "34304468"
        ],
        "answer": "34304448",
        "correct_value": 34304448,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000605",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1274 * 8785",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.9413375,
      "pure_math": {
        "question": "Estimate 1274 × 8785.",
        "options": [
          "11192110",
          "11192090",
          "11192080",
          "11192100"
        ],
        "answer": "11192090",
        "correct_value": 11192090,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1273 * 5384",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8272999999999999,
      "pure_math": {
        "question": "Estimate 1273 × 5384.",
        "options": [
          "6853832",
          "6853842",
          "6853852",
          "6853822"
        ],
        "answer": "6853832",
        "correct_value": 6853832,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3736 * 9032",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 3736 × 9032.",
        "options": [
          "33743572",
          "33743562",
          "33743542",
          "33743552"
        ],
        "answer": "33743552",
        "correct_value": 33743552,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000606",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5081 * 2047",
      "ns_shortcut": "Round to 5000×2000 for easy mental computation.",
      "shortcut_strength": 0.98015,
      "pure_math": {
        "question": "Estimate 5081 × 2047.",
        "options": [
          "10400807",
          "10400817",
          "10400827",
          "10400797"
        ],
        "answer": "10400807",
        "correct_value": 10400807,
        "explanation": "Round to compatible pair 5000×2000 = 10000000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5087 * 1499",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.86605,
      "pure_math": {
        "question": "Estimate 5087 × 1499.",
        "options": [
          "7625403",
          "7625433",
          "7625423",
          "7625413"
        ],
        "answer": "7625413",
        "correct_value": 7625413,
        "explanation": "One number rounds to 5000, other is farther from 2000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5858 * 5856",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 5858 × 5856.",
        "options": [
          "34304448",
          "34304438",
          "34304458",
          "34304468"
        ],
        "answer": "34304448",
        "correct_value": 34304448,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000607",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1274 * 8785",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.9413375,
      "pure_math": {
        "question": "Estimate 1274 × 8785.",
        "options": [
          "11192110",
          "11192090",
          "11192080",
          "11192100"
        ],
        "answer": "11192090",
        "correct_value": 11192090,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1273 * 5384",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8272999999999999,
      "pure_math": {
        "question": "Estimate 1273 × 5384.",
        "options": [
          "6853832",
          "6853842",
          "6853852",
          "6853822"
        ],
        "answer": "6853832",
        "correct_value": 6853832,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3736 * 9032",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 3736 × 9032.",
        "options": [
          "33743572",
          "33743562",
          "33743542",
          "33743552"
        ],
        "answer": "33743552",
        "correct_value": 33743552,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000608",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5009 * 1968",
      "ns_shortcut": "Round to 5000×2000 for easy mental computation.",
      "shortcut_strength": 0.9911,
      "pure_math": {
        "question": "Estimate 5009 × 1968.",
        "options": [
          "9857722",
          "9857702",
          "9857732",
          "9857712"
        ],
        "answer": "9857712",
        "correct_value": 9857712,
        "explanation": "Round to compatible pair 5000×2000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5065 * 1359",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.83325,
      "pure_math": {
        "question": "Estimate 5065 × 1359.",
        "options": [
          "6883335",
          "6883325",
          "6883345",
          "6883355"
        ],
        "answer": "6883335",
        "correct_value": 6883335,
        "explanation": "One number rounds to 5000, other is farther from 2000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9859 * 8865",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 9859 × 8865.",
        "options": [
          "87400035",
          "87400045",
          "87400055",
          "87400025"
        ],
        "answer": "87400035",
        "correct_value": 87400035,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000609",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5009 * 1968",
      "ns_shortcut": "Round to 5000×2000 for easy mental computation.",
      "shortcut_strength": 0.9911,
      "pure_math": {
        "question": "Estimate 5009 × 1968.",
        "options": [
          "9857722",
          "9857702",
          "9857732",
          "9857712"
        ],
        "answer": "9857712",
        "correct_value": 9857712,
        "explanation": "Round to compatible pair 5000×2000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5065 * 1359",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.83325,
      "pure_math": {
        "question": "Estimate 5065 × 1359.",
        "options": [
          "6883335",
          "6883325",
          "6883345",
          "6883355"
        ],
        "answer": "6883335",
        "correct_value": 6883335,
        "explanation": "One number rounds to 5000, other is farther from 2000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9859 * 8865",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 9859 × 8865.",
        "options": [
          "87400035",
          "87400045",
          "87400055",
          "87400025"
        ],
        "answer": "87400035",
        "correct_value": 87400035,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000610",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1273 * 7425",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.9548625,
      "pure_math": {
        "question": "Estimate 1273 × 7425.",
        "options": [
          "9452045",
          "9452015",
          "9452025",
          "9452035"
        ],
        "answer": "9452025",
        "correct_value": 9452025,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1226 * 9734",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8820250000000001,
      "pure_math": {
        "question": "Estimate 1226 × 9734.",
        "options": [
          "11933904",
          "11933894",
          "11933874",
          "11933884"
        ],
        "answer": "11933884",
        "correct_value": 11933884,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8575 * 1527",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 8575 × 1527.",
        "options": [
          "13094025",
          "13094015",
          "13094035",
          "13094045"
        ],
        "answer": "13094025",
        "correct_value": 13094025,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000611",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1273 * 7425",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.9548625,
      "pure_math": {
        "question": "Estimate 1273 × 7425.",
        "options": [
          "9452045",
          "9452015",
          "9452025",
          "9452035"
        ],
        "answer": "9452025",
        "correct_value": 9452025,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1226 * 9734",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8820250000000001,
      "pure_math": {
        "question": "Estimate 1226 × 9734.",
        "options": [
          "11933904",
          "11933894",
          "11933874",
          "11933884"
        ],
        "answer": "11933884",
        "correct_value": 11933884,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8575 * 1527",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 8575 × 1527.",
        "options": [
          "13094025",
          "13094015",
          "13094035",
          "13094045"
        ],
        "answer": "13094025",
        "correct_value": 13094025,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000612",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1233 * 7868",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.98495,
      "pure_math": {
        "question": "Estimate 1233 × 7868.",
        "options": [
          "9701264",
          "9701244",
          "9701254",
          "9701234"
        ],
        "answer": "9701244",
        "correct_value": 9701244,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1258 * 5343",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8307375,
      "pure_math": {
        "question": "Estimate 1258 × 5343.",
        "options": [
          "6721484",
          "6721504",
          "6721494",
          "6721514"
        ],
        "answer": "6721494",
        "correct_value": 6721494,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8725 * 6136",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 8725 × 6136.",
        "options": [
          "53536610",
          "53536620",
          "53536590",
          "53536600"
        ],
        "answer": "53536600",
        "correct_value": 53536600,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000613",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2540 * 3676",
      "ns_shortcut": "Round to 2500×4000 for easy mental computation.",
      "shortcut_strength": 0.9515,
      "pure_math": {
        "question": "Estimate 2540 × 3676.",
        "options": [
          "9337060",
          "9337040",
          "9337050",
          "9337030"
        ],
        "answer": "9337040",
        "correct_value": 9337040,
        "explanation": "Round to compatible pair 2500×4000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2508 * 3039",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.878275,
      "pure_math": {
        "question": "Estimate 2508 × 3039.",
        "options": [
          "7621822",
          "7621832",
          "7621802",
          "7621812"
        ],
        "answer": "7621812",
        "correct_value": 7621812,
        "explanation": "One number rounds to 2500, other is farther from 4000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5945 * 2628",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 5945 × 2628.",
        "options": [
          "15623450",
          "15623480",
          "15623470",
          "15623460"
        ],
        "answer": "15623460",
        "correct_value": 15623460,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000614",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1274 * 8677",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.9480875,
      "pure_math": {
        "question": "Estimate 1274 × 8677.",
        "options": [
          "11054488",
          "11054518",
          "11054498",
          "11054508"
        ],
        "answer": "11054498",
        "correct_value": 11054498,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1239 * 9766",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.885225,
      "pure_math": {
        "question": "Estimate 1239 × 9766.",
        "options": [
          "12100084",
          "12100094",
          "12100074",
          "12100064"
        ],
        "answer": "12100074",
        "correct_value": 12100074,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7143 * 4661",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 7143 × 4661.",
        "options": [
          "33293513",
          "33293543",
          "33293523",
          "33293533"
        ],
        "answer": "33293523",
        "correct_value": 33293523,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000615",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2539 * 3729",
      "ns_shortcut": "Round to 2500×4000 for easy mental computation.",
      "shortcut_strength": 0.958325,
      "pure_math": {
        "question": "Estimate 2539 × 3729.",
        "options": [
          "9467951",
          "9467941",
          "9467921",
          "9467931"
        ],
        "answer": "9467931",
        "correct_value": 9467931,
        "explanation": "Round to compatible pair 2500×4000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2518 * 5231",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.842525,
      "pure_math": {
        "question": "Estimate 2518 × 5231.",
        "options": [
          "13171668",
          "13171648",
          "13171678",
          "13171658"
        ],
        "answer": "13171658",
        "correct_value": 13171658,
        "explanation": "One number rounds to 2500, other is farther from 4000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5669 * 4738",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 5669 × 4738.",
        "options": [
          "26859742",
          "26859722",
          "26859712",
          "26859732"
        ],
        "answer": "26859722",
        "correct_value": 26859722,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000616",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1233 * 7868",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.98495,
      "pure_math": {
        "question": "Estimate 1233 × 7868.",
        "options": [
          "9701264",
          "9701244",
          "9701254",
          "9701234"
        ],
        "answer": "9701244",
        "correct_value": 9701244,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1258 * 5343",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8307375,
      "pure_math": {
        "question": "Estimate 1258 × 5343.",
        "options": [
          "6721484",
          "6721504",
          "6721494",
          "6721514"
        ],
        "answer": "6721494",
        "correct_value": 6721494,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8725 * 6136",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 8725 × 6136.",
        "options": [
          "53536610",
          "53536620",
          "53536590",
          "53536600"
        ],
        "answer": "53536600",
        "correct_value": 53536600,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000617",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4966 * 1988",
      "ns_shortcut": "Round to 5000×2000 for easy mental computation.",
      "shortcut_strength": 0.9936,
      "pure_math": {
        "question": "Estimate 4966 × 1988.",
        "options": [
          "9872408",
          "9872398",
          "9872428",
          "9872418"
        ],
        "answer": "9872408",
        "correct_value": 9872408,
        "explanation": "Round to compatible pair 5000×2000 = 10000000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4954 * 1446",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8569,
      "pure_math": {
        "question": "Estimate 4954 × 1446.",
        "options": [
          "7163504",
          "7163494",
          "7163474",
          "7163484"
        ],
        "answer": "7163484",
        "correct_value": 7163484,
        "explanation": "One number rounds to 5000, other is farther from 2000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6863 * 3034",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 6863 × 3034.",
        "options": [
          "20822342",
          "20822362",
          "20822352",
          "20822332"
        ],
        "answer": "20822342",
        "correct_value": 20822342,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000618",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2540 * 3676",
      "ns_shortcut": "Round to 2500×4000 for easy mental computation.",
      "shortcut_strength": 0.9515,
      "pure_math": {
        "question": "Estimate 2540 × 3676.",
        "options": [
          "9337060",
          "9337040",
          "9337050",
          "9337030"
        ],
        "answer": "9337040",
        "correct_value": 9337040,
        "explanation": "Round to compatible pair 2500×4000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2508 * 3039",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.878275,
      "pure_math": {
        "question": "Estimate 2508 × 3039.",
        "options": [
          "7621822",
          "7621832",
          "7621802",
          "7621812"
        ],
        "answer": "7621812",
        "correct_value": 7621812,
        "explanation": "One number rounds to 2500, other is farther from 4000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5945 * 2628",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 5945 × 2628.",
        "options": [
          "15623450",
          "15623480",
          "15623470",
          "15623460"
        ],
        "answer": "15623460",
        "correct_value": 15623460,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000619",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1274 * 8677",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.9480875,
      "pure_math": {
        "question": "Estimate 1274 × 8677.",
        "options": [
          "11054488",
          "11054518",
          "11054498",
          "11054508"
        ],
        "answer": "11054498",
        "correct_value": 11054498,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1239 * 9766",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.885225,
      "pure_math": {
        "question": "Estimate 1239 × 9766.",
        "options": [
          "12100084",
          "12100094",
          "12100074",
          "12100064"
        ],
        "answer": "12100074",
        "correct_value": 12100074,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7143 * 4661",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 7143 × 4661.",
        "options": [
          "33293513",
          "33293543",
          "33293523",
          "33293533"
        ],
        "answer": "33293523",
        "correct_value": 33293523,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000620",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2539 * 3729",
      "ns_shortcut": "Round to 2500×4000 for easy mental computation.",
      "shortcut_strength": 0.958325,
      "pure_math": {
        "question": "Estimate 2539 × 3729.",
        "options": [
          "9467951",
          "9467941",
          "9467921",
          "9467931"
        ],
        "answer": "9467931",
        "correct_value": 9467931,
        "explanation": "Round to compatible pair 2500×4000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2518 * 5231",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.842525,
      "pure_math": {
        "question": "Estimate 2518 × 5231.",
        "options": [
          "13171668",
          "13171648",
          "13171678",
          "13171658"
        ],
        "answer": "13171658",
        "correct_value": 13171658,
        "explanation": "One number rounds to 2500, other is farther from 4000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5669 * 4738",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 5669 × 4738.",
        "options": [
          "26859742",
          "26859722",
          "26859712",
          "26859732"
        ],
        "answer": "26859722",
        "correct_value": 26859722,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000621",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2510 * 4386",
      "ns_shortcut": "Round to 2500×4000 for easy mental computation.",
      "shortcut_strength": 0.94975,
      "pure_math": {
        "question": "Estimate 2510 × 4386.",
        "options": [
          "11008860",
          "11008850",
          "11008870",
          "11008880"
        ],
        "answer": "11008860",
        "correct_value": 11008860,
        "explanation": "Round to compatible pair 2500×4000 = 10000000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2463 * 5175",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8457250000000001,
      "pure_math": {
        "question": "Estimate 2463 × 5175.",
        "options": [
          "12746045",
          "12746035",
          "12746015",
          "12746025"
        ],
        "answer": "12746025",
        "correct_value": 12746025,
        "explanation": "One number rounds to 2500, other is farther from 4000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2846 * 5764",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 2846 × 5764.",
        "options": [
          "16404344",
          "16404364",
          "16404334",
          "16404354"
        ],
        "answer": "16404344",
        "correct_value": 16404344,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000622",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4910 * 1977",
      "ns_shortcut": "Round to 5000×2000 for easy mental computation.",
      "shortcut_strength": 0.98525,
      "pure_math": {
        "question": "Estimate 4910 × 1977.",
        "options": [
          "9707060",
          "9707080",
          "9707090",
          "9707070"
        ],
        "answer": "9707070",
        "correct_value": 9707070,
        "explanation": "Round to compatible pair 5000×2000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4955 * 2641",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.83525,
      "pure_math": {
        "question": "Estimate 4955 × 2641.",
        "options": [
          "13086175",
          "13086165",
          "13086155",
          "13086145"
        ],
        "answer": "13086155",
        "correct_value": 13086155,
        "explanation": "One number rounds to 5000, other is farther from 2000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1168 * 6839",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 1168 × 6839.",
        "options": [
          "7987952",
          "7987942",
          "7987972",
          "7987962"
        ],
        "answer": "7987952",
        "correct_value": 7987952,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000623",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4966 * 1988",
      "ns_shortcut": "Round to 5000×2000 for easy mental computation.",
      "shortcut_strength": 0.9936,
      "pure_math": {
        "question": "Estimate 4966 × 1988.",
        "options": [
          "9872408",
          "9872398",
          "9872428",
          "9872418"
        ],
        "answer": "9872408",
        "correct_value": 9872408,
        "explanation": "Round to compatible pair 5000×2000 = 10000000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4954 * 1446",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8569,
      "pure_math": {
        "question": "Estimate 4954 × 1446.",
        "options": [
          "7163504",
          "7163494",
          "7163474",
          "7163484"
        ],
        "answer": "7163484",
        "correct_value": 7163484,
        "explanation": "One number rounds to 5000, other is farther from 2000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6863 * 3034",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 6863 × 3034.",
        "options": [
          "20822342",
          "20822362",
          "20822352",
          "20822332"
        ],
        "answer": "20822342",
        "correct_value": 20822342,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000624",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2510 * 4386",
      "ns_shortcut": "Round to 2500×4000 for easy mental computation.",
      "shortcut_strength": 0.94975,
      "pure_math": {
        "question": "Estimate 2510 × 4386.",
        "options": [
          "11008860",
          "11008850",
          "11008870",
          "11008880"
        ],
        "answer": "11008860",
        "correct_value": 11008860,
        "explanation": "Round to compatible pair 2500×4000 = 10000000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2463 * 5175",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8457250000000001,
      "pure_math": {
        "question": "Estimate 2463 × 5175.",
        "options": [
          "12746045",
          "12746035",
          "12746015",
          "12746025"
        ],
        "answer": "12746025",
        "correct_value": 12746025,
        "explanation": "One number rounds to 2500, other is farther from 4000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2846 * 5764",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 2846 × 5764.",
        "options": [
          "16404344",
          "16404364",
          "16404334",
          "16404354"
        ],
        "answer": "16404344",
        "correct_value": 16404344,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000625",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4910 * 1977",
      "ns_shortcut": "Round to 5000×2000 for easy mental computation.",
      "shortcut_strength": 0.98525,
      "pure_math": {
        "question": "Estimate 4910 × 1977.",
        "options": [
          "9707060",
          "9707080",
          "9707090",
          "9707070"
        ],
        "answer": "9707070",
        "correct_value": 9707070,
        "explanation": "Round to compatible pair 5000×2000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4955 * 2641",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.83525,
      "pure_math": {
        "question": "Estimate 4955 × 2641.",
        "options": [
          "13086175",
          "13086165",
          "13086155",
          "13086145"
        ],
        "answer": "13086155",
        "correct_value": 13086155,
        "explanation": "One number rounds to 5000, other is farther from 2000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1168 * 6839",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 1168 × 6839.",
        "options": [
          "7987952",
          "7987942",
          "7987972",
          "7987962"
        ],
        "answer": "7987952",
        "correct_value": 7987952,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000626",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1227 * 7737",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.9743625,
      "pure_math": {
        "question": "Estimate 1227 × 7737.",
        "options": [
          "9493309",
          "9493299",
          "9493319",
          "9493289"
        ],
        "answer": "9493299",
        "correct_value": 9493299,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1229 * 10560",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8316,
      "pure_math": {
        "question": "Estimate 1229 × 10560.",
        "options": [
          "12978250",
          "12978240",
          "12978230",
          "12978260"
        ],
        "answer": "12978240",
        "correct_value": 12978240,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9233 * 1353",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 9233 × 1353.",
        "options": [
          "12492239",
          "12492259",
          "12492269",
          "12492249"
        ],
        "answer": "12492249",
        "correct_value": 12492249,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000627",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1227 * 7737",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.9743625,
      "pure_math": {
        "question": "Estimate 1227 × 7737.",
        "options": [
          "9493309",
          "9493299",
          "9493319",
          "9493289"
        ],
        "answer": "9493299",
        "correct_value": 9493299,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1229 * 10560",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8316,
      "pure_math": {
        "question": "Estimate 1229 × 10560.",
        "options": [
          "12978250",
          "12978240",
          "12978230",
          "12978260"
        ],
        "answer": "12978240",
        "correct_value": 12978240,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9233 * 1353",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 9233 × 1353.",
        "options": [
          "12492239",
          "12492259",
          "12492269",
          "12492249"
        ],
        "answer": "12492249",
        "correct_value": 12492249,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000628",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1248 * 7302",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.955575,
      "pure_math": {
        "question": "Estimate 1248 × 7302.",
        "options": [
          "9112886",
          "9112916",
          "9112896",
          "9112906"
        ],
        "answer": "9112896",
        "correct_value": 9112896,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1262 * 10295",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8517625,
      "pure_math": {
        "question": "Estimate 1262 × 10295.",
        "options": [
          "12992300",
          "12992280",
          "12992290",
          "12992310"
        ],
        "answer": "12992290",
        "correct_value": 12992290,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6542 * 1175",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 6542 × 1175.",
        "options": [
          "7686860",
          "7686840",
          "7686850",
          "7686870"
        ],
        "answer": "7686850",
        "correct_value": 7686850,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000629",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1248 * 7302",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.955575,
      "pure_math": {
        "question": "Estimate 1248 × 7302.",
        "options": [
          "9112886",
          "9112916",
          "9112896",
          "9112906"
        ],
        "answer": "9112896",
        "correct_value": 9112896,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1262 * 10295",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8517625,
      "pure_math": {
        "question": "Estimate 1262 × 10295.",
        "options": [
          "12992300",
          "12992280",
          "12992290",
          "12992310"
        ],
        "answer": "12992290",
        "correct_value": 12992290,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6542 * 1175",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 6542 × 1175.",
        "options": [
          "7686860",
          "7686840",
          "7686850",
          "7686870"
        ],
        "answer": "7686850",
        "correct_value": 7686850,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000630",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5090 * 1947",
      "ns_shortcut": "Round to 5000×2000 for easy mental computation.",
      "shortcut_strength": 0.97775,
      "pure_math": {
        "question": "Estimate 5090 × 1947.",
        "options": [
          "9910230",
          "9910250",
          "9910220",
          "9910240"
        ],
        "answer": "9910230",
        "correct_value": 9910230,
        "explanation": "Round to compatible pair 5000×2000 = 10000000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4989 * 1489",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.87115,
      "pure_math": {
        "question": "Estimate 4989 × 1489.",
        "options": [
          "7428621",
          "7428631",
          "7428611",
          "7428641"
        ],
        "answer": "7428621",
        "correct_value": 7428621,
        "explanation": "One number rounds to 5000, other is farther from 2000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4544 * 1768",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 4544 × 1768.",
        "options": [
          "8033802",
          "8033812",
          "8033782",
          "8033792"
        ],
        "answer": "8033792",
        "correct_value": 8033792,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000631",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5090 * 1947",
      "ns_shortcut": "Round to 5000×2000 for easy mental computation.",
      "shortcut_strength": 0.97775,
      "pure_math": {
        "question": "Estimate 5090 × 1947.",
        "options": [
          "9910230",
          "9910250",
          "9910220",
          "9910240"
        ],
        "answer": "9910230",
        "correct_value": 9910230,
        "explanation": "Round to compatible pair 5000×2000 = 10000000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4989 * 1489",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.87115,
      "pure_math": {
        "question": "Estimate 4989 × 1489.",
        "options": [
          "7428621",
          "7428631",
          "7428611",
          "7428641"
        ],
        "answer": "7428621",
        "correct_value": 7428621,
        "explanation": "One number rounds to 5000, other is farther from 2000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4544 * 1768",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 4544 × 1768.",
        "options": [
          "8033802",
          "8033812",
          "8033782",
          "8033792"
        ],
        "answer": "8033792",
        "correct_value": 8033792,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000632",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2472 * 3887",
      "ns_shortcut": "Round to 2500×4000 for easy mental computation.",
      "shortcut_strength": 0.980275,
      "pure_math": {
        "question": "Estimate 2472 × 3887.",
        "options": [
          "9608664",
          "9608684",
          "9608674",
          "9608654"
        ],
        "answer": "9608664",
        "correct_value": 9608664,
        "explanation": "Round to compatible pair 2500×4000 = 10000000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2504 * 5135",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.857325,
      "pure_math": {
        "question": "Estimate 2504 × 5135.",
        "options": [
          "12858040",
          "12858050",
          "12858060",
          "12858030"
        ],
        "answer": "12858040",
        "correct_value": 12858040,
        "explanation": "One number rounds to 2500, other is farther from 4000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1859 * 8461",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 1859 × 8461.",
        "options": [
          "15728989",
          "15729009",
          "15729019",
          "15728999"
        ],
        "answer": "15728999",
        "correct_value": 15728999,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000633",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4960 * 2196",
      "ns_shortcut": "Round to 5000×2000 for easy mental computation.",
      "shortcut_strength": 0.947,
      "pure_math": {
        "question": "Estimate 4960 × 2196.",
        "options": [
          "10892170",
          "10892180",
          "10892160",
          "10892150"
        ],
        "answer": "10892160",
        "correct_value": 10892160,
        "explanation": "Round to compatible pair 5000×2000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4999 * 1587",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.89665,
      "pure_math": {
        "question": "Estimate 4999 × 1587.",
        "options": [
          "7933413",
          "7933423",
          "7933403",
          "7933433"
        ],
        "answer": "7933413",
        "correct_value": 7933413,
        "explanation": "One number rounds to 5000, other is farther from 2000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9047 * 9028",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 9047 × 9028.",
        "options": [
          "81676306",
          "81676316",
          "81676336",
          "81676326"
        ],
        "answer": "81676316",
        "correct_value": 81676316,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000634",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1228 * 7243",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.9438875,
      "pure_math": {
        "question": "Estimate 1228 × 7243.",
        "options": [
          "8894414",
          "8894404",
          "8894394",
          "8894424"
        ],
        "answer": "8894404",
        "correct_value": 8894404,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1250 * 10446",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.847125,
      "pure_math": {
        "question": "Estimate 1250 × 10446.",
        "options": [
          "13057500",
          "13057490",
          "13057520",
          "13057510"
        ],
        "answer": "13057500",
        "correct_value": 13057500,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1554 * 1462",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 1554 × 1462.",
        "options": [
          "2271938",
          "2271948",
          "2271958",
          "2271968"
        ],
        "answer": "2271948",
        "correct_value": 2271948,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000635",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5060 * 1868",
      "ns_shortcut": "Round to 5000×2000 for easy mental computation.",
      "shortcut_strength": 0.961,
      "pure_math": {
        "question": "Estimate 5060 × 1868.",
        "options": [
          "9452090",
          "9452070",
          "9452080",
          "9452100"
        ],
        "answer": "9452080",
        "correct_value": 9452080,
        "explanation": "Round to compatible pair 5000×2000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5046 * 1382",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8409,
      "pure_math": {
        "question": "Estimate 5046 × 1382.",
        "options": [
          "6973572",
          "6973562",
          "6973592",
          "6973582"
        ],
        "answer": "6973572",
        "correct_value": 6973572,
        "explanation": "One number rounds to 5000, other is farther from 2000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2928 * 5764",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 2928 × 5764.",
        "options": [
          "16877012",
          "16876982",
          "16876992",
          "16877002"
        ],
        "answer": "16876992",
        "correct_value": 16876992,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000636",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1274 * 7201",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.9404625,
      "pure_math": {
        "question": "Estimate 1274 × 7201.",
        "options": [
          "9174094",
          "9174074",
          "9174084",
          "9174064"
        ],
        "answer": "9174074",
        "correct_value": 9174074,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1262 * 9859",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8790125,
      "pure_math": {
        "question": "Estimate 1262 × 9859.",
        "options": [
          "12442068",
          "12442048",
          "12442058",
          "12442078"
        ],
        "answer": "12442058",
        "correct_value": 12442058,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3753 * 5259",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 3753 × 5259.",
        "options": [
          "19737037",
          "19737027",
          "19737017",
          "19737047"
        ],
        "answer": "19737027",
        "correct_value": 19737027,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000637",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2472 * 3887",
      "ns_shortcut": "Round to 2500×4000 for easy mental computation.",
      "shortcut_strength": 0.980275,
      "pure_math": {
        "question": "Estimate 2472 × 3887.",
        "options": [
          "9608664",
          "9608684",
          "9608674",
          "9608654"
        ],
        "answer": "9608664",
        "correct_value": 9608664,
        "explanation": "Round to compatible pair 2500×4000 = 10000000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2504 * 5135",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.857325,
      "pure_math": {
        "question": "Estimate 2504 × 5135.",
        "options": [
          "12858040",
          "12858050",
          "12858060",
          "12858030"
        ],
        "answer": "12858040",
        "correct_value": 12858040,
        "explanation": "One number rounds to 2500, other is farther from 4000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1859 * 8461",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 1859 × 8461.",
        "options": [
          "15728989",
          "15729009",
          "15729019",
          "15728999"
        ],
        "answer": "15728999",
        "correct_value": 15728999,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000638",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2548 * 3929",
      "ns_shortcut": "Round to 2500×4000 for easy mental computation.",
      "shortcut_strength": 0.981525,
      "pure_math": {
        "question": "Estimate 2548 × 3929.",
        "options": [
          "10011112",
          "10011092",
          "10011082",
          "10011102"
        ],
        "answer": "10011092",
        "correct_value": 10011092,
        "explanation": "Round to compatible pair 2500×4000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2472 * 2853",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.851025,
      "pure_math": {
        "question": "Estimate 2472 × 2853.",
        "options": [
          "7052626",
          "7052616",
          "7052606",
          "7052636"
        ],
        "answer": "7052616",
        "correct_value": 7052616,
        "explanation": "One number rounds to 2500, other is farther from 4000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8668 * 1774",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 8668 × 1774.",
        "options": [
          "15377052",
          "15377032",
          "15377042",
          "15377022"
        ],
        "answer": "15377032",
        "correct_value": 15377032,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000639",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4960 * 2196",
      "ns_shortcut": "Round to 5000×2000 for easy mental computation.",
      "shortcut_strength": 0.947,
      "pure_math": {
        "question": "Estimate 4960 × 2196.",
        "options": [
          "10892170",
          "10892180",
          "10892160",
          "10892150"
        ],
        "answer": "10892160",
        "correct_value": 10892160,
        "explanation": "Round to compatible pair 5000×2000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4999 * 1587",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.89665,
      "pure_math": {
        "question": "Estimate 4999 × 1587.",
        "options": [
          "7933413",
          "7933423",
          "7933403",
          "7933433"
        ],
        "answer": "7933413",
        "correct_value": 7933413,
        "explanation": "One number rounds to 5000, other is farther from 2000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9047 * 9028",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 9047 × 9028.",
        "options": [
          "81676306",
          "81676316",
          "81676336",
          "81676326"
        ],
        "answer": "81676316",
        "correct_value": 81676316,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000640",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1228 * 7243",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.9438875,
      "pure_math": {
        "question": "Estimate 1228 × 7243.",
        "options": [
          "8894414",
          "8894404",
          "8894394",
          "8894424"
        ],
        "answer": "8894404",
        "correct_value": 8894404,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1250 * 10446",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.847125,
      "pure_math": {
        "question": "Estimate 1250 × 10446.",
        "options": [
          "13057500",
          "13057490",
          "13057520",
          "13057510"
        ],
        "answer": "13057500",
        "correct_value": 13057500,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1554 * 1462",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 1554 × 1462.",
        "options": [
          "2271938",
          "2271948",
          "2271958",
          "2271968"
        ],
        "answer": "2271948",
        "correct_value": 2271948,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000641",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1231 * 8094",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.986525,
      "pure_math": {
        "question": "Estimate 1231 × 8094.",
        "options": [
          "9963724",
          "9963714",
          "9963704",
          "9963734"
        ],
        "answer": "9963714",
        "correct_value": 9963714,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1258 * 5897",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8653625,
      "pure_math": {
        "question": "Estimate 1258 × 5897.",
        "options": [
          "7418436",
          "7418426",
          "7418446",
          "7418416"
        ],
        "answer": "7418426",
        "correct_value": 7418426,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7031 * 2366",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 7031 × 2366.",
        "options": [
          "16635356",
          "16635336",
          "16635346",
          "16635366"
        ],
        "answer": "16635346",
        "correct_value": 16635346,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000642",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5082 * 1800",
      "ns_shortcut": "Round to 5000×2000 for easy mental computation.",
      "shortcut_strength": 0.9418,
      "pure_math": {
        "question": "Estimate 5082 × 1800.",
        "options": [
          "9147610",
          "9147590",
          "9147620",
          "9147600"
        ],
        "answer": "9147600",
        "correct_value": 9147600,
        "explanation": "Round to compatible pair 5000×2000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4938 * 2655",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.83005,
      "pure_math": {
        "question": "Estimate 4938 × 2655.",
        "options": [
          "13110400",
          "13110380",
          "13110390",
          "13110410"
        ],
        "answer": "13110390",
        "correct_value": 13110390,
        "explanation": "One number rounds to 5000, other is farther from 2000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4534 * 9665",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 4534 × 9665.",
        "options": [
          "43821110",
          "43821120",
          "43821100",
          "43821130"
        ],
        "answer": "43821110",
        "correct_value": 43821110,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000643",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5060 * 1868",
      "ns_shortcut": "Round to 5000×2000 for easy mental computation.",
      "shortcut_strength": 0.961,
      "pure_math": {
        "question": "Estimate 5060 × 1868.",
        "options": [
          "9452090",
          "9452070",
          "9452080",
          "9452100"
        ],
        "answer": "9452080",
        "correct_value": 9452080,
        "explanation": "Round to compatible pair 5000×2000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5046 * 1382",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8409,
      "pure_math": {
        "question": "Estimate 5046 × 1382.",
        "options": [
          "6973572",
          "6973562",
          "6973592",
          "6973582"
        ],
        "answer": "6973572",
        "correct_value": 6973572,
        "explanation": "One number rounds to 5000, other is farther from 2000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2928 * 5764",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 2928 × 5764.",
        "options": [
          "16877012",
          "16876982",
          "16876992",
          "16877002"
        ],
        "answer": "16876992",
        "correct_value": 16876992,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000644",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2510 * 3724",
      "ns_shortcut": "Round to 2500×4000 for easy mental computation.",
      "shortcut_strength": 0.9635,
      "pure_math": {
        "question": "Estimate 2510 × 3724.",
        "options": [
          "9347260",
          "9347250",
          "9347230",
          "9347240"
        ],
        "answer": "9347240",
        "correct_value": 9347240,
        "explanation": "Round to compatible pair 2500×4000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2451 * 2846",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.84595,
      "pure_math": {
        "question": "Estimate 2451 × 2846.",
        "options": [
          "6975546",
          "6975556",
          "6975566",
          "6975536"
        ],
        "answer": "6975546",
        "correct_value": 6975546,
        "explanation": "One number rounds to 2500, other is farther from 4000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4235 * 1437",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 4235 × 1437.",
        "options": [
          "6085685",
          "6085715",
          "6085695",
          "6085705"
        ],
        "answer": "6085695",
        "correct_value": 6085695,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000645",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1274 * 7201",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.9404625,
      "pure_math": {
        "question": "Estimate 1274 × 7201.",
        "options": [
          "9174094",
          "9174074",
          "9174084",
          "9174064"
        ],
        "answer": "9174074",
        "correct_value": 9174074,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1262 * 9859",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8790125,
      "pure_math": {
        "question": "Estimate 1262 × 9859.",
        "options": [
          "12442068",
          "12442048",
          "12442058",
          "12442078"
        ],
        "answer": "12442058",
        "correct_value": 12442058,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3753 * 5259",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 3753 × 5259.",
        "options": [
          "19737037",
          "19737027",
          "19737017",
          "19737047"
        ],
        "answer": "19737027",
        "correct_value": 19737027,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000646",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2473 * 4227",
      "ns_shortcut": "Round to 2500×4000 for easy mental computation.",
      "shortcut_strength": 0.966225,
      "pure_math": {
        "question": "Estimate 2473 × 4227.",
        "options": [
          "10453371",
          "10453391",
          "10453381",
          "10453361"
        ],
        "answer": "10453371",
        "correct_value": 10453371,
        "explanation": "Round to compatible pair 2500×4000 = 10000000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2526 * 2722",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.83505,
      "pure_math": {
        "question": "Estimate 2526 × 2722.",
        "options": [
          "6875782",
          "6875762",
          "6875792",
          "6875772"
        ],
        "answer": "6875772",
        "correct_value": 6875772,
        "explanation": "One number rounds to 2500, other is farther from 4000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5568 * 1443",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 5568 × 1443.",
        "options": [
          "8034634",
          "8034644",
          "8034624",
          "8034614"
        ],
        "answer": "8034624",
        "correct_value": 8034624,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000647",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2530 * 3992",
      "ns_shortcut": "Round to 2500×4000 for easy mental computation.",
      "shortcut_strength": 0.993,
      "pure_math": {
        "question": "Estimate 2530 × 3992.",
        "options": [
          "10099760",
          "10099770",
          "10099750",
          "10099780"
        ],
        "answer": "10099760",
        "correct_value": 10099760,
        "explanation": "Round to compatible pair 2500×4000 = 10000000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2470 * 5025",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.865875,
      "pure_math": {
        "question": "Estimate 2470 × 5025.",
        "options": [
          "12411760",
          "12411750",
          "12411770",
          "12411740"
        ],
        "answer": "12411750",
        "correct_value": 12411750,
        "explanation": "One number rounds to 2500, other is farther from 4000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4536 * 7228",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 4536 × 7228.",
        "options": [
          "32786218",
          "32786228",
          "32786198",
          "32786208"
        ],
        "answer": "32786208",
        "correct_value": 32786208,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000648",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2520 * 3623",
      "ns_shortcut": "Round to 2500×4000 for easy mental computation.",
      "shortcut_strength": 0.948875,
      "pure_math": {
        "question": "Estimate 2520 × 3623.",
        "options": [
          "9129950",
          "9129980",
          "9129970",
          "9129960"
        ],
        "answer": "9129960",
        "correct_value": 9129960,
        "explanation": "Round to compatible pair 2500×4000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2530 * 4978",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.87175,
      "pure_math": {
        "question": "Estimate 2530 × 4978.",
        "options": [
          "12594340",
          "12594330",
          "12594360",
          "12594350"
        ],
        "answer": "12594340",
        "correct_value": 12594340,
        "explanation": "One number rounds to 2500, other is farther from 4000."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1446 * 1354",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 1446 × 1354.",
        "options": [
          "1957884",
          "1957904",
          "1957894",
          "1957874"
        ],
        "answer": "1957884",
        "correct_value": 1957884,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000649",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1266 * 7268",
      "ns_shortcut": "Round to 1250×8000 for easy mental computation.",
      "shortcut_strength": 0.94785,
      "pure_math": {
        "question": "Estimate 1266 × 7268.",
        "options": [
          "9201308",
          "9201288",
          "9201278",
          "9201298"
        ],
        "answer": "9201288",
        "correct_value": 9201288,
        "explanation": "Round to compatible pair 1250×8000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1255 * 10479",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.8430625,
      "pure_math": {
        "question": "Estimate 1255 × 10479.",
        "options": [
          "13151155",
          "13151145",
          "13151165",
          "13151135"
        ],
        "answer": "13151145",
        "correct_value": 13151145,
        "explanation": "One number rounds to 1250, other is farther from 8000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5352 * 4434",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 5352 × 4434.",
        "options": [
          "23730758",
          "23730788",
          "23730778",
          "23730768"
        ],
        "answer": "23730768",
        "correct_value": 23730768,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000650",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4925 * 2150",
      "ns_shortcut": "Round to 5000×2000 for easy mental computation.",
      "shortcut_strength": 0.955,
      "pure_math": {
        "question": "Estimate 4925 × 2150.",
        "options": [
          "10588770",
          "10588760",
          "10588740",
          "10588750"
        ],
        "answer": "10588750",
        "correct_value": 10588750,
        "explanation": "Round to compatible pair 5000×2000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5002 * 2659",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.83505,
      "pure_math": {
        "question": "Estimate 5002 × 2659.",
        "options": [
          "13300338",
          "13300328",
          "13300318",
          "13300308"
        ],
        "answer": "13300318",
        "correct_value": 13300318,
        "explanation": "One number rounds to 5000, other is farther from 2000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9874 * 9535",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 9874 × 9535.",
        "options": [
          "94148600",
          "94148590",
          "94148580",
          "94148610"
        ],
        "answer": "94148590",
        "correct_value": 94148590,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000651",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2548 * 3929",
      "ns_shortcut": "Round to 2500×4000 for easy mental computation.",
      "shortcut_strength": 0.981525,
      "pure_math": {
        "question": "Estimate 2548 × 3929.",
        "options": [
          "10011112",
          "10011092",
          "10011082",
          "10011102"
        ],
        "answer": "10011092",
        "correct_value": 10011092,
        "explanation": "Round to compatible pair 2500×4000 = 10000000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2472 * 2853",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.851025,
      "pure_math": {
        "question": "Estimate 2472 × 2853.",
        "options": [
          "7052626",
          "7052616",
          "7052606",
          "7052636"
        ],
        "answer": "7052616",
        "correct_value": 7052616,
        "explanation": "One number rounds to 2500, other is farther from 4000."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8668 * 1774",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 8668 × 1774.",
        "options": [
          "15377052",
          "15377032",
          "15377042",
          "15377022"
        ],
        "answer": "15377032",
        "correct_value": 15377032,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "landmark_comparison_000652",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9% of 48380 vs 22179",
      "ns_shortcut": "Use 10% as landmark: 10% of 48380 = 4838.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 9% of 48380 greater than 22179?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 4354.2,
        "explanation": "9% ≈ 10%. 10% of 48380 = 4838. Compare to 22179."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "15% of 48380 vs 22179",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 15% of 48380 greater than 22179?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 7257.0,
        "explanation": "15% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 48380 vs 22179",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 48380 greater than 22179?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 40155.4,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000653",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "48% of 75650 vs 34563",
      "ns_shortcut": "Use 50% as landmark: 50% of 75650 = 37825.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 48% of 75650 greater than 34563?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 36312.0,
        "explanation": "48% ≈ 50%. 50% of 75650 = 37825. Compare to 34563."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "45% of 75650 vs 34563",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 45% of 75650 greater than 34563?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 34042.5,
        "explanation": "45% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 75650 vs 34563",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 75650 greater than 34563?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 62789.5,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000654",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10% of 95860 vs 25675",
      "ns_shortcut": "Use 10% as landmark: 10% of 95860 = 9586.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 10% of 95860 greater than 25675?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 9586.0,
        "explanation": "10% ≈ 10%. 10% of 95860 = 9586. Compare to 25675."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "13% of 95860 vs 25675",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Is 13% of 95860 greater than 25675?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 12461.8,
        "explanation": "13% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 95860 vs 25675",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 95860 greater than 25675?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 35468.2,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000655",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26% of 60670 vs 16769",
      "ns_shortcut": "Use 25% as landmark: 25% of 60670 = 15167.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 26% of 60670 greater than 16769?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 15774.2,
        "explanation": "26% ≈ 25%. 25% of 60670 = 15167. Compare to 16769."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "19% of 60670 vs 16769",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 19% of 60670 greater than 16769?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 11527.3,
        "explanation": "19% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 60670 vs 16769",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 60670 greater than 16769?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 22447.9,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000656",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25% of 38290 vs 9069",
      "ns_shortcut": "Use 25% as landmark: 25% of 38290 = 9572.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 25% of 38290 greater than 9069?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 9572.5,
        "explanation": "25% ≈ 25%. 25% of 38290 = 9572. Compare to 9069."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "19% of 38290 vs 9069",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 19% of 38290 greater than 9069?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 7275.1,
        "explanation": "19% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "43% of 38290 vs 9069",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 43% of 38290 greater than 9069?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 16464.7,
        "explanation": "43% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000657",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "50% of 43310 vs 15814",
      "ns_shortcut": "Use 50% as landmark: 50% of 43310 = 21655.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 50% of 43310 greater than 15814?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 21655.0,
        "explanation": "50% ≈ 50%. 50% of 43310 = 21655. Compare to 15814."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "53% of 43310 vs 15814",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Is 53% of 43310 greater than 15814?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 22954.3,
        "explanation": "53% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 43310 vs 15814",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 43310 greater than 15814?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 31616.3,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000658",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "52% of 36100 vs 12867",
      "ns_shortcut": "Use 50% as landmark: 50% of 36100 = 18050.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 52% of 36100 greater than 12867?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 18772.0,
        "explanation": "52% ≈ 50%. 50% of 36100 = 18050. Compare to 12867."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "54% of 36100 vs 12867",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 54% of 36100 greater than 12867?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 19494.0,
        "explanation": "54% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 36100 vs 12867",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 36100 greater than 12867?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 26353.0,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000659",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10% of 71650 vs 29517",
      "ns_shortcut": "Use 10% as landmark: 10% of 71650 = 7165.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 10% of 71650 greater than 29517?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 7165.0,
        "explanation": "10% ≈ 10%. 10% of 71650 = 7165. Compare to 29517."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "14% of 71650 vs 29517",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 14% of 71650 greater than 29517?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 10031.0,
        "explanation": "14% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "67% of 71650 vs 29517",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 67% of 71650 greater than 29517?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 48005.5,
        "explanation": "67% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000660",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "27% of 31870 vs 12925",
      "ns_shortcut": "Use 25% as landmark: 25% of 31870 = 7967.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 27% of 31870 greater than 12925?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 8604.9,
        "explanation": "27% ≈ 25%. 25% of 31870 = 7967. Compare to 12925."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "32% of 31870 vs 12925",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.9299999999999999,
      "pure_math": {
        "question": "Is 32% of 31870 greater than 12925?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 10198.4,
        "explanation": "32% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 31870 vs 12925",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 31870 greater than 12925?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 23265.1,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000661",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "27% of 97500 vs 21848",
      "ns_shortcut": "Use 25% as landmark: 25% of 97500 = 24375.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 27% of 97500 greater than 21848?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 26325.0,
        "explanation": "27% ≈ 25%. 25% of 97500 = 24375. Compare to 21848."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "21% of 97500 vs 21848",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 21% of 97500 greater than 21848?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 20475.0,
        "explanation": "21% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 97500 vs 21848",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 97500 greater than 21848?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 80925.0,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000662",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26% of 39180 vs 11688",
      "ns_shortcut": "Use 25% as landmark: 25% of 39180 = 9795.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 26% of 39180 greater than 11688?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 10186.8,
        "explanation": "26% ≈ 25%. 25% of 39180 = 9795. Compare to 11688."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "18% of 39180 vs 11688",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.9299999999999999,
      "pure_math": {
        "question": "Is 18% of 39180 greater than 11688?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 7052.4,
        "explanation": "18% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 39180 vs 11688",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 39180 greater than 11688?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 32519.4,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000663",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10% of 75230 vs 17577",
      "ns_shortcut": "Use 10% as landmark: 10% of 75230 = 7523.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 10% of 75230 greater than 17577?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 7523.0,
        "explanation": "10% ≈ 10%. 10% of 75230 = 7523. Compare to 17577."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "14% of 75230 vs 17577",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 14% of 75230 greater than 17577?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 10532.2,
        "explanation": "14% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 75230 vs 17577",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 75230 greater than 17577?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 27835.1,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000664",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "24% of 44600 vs 13866",
      "ns_shortcut": "Use 25% as landmark: 25% of 44600 = 11150.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 24% of 44600 greater than 13866?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 10704.0,
        "explanation": "24% ≈ 25%. 25% of 44600 = 11150. Compare to 13866."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "29% of 44600 vs 13866",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 29% of 44600 greater than 13866?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 12934.0,
        "explanation": "29% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 44600 vs 13866",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 44600 greater than 13866?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 32558.0,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000665",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "27% of 34690 vs 11606",
      "ns_shortcut": "Use 25% as landmark: 25% of 34690 = 8672.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 27% of 34690 greater than 11606?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 9366.3,
        "explanation": "27% ≈ 25%. 25% of 34690 = 8672. Compare to 11606."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "28% of 34690 vs 11606",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Is 28% of 34690 greater than 11606?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 9713.2,
        "explanation": "28% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "67% of 34690 vs 11606",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 67% of 34690 greater than 11606?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 23242.3,
        "explanation": "67% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000666",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "52% of 79090 vs 21700",
      "ns_shortcut": "Use 50% as landmark: 50% of 79090 = 39545.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 52% of 79090 greater than 21700?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 41126.8,
        "explanation": "52% ≈ 50%. 50% of 79090 = 39545. Compare to 21700."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "44% of 79090 vs 21700",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 44% of 79090 greater than 21700?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 34799.6,
        "explanation": "44% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 79090 vs 21700",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 79090 greater than 21700?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 29263.3,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000667",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "52% of 36720 vs 8924",
      "ns_shortcut": "Use 50% as landmark: 50% of 36720 = 18360.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 52% of 36720 greater than 8924?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 19094.4,
        "explanation": "52% ≈ 50%. 50% of 36720 = 18360. Compare to 8924."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "53% of 36720 vs 8924",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Is 53% of 36720 greater than 8924?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 19461.6,
        "explanation": "53% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "63% of 36720 vs 8924",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 63% of 36720 greater than 8924?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 23133.6,
        "explanation": "63% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000668",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10% of 93060 vs 31194",
      "ns_shortcut": "Use 10% as landmark: 10% of 93060 = 9306.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 10% of 93060 greater than 31194?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 9306.0,
        "explanation": "10% ≈ 10%. 10% of 93060 = 9306. Compare to 31194."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "16% of 93060 vs 31194",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 16% of 93060 greater than 31194?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 14889.6,
        "explanation": "16% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 93060 vs 31194",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 93060 greater than 31194?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 67933.8,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000669",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "27% of 18930 vs 6267",
      "ns_shortcut": "Use 25% as landmark: 25% of 18930 = 4732.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 27% of 18930 greater than 6267?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 5111.1,
        "explanation": "27% ≈ 25%. 25% of 18930 = 4732. Compare to 6267."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "18% of 18930 vs 6267",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.9299999999999999,
      "pure_math": {
        "question": "Is 18% of 18930 greater than 6267?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 3407.4,
        "explanation": "18% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 18930 vs 6267",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 18930 greater than 6267?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 13818.9,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000670",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "11% of 29950 vs 7166",
      "ns_shortcut": "Use 10% as landmark: 10% of 29950 = 2995.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 11% of 29950 greater than 7166?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 3294.5,
        "explanation": "11% ≈ 10%. 10% of 29950 = 2995. Compare to 7166."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "14% of 29950 vs 7166",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 14% of 29950 greater than 7166?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 4193.0,
        "explanation": "14% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "87% of 29950 vs 7166",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 87% of 29950 greater than 7166?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 26056.5,
        "explanation": "87% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000671",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25% of 79470 vs 33317",
      "ns_shortcut": "Use 25% as landmark: 25% of 79470 = 19867.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 25% of 79470 greater than 33317?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 19867.5,
        "explanation": "25% ≈ 25%. 25% of 79470 = 19867. Compare to 33317."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "20% of 79470 vs 33317",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 20% of 79470 greater than 33317?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 15894.0,
        "explanation": "20% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 79470 vs 33317",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 79470 greater than 33317?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 65960.1,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000672",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "11% of 52240 vs 13685",
      "ns_shortcut": "Use 10% as landmark: 10% of 52240 = 5224.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 11% of 52240 greater than 13685?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 5746.4,
        "explanation": "11% ≈ 10%. 10% of 52240 = 5224. Compare to 13685."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4% of 52240 vs 13685",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 4% of 52240 greater than 13685?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 2089.6,
        "explanation": "4% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "67% of 52240 vs 13685",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 67% of 52240 greater than 13685?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 35000.8,
        "explanation": "67% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000673",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26% of 16520 vs 4299",
      "ns_shortcut": "Use 25% as landmark: 25% of 16520 = 4130.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 26% of 16520 greater than 4299?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 4295.2,
        "explanation": "26% ≈ 25%. 25% of 16520 = 4130. Compare to 4299."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "18% of 16520 vs 4299",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.9299999999999999,
      "pure_math": {
        "question": "Is 18% of 16520 greater than 4299?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 2973.6,
        "explanation": "18% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "67% of 16520 vs 4299",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 67% of 16520 greater than 4299?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 11068.4,
        "explanation": "67% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000674",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25% of 51340 vs 17242",
      "ns_shortcut": "Use 25% as landmark: 25% of 51340 = 12835.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 25% of 51340 greater than 17242?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 12835.0,
        "explanation": "25% ≈ 25%. 25% of 51340 = 12835. Compare to 17242."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "29% of 51340 vs 17242",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 29% of 51340 greater than 17242?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 14888.6,
        "explanation": "29% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "67% of 51340 vs 17242",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 67% of 51340 greater than 17242?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 34397.8,
        "explanation": "67% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000675",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "51% of 68470 vs 27360",
      "ns_shortcut": "Use 50% as landmark: 50% of 68470 = 34235.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 51% of 68470 greater than 27360?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 34919.7,
        "explanation": "51% ≈ 50%. 50% of 68470 = 34235. Compare to 27360."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "53% of 68470 vs 27360",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Is 53% of 68470 greater than 27360?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 36289.1,
        "explanation": "53% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 68470 vs 27360",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 68470 greater than 27360?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 56830.1,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000676",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "27% of 41260 vs 11171",
      "ns_shortcut": "Use 25% as landmark: 25% of 41260 = 10315.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 27% of 41260 greater than 11171?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 11140.2,
        "explanation": "27% ≈ 25%. 25% of 41260 = 10315. Compare to 11171."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "20% of 41260 vs 11171",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 20% of 41260 greater than 11171?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 8252.0,
        "explanation": "20% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 41260 vs 11171",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 41260 greater than 11171?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 34245.8,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000677",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "48% of 23770 vs 9136",
      "ns_shortcut": "Use 50% as landmark: 50% of 23770 = 11885.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 48% of 23770 greater than 9136?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 11409.6,
        "explanation": "48% ≈ 50%. 50% of 23770 = 11885. Compare to 9136."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "44% of 23770 vs 9136",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 44% of 23770 greater than 9136?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 10458.8,
        "explanation": "44% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 23770 vs 9136",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 23770 greater than 9136?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 17352.1,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000678",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "23% of 55000 vs 22317",
      "ns_shortcut": "Use 25% as landmark: 25% of 55000 = 13750.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 23% of 55000 greater than 22317?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 12650.0,
        "explanation": "23% ≈ 25%. 25% of 55000 = 13750. Compare to 22317."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "28% of 55000 vs 22317",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Is 28% of 55000 greater than 22317?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 15400.0,
        "explanation": "28% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 55000 vs 22317",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 55000 greater than 22317?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 20350.0,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000679",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "48% of 63500 vs 24915",
      "ns_shortcut": "Use 50% as landmark: 50% of 63500 = 31750.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 48% of 63500 greater than 24915?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 30480.0,
        "explanation": "48% ≈ 50%. 50% of 63500 = 31750. Compare to 24915."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "44% of 63500 vs 24915",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 44% of 63500 greater than 24915?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 27940.0,
        "explanation": "44% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 63500 vs 24915",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 63500 greater than 24915?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 52705.0,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000680",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "23% of 72010 vs 15760",
      "ns_shortcut": "Use 25% as landmark: 25% of 72010 = 18002.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 23% of 72010 greater than 15760?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 16562.3,
        "explanation": "23% ≈ 25%. 25% of 72010 = 18002. Compare to 15760."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "32% of 72010 vs 15760",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.9299999999999999,
      "pure_math": {
        "question": "Is 32% of 72010 greater than 15760?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 23043.2,
        "explanation": "32% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "63% of 72010 vs 15760",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 63% of 72010 greater than 15760?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 45366.3,
        "explanation": "63% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000681",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9% of 52080 vs 22238",
      "ns_shortcut": "Use 10% as landmark: 10% of 52080 = 5208.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 9% of 52080 greater than 22238?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 4687.2,
        "explanation": "9% ≈ 10%. 10% of 52080 = 5208. Compare to 22238."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6% of 52080 vs 22238",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 6% of 52080 greater than 22238?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 3124.8,
        "explanation": "6% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 52080 vs 22238",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 52080 greater than 22238?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 43226.4,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000682",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8% of 52750 vs 15517",
      "ns_shortcut": "Use 10% as landmark: 10% of 52750 = 5275.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 8% of 52750 greater than 15517?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 4220.0,
        "explanation": "8% ≈ 10%. 10% of 52750 = 5275. Compare to 15517."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5% of 52750 vs 15517",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 5% of 52750 greater than 15517?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 2637.5,
        "explanation": "5% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 52750 vs 15517",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 52750 greater than 15517?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 43782.5,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000683",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "27% of 87480 vs 24547",
      "ns_shortcut": "Use 25% as landmark: 25% of 87480 = 21870.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 27% of 87480 greater than 24547?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 23619.6,
        "explanation": "27% ≈ 25%. 25% of 87480 = 21870. Compare to 24547."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "20% of 87480 vs 24547",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 20% of 87480 greater than 24547?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 17496.0,
        "explanation": "20% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 87480 vs 24547",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 87480 greater than 24547?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 72608.4,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000684",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "23% of 17490 vs 8451",
      "ns_shortcut": "Use 25% as landmark: 25% of 17490 = 4372.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 23% of 17490 greater than 8451?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 4022.7,
        "explanation": "23% ≈ 25%. 25% of 17490 = 4372. Compare to 8451."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "30% of 17490 vs 8451",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 30% of 17490 greater than 8451?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 5247.0,
        "explanation": "30% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 17490 vs 8451",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 17490 greater than 8451?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 6471.3,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000685",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "52% of 76710 vs 22129",
      "ns_shortcut": "Use 50% as landmark: 50% of 76710 = 38355.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 52% of 76710 greater than 22129?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 39889.2,
        "explanation": "52% ≈ 50%. 50% of 76710 = 38355. Compare to 22129."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "45% of 76710 vs 22129",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 45% of 76710 greater than 22129?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 34519.5,
        "explanation": "45% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "67% of 76710 vs 22129",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 67% of 76710 greater than 22129?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 51395.7,
        "explanation": "67% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000686",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10% of 85760 vs 36782",
      "ns_shortcut": "Use 10% as landmark: 10% of 85760 = 8576.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 10% of 85760 greater than 36782?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 8576.0,
        "explanation": "10% ≈ 10%. 10% of 85760 = 8576. Compare to 36782."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6% of 85760 vs 36782",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 6% of 85760 greater than 36782?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 5145.6,
        "explanation": "6% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 85760 vs 36782",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 85760 greater than 36782?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 31731.2,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000687",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "52% of 63180 vs 19879",
      "ns_shortcut": "Use 50% as landmark: 50% of 63180 = 31590.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 52% of 63180 greater than 19879?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 32853.6,
        "explanation": "52% ≈ 50%. 50% of 63180 = 31590. Compare to 19879."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "57% of 63180 vs 19879",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.9299999999999999,
      "pure_math": {
        "question": "Is 57% of 63180 greater than 19879?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 36012.6,
        "explanation": "57% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 63180 vs 19879",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 63180 greater than 19879?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 46121.4,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000688",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "27% of 63860 vs 30514",
      "ns_shortcut": "Use 25% as landmark: 25% of 63860 = 15965.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 27% of 63860 greater than 30514?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 17242.2,
        "explanation": "27% ≈ 25%. 25% of 63860 = 15965. Compare to 30514."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "20% of 63860 vs 30514",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 20% of 63860 greater than 30514?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 12772.0,
        "explanation": "20% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "67% of 63860 vs 30514",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 67% of 63860 greater than 30514?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 42786.2,
        "explanation": "67% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000689",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "24% of 62370 vs 23823",
      "ns_shortcut": "Use 25% as landmark: 25% of 62370 = 15592.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 24% of 62370 greater than 23823?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 14968.8,
        "explanation": "24% ≈ 25%. 25% of 62370 = 15592. Compare to 23823."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "29% of 62370 vs 23823",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 29% of 62370 greater than 23823?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 18087.3,
        "explanation": "29% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 62370 vs 23823",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 62370 greater than 23823?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 51767.1,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000690",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26% of 37850 vs 18596",
      "ns_shortcut": "Use 25% as landmark: 25% of 37850 = 9462.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 26% of 37850 greater than 18596?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 9841.0,
        "explanation": "26% ≈ 25%. 25% of 37850 = 9462. Compare to 18596."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "18% of 37850 vs 18596",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.9299999999999999,
      "pure_math": {
        "question": "Is 18% of 37850 greater than 18596?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 6813.0,
        "explanation": "18% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 37850 vs 18596",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 37850 greater than 18596?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 14004.5,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000691",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25% of 89710 vs 36335",
      "ns_shortcut": "Use 25% as landmark: 25% of 89710 = 22427.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 25% of 89710 greater than 36335?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 22427.5,
        "explanation": "25% ≈ 25%. 25% of 89710 = 22427. Compare to 36335."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "30% of 89710 vs 36335",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 30% of 89710 greater than 36335?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 26913.0,
        "explanation": "30% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "67% of 89710 vs 36335",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 67% of 89710 greater than 36335?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 60105.7,
        "explanation": "67% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000692",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10% of 61660 vs 27126",
      "ns_shortcut": "Use 10% as landmark: 10% of 61660 = 6166.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 10% of 61660 greater than 27126?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 6166.0,
        "explanation": "10% ≈ 10%. 10% of 61660 = 6166. Compare to 27126."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3% of 61660 vs 27126",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.9299999999999999,
      "pure_math": {
        "question": "Is 3% of 61660 greater than 27126?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 1849.8,
        "explanation": "3% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 61660 vs 27126",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 61660 greater than 27126?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 51177.8,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000693",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26% of 37310 vs 17689",
      "ns_shortcut": "Use 25% as landmark: 25% of 37310 = 9327.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 26% of 37310 greater than 17689?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 9700.6,
        "explanation": "26% ≈ 25%. 25% of 37310 = 9327. Compare to 17689."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "20% of 37310 vs 17689",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 20% of 37310 greater than 17689?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 7462.0,
        "explanation": "20% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 37310 vs 17689",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 37310 greater than 17689?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 30967.3,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000694",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "24% of 90400 vs 25771",
      "ns_shortcut": "Use 25% as landmark: 25% of 90400 = 22600.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 24% of 90400 greater than 25771?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 21696.0,
        "explanation": "24% ≈ 25%. 25% of 90400 = 22600. Compare to 25771."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "22% of 90400 vs 25771",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Is 22% of 90400 greater than 25771?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 19888.0,
        "explanation": "22% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 90400 vs 25771",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 90400 greater than 25771?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 65992.0,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000695",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "50% of 45760 vs 12614",
      "ns_shortcut": "Use 50% as landmark: 50% of 45760 = 22880.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 50% of 45760 greater than 12614?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 22880.0,
        "explanation": "50% ≈ 50%. 50% of 45760 = 22880. Compare to 12614."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "44% of 45760 vs 12614",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 44% of 45760 greater than 12614?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 20134.4,
        "explanation": "44% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 45760 vs 12614",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 45760 greater than 12614?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 37980.8,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000696",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "52% of 76930 vs 26921",
      "ns_shortcut": "Use 50% as landmark: 50% of 76930 = 38465.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 52% of 76930 greater than 26921?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 40003.6,
        "explanation": "52% ≈ 50%. 50% of 76930 = 38465. Compare to 26921."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "55% of 76930 vs 26921",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 55% of 76930 greater than 26921?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 42311.5,
        "explanation": "55% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "67% of 76930 vs 26921",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 67% of 76930 greater than 26921?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 51543.1,
        "explanation": "67% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000697",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "12% of 27300 vs 10901",
      "ns_shortcut": "Use 10% as landmark: 10% of 27300 = 2730.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 12% of 27300 greater than 10901?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 3276.0,
        "explanation": "12% ≈ 10%. 10% of 27300 = 2730. Compare to 10901."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "14% of 27300 vs 10901",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 14% of 27300 greater than 10901?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 3822.0,
        "explanation": "14% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 27300 vs 10901",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 27300 greater than 10901?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 19929.0,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000698",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26% of 91070 vs 43013",
      "ns_shortcut": "Use 25% as landmark: 25% of 91070 = 22767.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 26% of 91070 greater than 43013?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 23678.2,
        "explanation": "26% ≈ 25%. 25% of 91070 = 22767. Compare to 43013."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "21% of 91070 vs 43013",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 21% of 91070 greater than 43013?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 19124.7,
        "explanation": "21% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 91070 vs 43013",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 91070 greater than 43013?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 66481.1,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000699",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "11% of 57250 vs 11559",
      "ns_shortcut": "Use 10% as landmark: 10% of 57250 = 5725.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 11% of 57250 greater than 11559?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 6297.5,
        "explanation": "11% ≈ 10%. 10% of 57250 = 5725. Compare to 11559."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7% of 57250 vs 11559",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Is 7% of 57250 greater than 11559?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 4007.5,
        "explanation": "7% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 57250 vs 11559",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 57250 greater than 11559?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 41792.5,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000700",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25% of 26260 vs 11086",
      "ns_shortcut": "Use 25% as landmark: 25% of 26260 = 6565.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 25% of 26260 greater than 11086?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 6565.0,
        "explanation": "25% ≈ 25%. 25% of 26260 = 6565. Compare to 11086."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "20% of 26260 vs 11086",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 20% of 26260 greater than 11086?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 5252.0,
        "explanation": "20% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 26260 vs 11086",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 26260 greater than 11086?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 9716.2,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000701",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8% of 21520 vs 10615",
      "ns_shortcut": "Use 10% as landmark: 10% of 21520 = 2152.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 8% of 21520 greater than 10615?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 1721.6,
        "explanation": "8% ≈ 10%. 10% of 21520 = 2152. Compare to 10615."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "17% of 21520 vs 10615",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.9299999999999999,
      "pure_math": {
        "question": "Is 17% of 21520 greater than 10615?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 3658.4,
        "explanation": "17% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 21520 vs 10615",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 21520 greater than 10615?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 17861.6,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "equation_reasoning_000702",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8731 × 2490 × 7066 = ___ × 7066 × 8731",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  8731 × 2490 × 7066 = ___ × 7066 × 8731",
        "options": [
          "2480",
          "2500",
          "2510",
          "2490"
        ],
        "answer": "2490",
        "correct_value": 2490,
        "explanation": "A and C appear on both sides; blank = B = 2490."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9377 + 4162 + ___ = 4162 + 3644 + 8500",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  9377 + 4162 + ___ = 4162 + 3644 + 8500",
        "options": [
          "2777",
          "2767",
          "2757",
          "2787"
        ],
        "answer": "2767",
        "correct_value": 2767,
        "explanation": "B cancels; blank = C + D − A = 3644 + 8500 − 9377 = 2767."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3870 + 8736 + ___ = 4273 + 6287",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  3870 + 8736 + ___ = 4273 + 6287",
        "options": [
          "-2034",
          "-2046",
          "-2064",
          "-2044"
        ],
        "answer": "-2046",
        "correct_value": -2046,
        "explanation": "No matching terms; blank = 4273 + 6287 − 3870 − 8736 = -2046."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000703",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4391 + 8555 + ___ = 8555 + 8523 + 4391",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  4391 + 8555 + ___ = 8555 + 8523 + 4391",
        "options": [
          "8523",
          "8513",
          "8543",
          "8533"
        ],
        "answer": "8523",
        "correct_value": 8523,
        "explanation": "A and B appear on both sides and cancel; blank = C = 8523."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4963 + 3897 + ___ = 3897 + 8559 + 9195",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  4963 + 3897 + ___ = 3897 + 8559 + 9195",
        "options": [
          "12781",
          "12801",
          "12811",
          "12791"
        ],
        "answer": "12791",
        "correct_value": 12791,
        "explanation": "B cancels; blank = C + D − A = 8559 + 9195 − 4963 = 12791."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3609 + 5011 + ___ = 8572 + 2144",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  3609 + 5011 + ___ = 8572 + 2144",
        "options": [
          "2106",
          "2086",
          "2116",
          "2096"
        ],
        "answer": "2096",
        "correct_value": 2096,
        "explanation": "No matching terms; blank = 8572 + 2144 − 3609 − 5011 = 2096."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000704",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9515 + 8703 = ___ + 7313",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  9515 + 8703 = ___ + 7313",
        "options": [
          "10895",
          "10925",
          "10915",
          "10905"
        ],
        "answer": "10905",
        "correct_value": 10905,
        "explanation": "Blank = A + B − C = 9515 + 8703 − 7313 = 10905."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9803 + 2982 + ___ = 2982 + 9751 + 1388",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  9803 + 2982 + ___ = 2982 + 9751 + 1388",
        "options": [
          "1356",
          "1336",
          "1346",
          "1326"
        ],
        "answer": "1336",
        "correct_value": 1336,
        "explanation": "B cancels; blank = C + D − A = 9751 + 1388 − 9803 = 1336."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5799 + 7527 + ___ = 1653 + 6953",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  5799 + 7527 + ___ = 1653 + 6953",
        "options": [
          "-4720",
          "-4710",
          "-4700",
          "-4730"
        ],
        "answer": "-4720",
        "correct_value": -4720,
        "explanation": "No matching terms; blank = 1653 + 6953 − 5799 − 7527 = -4720."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000705",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3032 + 2697 = ___ + 3391",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  3032 + 2697 = ___ + 3391",
        "options": [
          "2348",
          "2338",
          "2328",
          "2358"
        ],
        "answer": "2338",
        "correct_value": 2338,
        "explanation": "Blank = A + B − C = 3032 + 2697 − 3391 = 2338."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3768 + 7004 + ___ = 7004 + 7764 + 6567",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  3768 + 7004 + ___ = 7004 + 7764 + 6567",
        "options": [
          "10583",
          "10553",
          "10563",
          "10573"
        ],
        "answer": "10563",
        "correct_value": 10563,
        "explanation": "B cancels; blank = C + D − A = 7764 + 6567 − 3768 = 10563."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4442 + 5333 + ___ = 2591 + 6407",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  4442 + 5333 + ___ = 2591 + 6407",
        "options": [
          "-793",
          "-763",
          "-773",
          "-777"
        ],
        "answer": "-777",
        "correct_value": -777,
        "explanation": "No matching terms; blank = 2591 + 6407 − 4442 − 5333 = -777."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000706",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5259 × 6610 × 5838 = ___ × 5838 × 5259",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  5259 × 6610 × 5838 = ___ × 5838 × 5259",
        "options": [
          "6610",
          "6630",
          "6620",
          "6600"
        ],
        "answer": "6610",
        "correct_value": 6610,
        "explanation": "A and C appear on both sides; blank = B = 6610."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5225 + 5510 + ___ = 5510 + 1585 + 3294",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  5225 + 5510 + ___ = 5510 + 1585 + 3294",
        "options": [
          "-346",
          "-364",
          "-334",
          "-344"
        ],
        "answer": "-346",
        "correct_value": -346,
        "explanation": "B cancels; blank = C + D − A = 1585 + 3294 − 5225 = -346."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1425 + 4621 + ___ = 7076 + 6942",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  1425 + 4621 + ___ = 7076 + 6942",
        "options": [
          "7962",
          "7972",
          "7982",
          "7992"
        ],
        "answer": "7972",
        "correct_value": 7972,
        "explanation": "No matching terms; blank = 7076 + 6942 − 1425 − 4621 = 7972."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000707",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8787 × (8206 + 5831) = 8787 × ___ + 8787 × 5831",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  8787 × (8206 + 5831) = 8787 × ___ + 8787 × 5831",
        "options": [
          "8196",
          "8206",
          "8226",
          "8216"
        ],
        "answer": "8206",
        "correct_value": 8206,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 8206."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3400 + 5789 + ___ = 5789 + 7295 + 5215",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  3400 + 5789 + ___ = 5789 + 7295 + 5215",
        "options": [
          "9100",
          "9130",
          "9110",
          "9120"
        ],
        "answer": "9110",
        "correct_value": 9110,
        "explanation": "B cancels; blank = C + D − A = 7295 + 5215 − 3400 = 9110."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5963 + 3430 + ___ = 1197 + 5250",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  5963 + 3430 + ___ = 1197 + 5250",
        "options": [
          "-2946",
          "-2944",
          "-2964",
          "-2934"
        ],
        "answer": "-2946",
        "correct_value": -2946,
        "explanation": "No matching terms; blank = 1197 + 5250 − 5963 − 3430 = -2946."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000708",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3791 + 6639 = ___ + 3553",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  3791 + 6639 = ___ + 3553",
        "options": [
          "6877",
          "6887",
          "6867",
          "6897"
        ],
        "answer": "6877",
        "correct_value": 6877,
        "explanation": "Blank = A + B − C = 3791 + 6639 − 3553 = 6877."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7192 + 8950 + ___ = 8950 + 3770 + 9605",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  7192 + 8950 + ___ = 8950 + 3770 + 9605",
        "options": [
          "6203",
          "6193",
          "6183",
          "6173"
        ],
        "answer": "6183",
        "correct_value": 6183,
        "explanation": "B cancels; blank = C + D − A = 3770 + 9605 − 7192 = 6183."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7223 + 1233 + ___ = 2060 + 6609",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  7223 + 1233 + ___ = 2060 + 6609",
        "options": [
          "233",
          "213",
          "203",
          "223"
        ],
        "answer": "213",
        "correct_value": 213,
        "explanation": "No matching terms; blank = 2060 + 6609 − 7223 − 1233 = 213."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000709",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3459 × 5559 × 2959 = ___ × 2959 × 3459",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  3459 × 5559 × 2959 = ___ × 2959 × 3459",
        "options": [
          "5559",
          "5579",
          "5549",
          "5569"
        ],
        "answer": "5559",
        "correct_value": 5559,
        "explanation": "A and C appear on both sides; blank = B = 5559."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8525 + 1199 + ___ = 1199 + 9587 + 4741",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  8525 + 1199 + ___ = 1199 + 9587 + 4741",
        "options": [
          "5823",
          "5803",
          "5793",
          "5813"
        ],
        "answer": "5803",
        "correct_value": 5803,
        "explanation": "B cancels; blank = C + D − A = 9587 + 4741 − 8525 = 5803."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7528 + 2619 + ___ = 6398 + 9313",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  7528 + 2619 + ___ = 6398 + 9313",
        "options": [
          "5584",
          "5554",
          "5574",
          "5564"
        ],
        "answer": "5564",
        "correct_value": 5564,
        "explanation": "No matching terms; blank = 6398 + 9313 − 7528 − 2619 = 5564."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000710",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8317 + 9567 + ___ = 9567 + 5062 + 8317",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  8317 + 9567 + ___ = 9567 + 5062 + 8317",
        "options": [
          "5082",
          "5062",
          "5052",
          "5072"
        ],
        "answer": "5062",
        "correct_value": 5062,
        "explanation": "A and B appear on both sides and cancel; blank = C = 5062."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5015 + 4741 + ___ = 4741 + 8472 + 3907",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  5015 + 4741 + ___ = 4741 + 8472 + 3907",
        "options": [
          "7354",
          "7374",
          "7384",
          "7364"
        ],
        "answer": "7364",
        "correct_value": 7364,
        "explanation": "B cancels; blank = C + D − A = 8472 + 3907 − 5015 = 7364."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5546 + 2496 + ___ = 4113 + 2043",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  5546 + 2496 + ___ = 4113 + 2043",
        "options": [
          "-1886",
          "-1904",
          "-1874",
          "-1884"
        ],
        "answer": "-1886",
        "correct_value": -1886,
        "explanation": "No matching terms; blank = 4113 + 2043 − 5546 − 2496 = -1886."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000711",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4403 + 4728 + ___ = 4728 + 4996 + 4403",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  4403 + 4728 + ___ = 4728 + 4996 + 4403",
        "options": [
          "5016",
          "4996",
          "5006",
          "4986"
        ],
        "answer": "4996",
        "correct_value": 4996,
        "explanation": "A and B appear on both sides and cancel; blank = C = 4996."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9797 + 1836 + ___ = 1836 + 6224 + 2196",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  9797 + 1836 + ___ = 1836 + 6224 + 2196",
        "options": [
          "-1363",
          "-1377",
          "-1393",
          "-1373"
        ],
        "answer": "-1377",
        "correct_value": -1377,
        "explanation": "B cancels; blank = C + D − A = 6224 + 2196 − 9797 = -1377."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8240 + 2366 + ___ = 8799 + 4234",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  8240 + 2366 + ___ = 8799 + 4234",
        "options": [
          "2437",
          "2417",
          "2447",
          "2427"
        ],
        "answer": "2427",
        "correct_value": 2427,
        "explanation": "No matching terms; blank = 8799 + 4234 − 8240 − 2366 = 2427."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000712",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5914 + 1157 = ___ + 8041",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  5914 + 1157 = ___ + 8041",
        "options": [
          "-980",
          "-960",
          "-950",
          "-970"
        ],
        "answer": "-970",
        "correct_value": -970,
        "explanation": "Blank = A + B − C = 5914 + 1157 − 8041 = -970."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4191 + 8475 + ___ = 8475 + 1008 + 5124",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  4191 + 8475 + ___ = 8475 + 1008 + 5124",
        "options": [
          "1941",
          "1951",
          "1961",
          "1931"
        ],
        "answer": "1941",
        "correct_value": 1941,
        "explanation": "B cancels; blank = C + D − A = 1008 + 5124 − 4191 = 1941."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9070 + 3892 + ___ = 6384 + 9311",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  9070 + 3892 + ___ = 6384 + 9311",
        "options": [
          "2733",
          "2743",
          "2753",
          "2723"
        ],
        "answer": "2733",
        "correct_value": 2733,
        "explanation": "No matching terms; blank = 6384 + 9311 − 9070 − 3892 = 2733."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000713",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5328 × (9719 + 5079) = 5328 × ___ + 5328 × 5079",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  5328 × (9719 + 5079) = 5328 × ___ + 5328 × 5079",
        "options": [
          "9719",
          "9709",
          "9729",
          "9739"
        ],
        "answer": "9719",
        "correct_value": 9719,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 9719."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8209 + 2826 + ___ = 2826 + 3984 + 8988",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  8209 + 2826 + ___ = 2826 + 3984 + 8988",
        "options": [
          "4753",
          "4783",
          "4773",
          "4763"
        ],
        "answer": "4763",
        "correct_value": 4763,
        "explanation": "B cancels; blank = C + D − A = 3984 + 8988 − 8209 = 4763."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9122 + 3672 + ___ = 3929 + 2074",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  9122 + 3672 + ___ = 3929 + 2074",
        "options": [
          "-6791",
          "-6789",
          "-6779",
          "-6809"
        ],
        "answer": "-6791",
        "correct_value": -6791,
        "explanation": "No matching terms; blank = 3929 + 2074 − 9122 − 3672 = -6791."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000714",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8261 + 6610 + ___ = 6610 + 9824 + 8261",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  8261 + 6610 + ___ = 6610 + 9824 + 8261",
        "options": [
          "9814",
          "9844",
          "9824",
          "9834"
        ],
        "answer": "9824",
        "correct_value": 9824,
        "explanation": "A and B appear on both sides and cancel; blank = C = 9824."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4797 + 4493 + ___ = 4493 + 6033 + 9221",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  4797 + 4493 + ___ = 4493 + 6033 + 9221",
        "options": [
          "10457",
          "10447",
          "10467",
          "10477"
        ],
        "answer": "10457",
        "correct_value": 10457,
        "explanation": "B cancels; blank = C + D − A = 6033 + 9221 − 4797 = 10457."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2686 + 5916 + ___ = 4445 + 3532",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  2686 + 5916 + ___ = 4445 + 3532",
        "options": [
          "-615",
          "-635",
          "-625",
          "-605"
        ],
        "answer": "-625",
        "correct_value": -625,
        "explanation": "No matching terms; blank = 4445 + 3532 − 2686 − 5916 = -625."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000715",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3814 + 3587 = ___ + 3574",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  3814 + 3587 = ___ + 3574",
        "options": [
          "3827",
          "3837",
          "3817",
          "3847"
        ],
        "answer": "3827",
        "correct_value": 3827,
        "explanation": "Blank = A + B − C = 3814 + 3587 − 3574 = 3827."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7830 + 5413 + ___ = 5413 + 4747 + 5306",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  7830 + 5413 + ___ = 5413 + 4747 + 5306",
        "options": [
          "2223",
          "2243",
          "2233",
          "2213"
        ],
        "answer": "2223",
        "correct_value": 2223,
        "explanation": "B cancels; blank = C + D − A = 4747 + 5306 − 7830 = 2223."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3375 + 6017 + ___ = 6467 + 6798",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  3375 + 6017 + ___ = 6467 + 6798",
        "options": [
          "3873",
          "3863",
          "3883",
          "3893"
        ],
        "answer": "3873",
        "correct_value": 3873,
        "explanation": "No matching terms; blank = 6467 + 6798 − 3375 − 6017 = 3873."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000716",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "7447 + 7834 = ___ + 1092",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  7447 + 7834 = ___ + 1092",
        "options": [
          "14209",
          "14199",
          "14189",
          "14179"
        ],
        "answer": "14189",
        "correct_value": 14189,
        "explanation": "Blank = A + B − C = 7447 + 7834 − 1092 = 14189."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6793 + 3292 + ___ = 3292 + 8485 + 5492",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  6793 + 3292 + ___ = 3292 + 8485 + 5492",
        "options": [
          "7194",
          "7174",
          "7204",
          "7184"
        ],
        "answer": "7184",
        "correct_value": 7184,
        "explanation": "B cancels; blank = C + D − A = 8485 + 5492 − 6793 = 7184."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4417 + 5193 + ___ = 5829 + 7119",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  4417 + 5193 + ___ = 5829 + 7119",
        "options": [
          "3328",
          "3358",
          "3348",
          "3338"
        ],
        "answer": "3338",
        "correct_value": 3338,
        "explanation": "No matching terms; blank = 5829 + 7119 − 4417 − 5193 = 3338."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000717",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6336 + 4267 = ___ + 4522",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  6336 + 4267 = ___ + 4522",
        "options": [
          "6101",
          "6081",
          "6091",
          "6071"
        ],
        "answer": "6081",
        "correct_value": 6081,
        "explanation": "Blank = A + B − C = 6336 + 4267 − 4522 = 6081."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2219 + 4983 + ___ = 4983 + 3628 + 6332",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  2219 + 4983 + ___ = 4983 + 3628 + 6332",
        "options": [
          "7741",
          "7751",
          "7761",
          "7731"
        ],
        "answer": "7741",
        "correct_value": 7741,
        "explanation": "B cancels; blank = C + D − A = 3628 + 6332 − 2219 = 7741."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1753 + 7390 + ___ = 8979 + 5093",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  1753 + 7390 + ___ = 8979 + 5093",
        "options": [
          "4929",
          "4939",
          "4919",
          "4949"
        ],
        "answer": "4929",
        "correct_value": 4929,
        "explanation": "No matching terms; blank = 8979 + 5093 − 1753 − 7390 = 4929."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000718",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2661 + 1919 + ___ = 1919 + 6614 + 2661",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  2661 + 1919 + ___ = 1919 + 6614 + 2661",
        "options": [
          "6614",
          "6624",
          "6604",
          "6634"
        ],
        "answer": "6614",
        "correct_value": 6614,
        "explanation": "A and B appear on both sides and cancel; blank = C = 6614."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8178 + 5656 + ___ = 5656 + 2819 + 8730",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  8178 + 5656 + ___ = 5656 + 2819 + 8730",
        "options": [
          "3361",
          "3371",
          "3391",
          "3381"
        ],
        "answer": "3371",
        "correct_value": 3371,
        "explanation": "B cancels; blank = C + D − A = 2819 + 8730 − 8178 = 3371."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6317 + 7779 + ___ = 3486 + 3464",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  6317 + 7779 + ___ = 3486 + 3464",
        "options": [
          "-7144",
          "-7146",
          "-7164",
          "-7134"
        ],
        "answer": "-7146",
        "correct_value": -7146,
        "explanation": "No matching terms; blank = 3486 + 3464 − 6317 − 7779 = -7146."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000719",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8180 + 5017 + ___ = 5017 + 6371 + 8180",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  8180 + 5017 + ___ = 5017 + 6371 + 8180",
        "options": [
          "6371",
          "6381",
          "6361",
          "6391"
        ],
        "answer": "6371",
        "correct_value": 6371,
        "explanation": "A and B appear on both sides and cancel; blank = C = 6371."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1358 + 3301 + ___ = 3301 + 2114 + 6143",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  1358 + 3301 + ___ = 3301 + 2114 + 6143",
        "options": [
          "6889",
          "6899",
          "6909",
          "6919"
        ],
        "answer": "6899",
        "correct_value": 6899,
        "explanation": "B cancels; blank = C + D − A = 2114 + 6143 − 1358 = 6899."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4016 + 6263 + ___ = 8673 + 4730",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  4016 + 6263 + ___ = 8673 + 4730",
        "options": [
          "3124",
          "3144",
          "3134",
          "3114"
        ],
        "answer": "3124",
        "correct_value": 3124,
        "explanation": "No matching terms; blank = 8673 + 4730 − 4016 − 6263 = 3124."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000720",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5243 × 5183 × 1379 = ___ × 1379 × 5243",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  5243 × 5183 × 1379 = ___ × 1379 × 5243",
        "options": [
          "5203",
          "5173",
          "5183",
          "5193"
        ],
        "answer": "5183",
        "correct_value": 5183,
        "explanation": "A and C appear on both sides; blank = B = 5183."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8001 + 7493 + ___ = 7493 + 8968 + 1786",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  8001 + 7493 + ___ = 7493 + 8968 + 1786",
        "options": [
          "2743",
          "2763",
          "2773",
          "2753"
        ],
        "answer": "2753",
        "correct_value": 2753,
        "explanation": "B cancels; blank = C + D − A = 8968 + 1786 − 8001 = 2753."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1265 + 8163 + ___ = 1525 + 9261",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  1265 + 8163 + ___ = 1525 + 9261",
        "options": [
          "1358",
          "1368",
          "1348",
          "1378"
        ],
        "answer": "1358",
        "correct_value": 1358,
        "explanation": "No matching terms; blank = 1525 + 9261 − 1265 − 8163 = 1358."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000721",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6468 × (2099 + 2237) = 6468 × ___ + 6468 × 2237",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  6468 × (2099 + 2237) = 6468 × ___ + 6468 × 2237",
        "options": [
          "2109",
          "2089",
          "2119",
          "2099"
        ],
        "answer": "2099",
        "correct_value": 2099,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 2099."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9712 + 3592 + ___ = 3592 + 9413 + 2437",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  9712 + 3592 + ___ = 3592 + 9413 + 2437",
        "options": [
          "2148",
          "2138",
          "2158",
          "2128"
        ],
        "answer": "2138",
        "correct_value": 2138,
        "explanation": "B cancels; blank = C + D − A = 9413 + 2437 − 9712 = 2138."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2197 + 8060 + ___ = 5536 + 8630",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  2197 + 8060 + ___ = 5536 + 8630",
        "options": [
          "3919",
          "3909",
          "3929",
          "3899"
        ],
        "answer": "3909",
        "correct_value": 3909,
        "explanation": "No matching terms; blank = 5536 + 8630 − 2197 − 8060 = 3909."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000722",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2196 × (3976 + 6567) = 2196 × ___ + 2196 × 6567",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  2196 × (3976 + 6567) = 2196 × ___ + 2196 × 6567",
        "options": [
          "3976",
          "3986",
          "3996",
          "3966"
        ],
        "answer": "3976",
        "correct_value": 3976,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 3976."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1351 + 7577 + ___ = 7577 + 5813 + 1104",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  1351 + 7577 + ___ = 7577 + 5813 + 1104",
        "options": [
          "5576",
          "5586",
          "5566",
          "5556"
        ],
        "answer": "5566",
        "correct_value": 5566,
        "explanation": "B cancels; blank = C + D − A = 5813 + 1104 − 1351 = 5566."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4690 + 6281 + ___ = 7998 + 3465",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  4690 + 6281 + ___ = 7998 + 3465",
        "options": [
          "482",
          "502",
          "492",
          "512"
        ],
        "answer": "492",
        "correct_value": 492,
        "explanation": "No matching terms; blank = 7998 + 3465 − 4690 − 6281 = 492."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000723",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4282 + 6810 = ___ + 3500",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  4282 + 6810 = ___ + 3500",
        "options": [
          "7582",
          "7612",
          "7592",
          "7602"
        ],
        "answer": "7592",
        "correct_value": 7592,
        "explanation": "Blank = A + B − C = 4282 + 6810 − 3500 = 7592."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6054 + 3975 + ___ = 3975 + 2653 + 1429",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  6054 + 3975 + ___ = 3975 + 2653 + 1429",
        "options": [
          "-1958",
          "-1968",
          "-1988",
          "-1972"
        ],
        "answer": "-1972",
        "correct_value": -1972,
        "explanation": "B cancels; blank = C + D − A = 2653 + 1429 − 6054 = -1972."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2134 + 6365 + ___ = 6166 + 4770",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  2134 + 6365 + ___ = 6166 + 4770",
        "options": [
          "2457",
          "2427",
          "2437",
          "2447"
        ],
        "answer": "2437",
        "correct_value": 2437,
        "explanation": "No matching terms; blank = 6166 + 4770 − 2134 − 6365 = 2437."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000724",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "7951 × 5441 × 4817 = ___ × 4817 × 7951",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  7951 × 5441 × 4817 = ___ × 4817 × 7951",
        "options": [
          "5461",
          "5441",
          "5431",
          "5451"
        ],
        "answer": "5441",
        "correct_value": 5441,
        "explanation": "A and C appear on both sides; blank = B = 5441."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3249 + 8203 + ___ = 8203 + 3017 + 7145",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  3249 + 8203 + ___ = 8203 + 3017 + 7145",
        "options": [
          "6933",
          "6903",
          "6923",
          "6913"
        ],
        "answer": "6913",
        "correct_value": 6913,
        "explanation": "B cancels; blank = C + D − A = 3017 + 7145 − 3249 = 6913."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7232 + 1806 + ___ = 8320 + 8185",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  7232 + 1806 + ___ = 8320 + 8185",
        "options": [
          "7477",
          "7487",
          "7467",
          "7457"
        ],
        "answer": "7467",
        "correct_value": 7467,
        "explanation": "No matching terms; blank = 8320 + 8185 − 7232 − 1806 = 7467."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000725",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3042 + 2521 = ___ + 3868",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  3042 + 2521 = ___ + 3868",
        "options": [
          "1705",
          "1715",
          "1685",
          "1695"
        ],
        "answer": "1695",
        "correct_value": 1695,
        "explanation": "Blank = A + B − C = 3042 + 2521 − 3868 = 1695."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2971 + 9013 + ___ = 9013 + 6871 + 6191",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  2971 + 9013 + ___ = 9013 + 6871 + 6191",
        "options": [
          "10101",
          "10111",
          "10091",
          "10081"
        ],
        "answer": "10091",
        "correct_value": 10091,
        "explanation": "B cancels; blank = C + D − A = 6871 + 6191 − 2971 = 10091."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2487 + 9305 + ___ = 6895 + 8831",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  2487 + 9305 + ___ = 6895 + 8831",
        "options": [
          "3944",
          "3934",
          "3924",
          "3954"
        ],
        "answer": "3934",
        "correct_value": 3934,
        "explanation": "No matching terms; blank = 6895 + 8831 − 2487 − 9305 = 3934."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000726",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1264 + 1118 = ___ + 7226",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  1264 + 1118 = ___ + 7226",
        "options": [
          "-4826",
          "-4844",
          "-4836",
          "-4856"
        ],
        "answer": "-4844",
        "correct_value": -4844,
        "explanation": "Blank = A + B − C = 1264 + 1118 − 7226 = -4844."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6811 + 6904 + ___ = 6904 + 6078 + 2069",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  6811 + 6904 + ___ = 6904 + 6078 + 2069",
        "options": [
          "1336",
          "1346",
          "1356",
          "1326"
        ],
        "answer": "1336",
        "correct_value": 1336,
        "explanation": "B cancels; blank = C + D − A = 6078 + 2069 − 6811 = 1336."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4757 + 2383 + ___ = 7384 + 8722",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  4757 + 2383 + ___ = 7384 + 8722",
        "options": [
          "8956",
          "8986",
          "8976",
          "8966"
        ],
        "answer": "8966",
        "correct_value": 8966,
        "explanation": "No matching terms; blank = 7384 + 8722 − 4757 − 2383 = 8966."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000727",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3305 + 5079 + ___ = 5079 + 3905 + 3305",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  3305 + 5079 + ___ = 5079 + 3905 + 3305",
        "options": [
          "3915",
          "3925",
          "3895",
          "3905"
        ],
        "answer": "3905",
        "correct_value": 3905,
        "explanation": "A and B appear on both sides and cancel; blank = C = 3905."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3297 + 8697 + ___ = 8697 + 1638 + 2002",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  3297 + 8697 + ___ = 8697 + 1638 + 2002",
        "options": [
          "343",
          "333",
          "363",
          "353"
        ],
        "answer": "343",
        "correct_value": 343,
        "explanation": "B cancels; blank = C + D − A = 1638 + 2002 − 3297 = 343."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7089 + 7797 + ___ = 3580 + 7868",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  7089 + 7797 + ___ = 3580 + 7868",
        "options": [
          "-3452",
          "-3422",
          "-3438",
          "-3432"
        ],
        "answer": "-3438",
        "correct_value": -3438,
        "explanation": "No matching terms; blank = 3580 + 7868 − 7089 − 7797 = -3438."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000728",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6981 × 2792 × 3660 = ___ × 3660 × 6981",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  6981 × 2792 × 3660 = ___ × 3660 × 6981",
        "options": [
          "2812",
          "2782",
          "2802",
          "2792"
        ],
        "answer": "2792",
        "correct_value": 2792,
        "explanation": "A and C appear on both sides; blank = B = 2792."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6014 + 7613 + ___ = 7613 + 7114 + 5344",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  6014 + 7613 + ___ = 7613 + 7114 + 5344",
        "options": [
          "6454",
          "6434",
          "6444",
          "6464"
        ],
        "answer": "6444",
        "correct_value": 6444,
        "explanation": "B cancels; blank = C + D − A = 7114 + 5344 − 6014 = 6444."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6432 + 1466 + ___ = 8708 + 1560",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  6432 + 1466 + ___ = 8708 + 1560",
        "options": [
          "2390",
          "2370",
          "2360",
          "2380"
        ],
        "answer": "2370",
        "correct_value": 2370,
        "explanation": "No matching terms; blank = 8708 + 1560 − 6432 − 1466 = 2370."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000729",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9604 + 3781 = ___ + 3591",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  9604 + 3781 = ___ + 3591",
        "options": [
          "9814",
          "9804",
          "9784",
          "9794"
        ],
        "answer": "9794",
        "correct_value": 9794,
        "explanation": "Blank = A + B − C = 9604 + 3781 − 3591 = 9794."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4648 + 2509 + ___ = 2509 + 7879 + 2086",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  4648 + 2509 + ___ = 2509 + 7879 + 2086",
        "options": [
          "5307",
          "5337",
          "5327",
          "5317"
        ],
        "answer": "5317",
        "correct_value": 5317,
        "explanation": "B cancels; blank = C + D − A = 7879 + 2086 − 4648 = 5317."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7800 + 9793 + ___ = 8215 + 3202",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  7800 + 9793 + ___ = 8215 + 3202",
        "options": [
          "-6194",
          "-6164",
          "-6174",
          "-6176"
        ],
        "answer": "-6176",
        "correct_value": -6176,
        "explanation": "No matching terms; blank = 8215 + 3202 − 7800 − 9793 = -6176."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000730",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5208 + 3100 = ___ + 6290",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  5208 + 3100 = ___ + 6290",
        "options": [
          "2028",
          "2018",
          "2008",
          "2038"
        ],
        "answer": "2018",
        "correct_value": 2018,
        "explanation": "Blank = A + B − C = 5208 + 3100 − 6290 = 2018."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8828 + 9074 + ___ = 9074 + 4215 + 3061",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  8828 + 9074 + ___ = 9074 + 4215 + 3061",
        "options": [
          "-1568",
          "-1552",
          "-1538",
          "-1548"
        ],
        "answer": "-1552",
        "correct_value": -1552,
        "explanation": "B cancels; blank = C + D − A = 4215 + 3061 − 8828 = -1552."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3336 + 4695 + ___ = 2346 + 2553",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  3336 + 4695 + ___ = 2346 + 2553",
        "options": [
          "-3118",
          "-3132",
          "-3128",
          "-3148"
        ],
        "answer": "-3132",
        "correct_value": -3132,
        "explanation": "No matching terms; blank = 2346 + 2553 − 3336 − 4695 = -3132."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000731",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4706 × 5106 × 4024 = ___ × 4024 × 4706",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  4706 × 5106 × 4024 = ___ × 4024 × 4706",
        "options": [
          "5106",
          "5096",
          "5116",
          "5126"
        ],
        "answer": "5106",
        "correct_value": 5106,
        "explanation": "A and C appear on both sides; blank = B = 5106."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9518 + 9468 + ___ = 9468 + 5370 + 3157",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  9518 + 9468 + ___ = 9468 + 5370 + 3157",
        "options": [
          "-991",
          "-1009",
          "-989",
          "-979"
        ],
        "answer": "-991",
        "correct_value": -991,
        "explanation": "B cancels; blank = C + D − A = 5370 + 3157 − 9518 = -991."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3379 + 1560 + ___ = 7308 + 1786",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  3379 + 1560 + ___ = 7308 + 1786",
        "options": [
          "4145",
          "4175",
          "4155",
          "4165"
        ],
        "answer": "4155",
        "correct_value": 4155,
        "explanation": "No matching terms; blank = 7308 + 1786 − 3379 − 1560 = 4155."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000732",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1558 × 4896 × 3652 = ___ × 3652 × 1558",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  1558 × 4896 × 3652 = ___ × 3652 × 1558",
        "options": [
          "4916",
          "4896",
          "4906",
          "4886"
        ],
        "answer": "4896",
        "correct_value": 4896,
        "explanation": "A and C appear on both sides; blank = B = 4896."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8877 + 8927 + ___ = 8927 + 6634 + 4076",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  8877 + 8927 + ___ = 8927 + 6634 + 4076",
        "options": [
          "1853",
          "1833",
          "1843",
          "1823"
        ],
        "answer": "1833",
        "correct_value": 1833,
        "explanation": "B cancels; blank = C + D − A = 6634 + 4076 − 8877 = 1833."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8425 + 5305 + ___ = 9943 + 8206",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  8425 + 5305 + ___ = 9943 + 8206",
        "options": [
          "4409",
          "4429",
          "4439",
          "4419"
        ],
        "answer": "4419",
        "correct_value": 4419,
        "explanation": "No matching terms; blank = 9943 + 8206 − 8425 − 5305 = 4419."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000733",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6525 × (4052 + 5182) = 6525 × ___ + 6525 × 5182",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  6525 × (4052 + 5182) = 6525 × ___ + 6525 × 5182",
        "options": [
          "4052",
          "4042",
          "4062",
          "4072"
        ],
        "answer": "4052",
        "correct_value": 4052,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 4052."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2581 + 6609 + ___ = 6609 + 9504 + 5306",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  2581 + 6609 + ___ = 6609 + 9504 + 5306",
        "options": [
          "12219",
          "12249",
          "12239",
          "12229"
        ],
        "answer": "12229",
        "correct_value": 12229,
        "explanation": "B cancels; blank = C + D − A = 9504 + 5306 − 2581 = 12229."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1416 + 9901 + ___ = 3068 + 2549",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  1416 + 9901 + ___ = 3068 + 2549",
        "options": [
          "-5680",
          "-5700",
          "-5710",
          "-5690"
        ],
        "answer": "-5700",
        "correct_value": -5700,
        "explanation": "No matching terms; blank = 3068 + 2549 − 1416 − 9901 = -5700."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000734",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5844 + 3069 + ___ = 3069 + 6695 + 5844",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  5844 + 3069 + ___ = 3069 + 6695 + 5844",
        "options": [
          "6695",
          "6685",
          "6705",
          "6715"
        ],
        "answer": "6695",
        "correct_value": 6695,
        "explanation": "A and B appear on both sides and cancel; blank = C = 6695."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2359 + 9269 + ___ = 9269 + 3991 + 7513",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  2359 + 9269 + ___ = 9269 + 3991 + 7513",
        "options": [
          "9135",
          "9165",
          "9145",
          "9155"
        ],
        "answer": "9145",
        "correct_value": 9145,
        "explanation": "B cancels; blank = C + D − A = 3991 + 7513 − 2359 = 9145."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1273 + 4255 + ___ = 6798 + 9611",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  1273 + 4255 + ___ = 6798 + 9611",
        "options": [
          "10871",
          "10881",
          "10901",
          "10891"
        ],
        "answer": "10881",
        "correct_value": 10881,
        "explanation": "No matching terms; blank = 6798 + 9611 − 1273 − 4255 = 10881."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000735",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9838 × (4775 + 9697) = 9838 × ___ + 9838 × 9697",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  9838 × (4775 + 9697) = 9838 × ___ + 9838 × 9697",
        "options": [
          "4795",
          "4775",
          "4765",
          "4785"
        ],
        "answer": "4775",
        "correct_value": 4775,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 4775."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2640 + 3713 + ___ = 3713 + 4707 + 3491",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  2640 + 3713 + ___ = 3713 + 4707 + 3491",
        "options": [
          "5578",
          "5568",
          "5558",
          "5548"
        ],
        "answer": "5558",
        "correct_value": 5558,
        "explanation": "B cancels; blank = C + D − A = 4707 + 3491 − 2640 = 5558."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1801 + 7567 + ___ = 5857 + 7386",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  1801 + 7567 + ___ = 5857 + 7386",
        "options": [
          "3875",
          "3895",
          "3885",
          "3865"
        ],
        "answer": "3875",
        "correct_value": 3875,
        "explanation": "No matching terms; blank = 5857 + 7386 − 1801 − 7567 = 3875."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000736",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3230 × (5915 + 1005) = 3230 × ___ + 3230 × 1005",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  3230 × (5915 + 1005) = 3230 × ___ + 3230 × 1005",
        "options": [
          "5905",
          "5935",
          "5925",
          "5915"
        ],
        "answer": "5915",
        "correct_value": 5915,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 5915."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4420 + 2094 + ___ = 2094 + 1970 + 7723",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  4420 + 2094 + ___ = 2094 + 1970 + 7723",
        "options": [
          "5293",
          "5263",
          "5273",
          "5283"
        ],
        "answer": "5273",
        "correct_value": 5273,
        "explanation": "B cancels; blank = C + D − A = 1970 + 7723 − 4420 = 5273."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3625 + 4972 + ___ = 7410 + 3612",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  3625 + 4972 + ___ = 7410 + 3612",
        "options": [
          "2445",
          "2425",
          "2435",
          "2415"
        ],
        "answer": "2425",
        "correct_value": 2425,
        "explanation": "No matching terms; blank = 7410 + 3612 − 3625 − 4972 = 2425."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000737",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6741 × 2155 × 4707 = ___ × 4707 × 6741",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  6741 × 2155 × 4707 = ___ × 4707 × 6741",
        "options": [
          "2145",
          "2165",
          "2155",
          "2175"
        ],
        "answer": "2155",
        "correct_value": 2155,
        "explanation": "A and C appear on both sides; blank = B = 2155."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3022 + 3487 + ___ = 3487 + 4372 + 8264",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  3022 + 3487 + ___ = 3487 + 4372 + 8264",
        "options": [
          "9614",
          "9604",
          "9634",
          "9624"
        ],
        "answer": "9614",
        "correct_value": 9614,
        "explanation": "B cancels; blank = C + D − A = 4372 + 8264 − 3022 = 9614."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6365 + 1176 + ___ = 2921 + 9529",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  6365 + 1176 + ___ = 2921 + 9529",
        "options": [
          "4919",
          "4909",
          "4899",
          "4929"
        ],
        "answer": "4909",
        "correct_value": 4909,
        "explanation": "No matching terms; blank = 2921 + 9529 − 6365 − 1176 = 4909."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000738",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4804 + 8180 = ___ + 5895",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  4804 + 8180 = ___ + 5895",
        "options": [
          "7079",
          "7099",
          "7109",
          "7089"
        ],
        "answer": "7089",
        "correct_value": 7089,
        "explanation": "Blank = A + B − C = 4804 + 8180 − 5895 = 7089."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3517 + 2153 + ___ = 2153 + 6593 + 5458",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  3517 + 2153 + ___ = 2153 + 6593 + 5458",
        "options": [
          "8524",
          "8554",
          "8544",
          "8534"
        ],
        "answer": "8534",
        "correct_value": 8534,
        "explanation": "B cancels; blank = C + D − A = 6593 + 5458 − 3517 = 8534."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2848 + 8643 + ___ = 7978 + 3759",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  2848 + 8643 + ___ = 7978 + 3759",
        "options": [
          "266",
          "246",
          "256",
          "236"
        ],
        "answer": "246",
        "correct_value": 246,
        "explanation": "No matching terms; blank = 7978 + 3759 − 2848 − 8643 = 246."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000739",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2451 + 6940 + ___ = 6940 + 4953 + 2451",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  2451 + 6940 + ___ = 6940 + 4953 + 2451",
        "options": [
          "4953",
          "4963",
          "4973",
          "4943"
        ],
        "answer": "4953",
        "correct_value": 4953,
        "explanation": "A and B appear on both sides and cancel; blank = C = 4953."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7908 + 1928 + ___ = 1928 + 2723 + 5590",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  7908 + 1928 + ___ = 1928 + 2723 + 5590",
        "options": [
          "405",
          "395",
          "415",
          "425"
        ],
        "answer": "405",
        "correct_value": 405,
        "explanation": "B cancels; blank = C + D − A = 2723 + 5590 − 7908 = 405."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7875 + 5116 + ___ = 6843 + 2361",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  7875 + 5116 + ___ = 6843 + 2361",
        "options": [
          "-3773",
          "-3783",
          "-3803",
          "-3787"
        ],
        "answer": "-3787",
        "correct_value": -3787,
        "explanation": "No matching terms; blank = 6843 + 2361 − 7875 − 5116 = -3787."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000740",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9109 × 4627 × 8106 = ___ × 8106 × 9109",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  9109 × 4627 × 8106 = ___ × 8106 × 9109",
        "options": [
          "4617",
          "4637",
          "4627",
          "4647"
        ],
        "answer": "4627",
        "correct_value": 4627,
        "explanation": "A and C appear on both sides; blank = B = 4627."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7157 + 9502 + ___ = 9502 + 7268 + 1689",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  7157 + 9502 + ___ = 9502 + 7268 + 1689",
        "options": [
          "1810",
          "1790",
          "1820",
          "1800"
        ],
        "answer": "1800",
        "correct_value": 1800,
        "explanation": "B cancels; blank = C + D − A = 7268 + 1689 − 7157 = 1800."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2555 + 2924 + ___ = 4909 + 6909",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  2555 + 2924 + ___ = 4909 + 6909",
        "options": [
          "6359",
          "6339",
          "6349",
          "6329"
        ],
        "answer": "6339",
        "correct_value": 6339,
        "explanation": "No matching terms; blank = 4909 + 6909 − 2555 − 2924 = 6339."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000741",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8212 × (8548 + 9564) = 8212 × ___ + 8212 × 9564",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  8212 × (8548 + 9564) = 8212 × ___ + 8212 × 9564",
        "options": [
          "8538",
          "8568",
          "8558",
          "8548"
        ],
        "answer": "8548",
        "correct_value": 8548,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 8548."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1420 + 4539 + ___ = 4539 + 3961 + 1395",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  1420 + 4539 + ___ = 4539 + 3961 + 1395",
        "options": [
          "3926",
          "3946",
          "3936",
          "3956"
        ],
        "answer": "3936",
        "correct_value": 3936,
        "explanation": "B cancels; blank = C + D − A = 3961 + 1395 − 1420 = 3936."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7752 + 1464 + ___ = 8481 + 5153",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  7752 + 1464 + ___ = 8481 + 5153",
        "options": [
          "4418",
          "4428",
          "4408",
          "4438"
        ],
        "answer": "4418",
        "correct_value": 4418,
        "explanation": "No matching terms; blank = 8481 + 5153 − 7752 − 1464 = 4418."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000742",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5074 × (5532 + 8307) = 5074 × ___ + 5074 × 8307",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  5074 × (5532 + 8307) = 5074 × ___ + 5074 × 8307",
        "options": [
          "5522",
          "5552",
          "5542",
          "5532"
        ],
        "answer": "5532",
        "correct_value": 5532,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 5532."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5311 + 3631 + ___ = 3631 + 4430 + 9966",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  5311 + 3631 + ___ = 3631 + 4430 + 9966",
        "options": [
          "9085",
          "9095",
          "9075",
          "9105"
        ],
        "answer": "9085",
        "correct_value": 9085,
        "explanation": "B cancels; blank = C + D − A = 4430 + 9966 − 5311 = 9085."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6710 + 3818 + ___ = 9189 + 2456",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  6710 + 3818 + ___ = 9189 + 2456",
        "options": [
          "1107",
          "1117",
          "1127",
          "1137"
        ],
        "answer": "1117",
        "correct_value": 1117,
        "explanation": "No matching terms; blank = 9189 + 2456 − 6710 − 3818 = 1117."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000743",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6010 × (2659 + 2481) = 6010 × ___ + 6010 × 2481",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  6010 × (2659 + 2481) = 6010 × ___ + 6010 × 2481",
        "options": [
          "2659",
          "2679",
          "2669",
          "2649"
        ],
        "answer": "2659",
        "correct_value": 2659,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 2659."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4050 + 7270 + ___ = 7270 + 4312 + 5336",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  4050 + 7270 + ___ = 7270 + 4312 + 5336",
        "options": [
          "5598",
          "5618",
          "5608",
          "5588"
        ],
        "answer": "5598",
        "correct_value": 5598,
        "explanation": "B cancels; blank = C + D − A = 4312 + 5336 − 4050 = 5598."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8172 + 6922 + ___ = 3608 + 3761",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  8172 + 6922 + ___ = 3608 + 3761",
        "options": [
          "-7715",
          "-7735",
          "-7725",
          "-7705"
        ],
        "answer": "-7725",
        "correct_value": -7725,
        "explanation": "No matching terms; blank = 3608 + 3761 − 8172 − 6922 = -7725."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000744",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6087 × 9292 × 5853 = ___ × 5853 × 6087",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  6087 × 9292 × 5853 = ___ × 5853 × 6087",
        "options": [
          "9312",
          "9292",
          "9282",
          "9302"
        ],
        "answer": "9292",
        "correct_value": 9292,
        "explanation": "A and C appear on both sides; blank = B = 9292."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4254 + 2529 + ___ = 2529 + 2483 + 7629",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  4254 + 2529 + ___ = 2529 + 2483 + 7629",
        "options": [
          "5848",
          "5868",
          "5858",
          "5878"
        ],
        "answer": "5858",
        "correct_value": 5858,
        "explanation": "B cancels; blank = C + D − A = 2483 + 7629 − 4254 = 5858."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9729 + 6796 + ___ = 7500 + 3179",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  9729 + 6796 + ___ = 7500 + 3179",
        "options": [
          "-5834",
          "-5844",
          "-5846",
          "-5864"
        ],
        "answer": "-5846",
        "correct_value": -5846,
        "explanation": "No matching terms; blank = 7500 + 3179 − 9729 − 6796 = -5846."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000745",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6305 + 4683 + ___ = 4683 + 8250 + 6305",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  6305 + 4683 + ___ = 4683 + 8250 + 6305",
        "options": [
          "8260",
          "8270",
          "8240",
          "8250"
        ],
        "answer": "8250",
        "correct_value": 8250,
        "explanation": "A and B appear on both sides and cancel; blank = C = 8250."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5485 + 1431 + ___ = 1431 + 9101 + 4677",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  5485 + 1431 + ___ = 1431 + 9101 + 4677",
        "options": [
          "8283",
          "8313",
          "8293",
          "8303"
        ],
        "answer": "8293",
        "correct_value": 8293,
        "explanation": "B cancels; blank = C + D − A = 9101 + 4677 − 5485 = 8293."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8214 + 4538 + ___ = 3381 + 1203",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  8214 + 4538 + ___ = 3381 + 1203",
        "options": [
          "-8162",
          "-8182",
          "-8168",
          "-8152"
        ],
        "answer": "-8168",
        "correct_value": -8168,
        "explanation": "No matching terms; blank = 3381 + 1203 − 8214 − 4538 = -8168."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000746",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8191 + 7791 = ___ + 4149",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  8191 + 7791 = ___ + 4149",
        "options": [
          "11853",
          "11843",
          "11833",
          "11823"
        ],
        "answer": "11833",
        "correct_value": 11833,
        "explanation": "Blank = A + B − C = 8191 + 7791 − 4149 = 11833."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7342 + 5284 + ___ = 5284 + 6963 + 5318",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  7342 + 5284 + ___ = 5284 + 6963 + 5318",
        "options": [
          "4939",
          "4959",
          "4949",
          "4929"
        ],
        "answer": "4939",
        "correct_value": 4939,
        "explanation": "B cancels; blank = C + D − A = 6963 + 5318 − 7342 = 4939."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4845 + 6245 + ___ = 9853 + 6850",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  4845 + 6245 + ___ = 9853 + 6850",
        "options": [
          "5623",
          "5603",
          "5633",
          "5613"
        ],
        "answer": "5613",
        "correct_value": 5613,
        "explanation": "No matching terms; blank = 9853 + 6850 − 4845 − 6245 = 5613."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000747",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5045 × (9819 + 3109) = 5045 × ___ + 5045 × 3109",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  5045 × (9819 + 3109) = 5045 × ___ + 5045 × 3109",
        "options": [
          "9809",
          "9829",
          "9839",
          "9819"
        ],
        "answer": "9819",
        "correct_value": 9819,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 9819."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9771 + 6136 + ___ = 6136 + 2717 + 4732",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  9771 + 6136 + ___ = 6136 + 2717 + 4732",
        "options": [
          "-2318",
          "-2322",
          "-2338",
          "-2308"
        ],
        "answer": "-2322",
        "correct_value": -2322,
        "explanation": "B cancels; blank = C + D − A = 2717 + 4732 − 9771 = -2322."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8623 + 5409 + ___ = 1871 + 8540",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  8623 + 5409 + ___ = 1871 + 8540",
        "options": [
          "-3621",
          "-3609",
          "-3619",
          "-3639"
        ],
        "answer": "-3621",
        "correct_value": -3621,
        "explanation": "No matching terms; blank = 1871 + 8540 − 8623 − 5409 = -3621."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000748",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3807 + 1362 + ___ = 1362 + 8347 + 3807",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  3807 + 1362 + ___ = 1362 + 8347 + 3807",
        "options": [
          "8337",
          "8367",
          "8357",
          "8347"
        ],
        "answer": "8347",
        "correct_value": 8347,
        "explanation": "A and B appear on both sides and cancel; blank = C = 8347."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3422 + 2044 + ___ = 2044 + 6806 + 2071",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  3422 + 2044 + ___ = 2044 + 6806 + 2071",
        "options": [
          "5455",
          "5465",
          "5445",
          "5475"
        ],
        "answer": "5455",
        "correct_value": 5455,
        "explanation": "B cancels; blank = C + D − A = 6806 + 2071 − 3422 = 5455."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1451 + 9041 + ___ = 8058 + 3184",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  1451 + 9041 + ___ = 8058 + 3184",
        "options": [
          "770",
          "760",
          "750",
          "740"
        ],
        "answer": "750",
        "correct_value": 750,
        "explanation": "No matching terms; blank = 8058 + 3184 − 1451 − 9041 = 750."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000749",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9821 × (5991 + 6415) = 9821 × ___ + 9821 × 6415",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  9821 × (5991 + 6415) = 9821 × ___ + 9821 × 6415",
        "options": [
          "5991",
          "5981",
          "6011",
          "6001"
        ],
        "answer": "5991",
        "correct_value": 5991,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 5991."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3363 + 9841 + ___ = 9841 + 6152 + 1111",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  3363 + 9841 + ___ = 9841 + 6152 + 1111",
        "options": [
          "3890",
          "3910",
          "3920",
          "3900"
        ],
        "answer": "3900",
        "correct_value": 3900,
        "explanation": "B cancels; blank = C + D − A = 6152 + 1111 − 3363 = 3900."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2960 + 2163 + ___ = 2042 + 9679",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  2960 + 2163 + ___ = 2042 + 9679",
        "options": [
          "6608",
          "6598",
          "6618",
          "6588"
        ],
        "answer": "6598",
        "correct_value": 6598,
        "explanation": "No matching terms; blank = 2042 + 9679 − 2960 − 2163 = 6598."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000750",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5076 × 3938 × 3969 = ___ × 3969 × 5076",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  5076 × 3938 × 3969 = ___ × 3969 × 5076",
        "options": [
          "3928",
          "3948",
          "3958",
          "3938"
        ],
        "answer": "3938",
        "correct_value": 3938,
        "explanation": "A and C appear on both sides; blank = B = 3938."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2957 + 6436 + ___ = 6436 + 2459 + 2542",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  2957 + 6436 + ___ = 6436 + 2459 + 2542",
        "options": [
          "2044",
          "2054",
          "2064",
          "2034"
        ],
        "answer": "2044",
        "correct_value": 2044,
        "explanation": "B cancels; blank = C + D − A = 2459 + 2542 − 2957 = 2044."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7677 + 7247 + ___ = 8772 + 3269",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  7677 + 7247 + ___ = 8772 + 3269",
        "options": [
          "-2877",
          "-2897",
          "-2883",
          "-2867"
        ],
        "answer": "-2883",
        "correct_value": -2883,
        "explanation": "No matching terms; blank = 8772 + 3269 − 7677 − 7247 = -2883."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000751",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6818 × (3906 + 8051) = 6818 × ___ + 6818 × 8051",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  6818 × (3906 + 8051) = 6818 × ___ + 6818 × 8051",
        "options": [
          "3896",
          "3906",
          "3916",
          "3926"
        ],
        "answer": "3906",
        "correct_value": 3906,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 3906."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4023 + 5268 + ___ = 5268 + 7576 + 4286",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  4023 + 5268 + ___ = 5268 + 7576 + 4286",
        "options": [
          "7859",
          "7839",
          "7829",
          "7849"
        ],
        "answer": "7839",
        "correct_value": 7839,
        "explanation": "B cancels; blank = C + D − A = 7576 + 4286 − 4023 = 7839."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6565 + 8401 + ___ = 2540 + 9583",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  6565 + 8401 + ___ = 2540 + 9583",
        "options": [
          "-2837",
          "-2857",
          "-2843",
          "-2827"
        ],
        "answer": "-2843",
        "correct_value": -2843,
        "explanation": "No matching terms; blank = 2540 + 9583 − 6565 − 8401 = -2843."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "option_elimination_000752",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4077 × 6150",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 4077 × 6150?",
        "options": [
          "25073551",
          "25073552",
          "25073550",
          "25073549"
        ],
        "answer": "25073550",
        "correct_value": 25073550,
        "explanation": "Product divisible by 9 (both factors divisible by 3); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8240 × 8382",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 8240 × 8382?",
        "options": [
          "69067681",
          "69067679",
          "69067680",
          "69067670"
        ],
        "answer": "69067680",
        "correct_value": 69067680,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6329 × 7169",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6329 × 7169?",
        "options": [
          "53862601",
          "53092601",
          "44992601",
          "45372601"
        ],
        "answer": "45372601",
        "correct_value": 45372601,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000753",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6918 × 8652",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 6918 × 8652?",
        "options": [
          "598545432",
          "125694519",
          "5985450",
          "59854536"
        ],
        "answer": "59854536",
        "correct_value": 59854536,
        "explanation": "Product has 8 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7335 × 4896",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 7335 × 4896?",
        "options": [
          "35912161",
          "35912140",
          "35912159",
          "35912160"
        ],
        "answer": "35912160",
        "correct_value": 35912160,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6129 × 3929",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6129 × 3929?",
        "options": [
          "22120841",
          "24080841",
          "22320841",
          "27220841"
        ],
        "answer": "24080841",
        "correct_value": 24080841,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000754",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1220 × 5134",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 1220 × 5134?",
        "options": [
          "6263483",
          "6263479",
          "6263481",
          "6263480"
        ],
        "answer": "6263480",
        "correct_value": 6263480,
        "explanation": "Product ends in 0 (5 × even); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7810 × 8136",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 7810 × 8136?",
        "options": [
          "63542159",
          "63542160",
          "63542170",
          "63542161"
        ],
        "answer": "63542160",
        "correct_value": 63542160,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3947 × 4463",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 3947 × 4463?",
        "options": [
          "18675461",
          "17615461",
          "14985461",
          "17575461"
        ],
        "answer": "17615461",
        "correct_value": 17615461,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000755",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4893 × 1523",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 4893 × 1523?",
        "options": [
          "7452040",
          "7452042",
          "7452038",
          "7452039"
        ],
        "answer": "7452039",
        "correct_value": 7452039,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3210 × 3880",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 3210 × 3880?",
        "options": [
          "12454780",
          "12454799",
          "12454801",
          "12454800"
        ],
        "answer": "12454800",
        "correct_value": 12454800,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9357 × 5973",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 9357 × 5973?",
        "options": [
          "63209361",
          "55889361",
          "57259361",
          "63039361"
        ],
        "answer": "55889361",
        "correct_value": 55889361,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000756",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1864 × 4190",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 1864 × 4190?",
        "options": [
          "7810160",
          "781016",
          "14839304",
          "14058288"
        ],
        "answer": "7810160",
        "correct_value": 7810160,
        "explanation": "Product has 7 digits; only one option matches."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2190 × 7082",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 2190 × 7082?",
        "options": [
          "15509570",
          "15509580",
          "15509581",
          "15509579"
        ],
        "answer": "15509580",
        "correct_value": 15509580,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2745 × 9369",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 2745 × 9369?",
        "options": [
          "24647905",
          "24967905",
          "30457905",
          "25717905"
        ],
        "answer": "25717905",
        "correct_value": 25717905,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000757",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3083 × 4139",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 3083 × 4139?",
        "options": [
          "12760537",
          "12760540",
          "12760536",
          "12760538"
        ],
        "answer": "12760537",
        "correct_value": 12760537,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2635 × 7916",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 2635 × 7916?",
        "options": [
          "20858661",
          "20858659",
          "20858660",
          "20858680"
        ],
        "answer": "20858660",
        "correct_value": 20858660,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8927 × 2827",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 8927 × 2827?",
        "options": [
          "21436629",
          "29656629",
          "25236629",
          "26726629"
        ],
        "answer": "25236629",
        "correct_value": 25236629,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000758",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "7525 × 5474",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 7525 × 5474?",
        "options": [
          "41191853",
          "41191849",
          "41191851",
          "41191850"
        ],
        "answer": "41191850",
        "correct_value": 41191850,
        "explanation": "Product ends in 0 (5 × even); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5660 × 3744",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 5660 × 3744?",
        "options": [
          "21191020",
          "21191041",
          "21191039",
          "21191040"
        ],
        "answer": "21191040",
        "correct_value": 21191040,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1649 × 9833",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 1649 × 9833?",
        "options": [
          "16214617",
          "17424617",
          "14514617",
          "16024617"
        ],
        "answer": "16214617",
        "correct_value": 16214617,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000759",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "7167 × 1638",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 7167 × 1638?",
        "options": [
          "11739545",
          "11739546",
          "11739548",
          "11739547"
        ],
        "answer": "11739546",
        "correct_value": 11739546,
        "explanation": "Product divisible by 9 (both factors divisible by 3); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4760 × 9768",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 4760 × 9768?",
        "options": [
          "46495681",
          "46495679",
          "46495690",
          "46495680"
        ],
        "answer": "46495680",
        "correct_value": 46495680,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7949 × 7647",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 7949 × 7647?",
        "options": [
          "60786003",
          "68796003",
          "53716003",
          "57036003"
        ],
        "answer": "60786003",
        "correct_value": 60786003,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000760",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5927 × 1249",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 5927 × 1249?",
        "options": [
          "7402822",
          "7402826",
          "7402823",
          "7402824"
        ],
        "answer": "7402823",
        "correct_value": 7402823,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3475 × 1180",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 3475 × 1180?",
        "options": [
          "4100499",
          "4100510",
          "4100501",
          "4100500"
        ],
        "answer": "4100500",
        "correct_value": 4100500,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6167 × 3645",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6167 × 3645?",
        "options": [
          "20748715",
          "22478715",
          "20618715",
          "23088715"
        ],
        "answer": "22478715",
        "correct_value": 22478715,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000761",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4770 × 3207",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 4770 × 3207?",
        "options": [
          "15297389",
          "15297391",
          "15297390",
          "15297392"
        ],
        "answer": "15297390",
        "correct_value": 15297390,
        "explanation": "Product divisible by 9 (both factors divisible by 3); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1810 × 3370",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 1810 × 3370?",
        "options": [
          "6099701",
          "6099700",
          "6099680",
          "6099699"
        ],
        "answer": "6099700",
        "correct_value": 6099700,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1433 × 1427",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 1433 × 1427?",
        "options": [
          "2303891",
          "2213891",
          "1839891",
          "2044891"
        ],
        "answer": "2044891",
        "correct_value": 2044891,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000762",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8898 × 4584",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 8898 × 4584?",
        "options": [
          "40788431",
          "40788432",
          "40788434",
          "40788433"
        ],
        "answer": "40788432",
        "correct_value": 40788432,
        "explanation": "Product divisible by 9 (both factors divisible by 3); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8310 × 9680",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 8310 × 9680?",
        "options": [
          "80440800",
          "80440801",
          "80440799",
          "80440820"
        ],
        "answer": "80440800",
        "correct_value": 80440800,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9873 × 5635",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 9873 × 5635?",
        "options": [
          "55634355",
          "48734355",
          "66614355",
          "61604355"
        ],
        "answer": "55634355",
        "correct_value": 55634355,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000763",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1621 × 2615",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 1621 × 2615?",
        "options": [
          "4238918",
          "4238914",
          "4238916",
          "4238915"
        ],
        "answer": "4238915",
        "correct_value": 4238915,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6955 × 7216",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 6955 × 7216?",
        "options": [
          "50187290",
          "50187279",
          "50187281",
          "50187280"
        ],
        "answer": "50187280",
        "correct_value": 50187280,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5867 × 4971",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5867 × 4971?",
        "options": [
          "25344857",
          "24414857",
          "26274857",
          "29164857"
        ],
        "answer": "29164857",
        "correct_value": 29164857,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000764",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8805 × 4756",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 8805 × 4756?",
        "options": [
          "41876583",
          "41876579",
          "41876581",
          "41876580"
        ],
        "answer": "41876580",
        "correct_value": 41876580,
        "explanation": "Product ends in 0 (5 × even); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1555 × 8380",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 1555 × 8380?",
        "options": [
          "13030899",
          "13030901",
          "13030900",
          "13030880"
        ],
        "answer": "13030900",
        "correct_value": 13030900,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1461 × 9049",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 1461 × 9049?",
        "options": [
          "14200589",
          "13220589",
          "15160589",
          "13640589"
        ],
        "answer": "13220589",
        "correct_value": 13220589,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000765",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1104 × 5487",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 1104 × 5487?",
        "options": [
          "6057649",
          "6057647",
          "6057650",
          "6057648"
        ],
        "answer": "6057648",
        "correct_value": 6057648,
        "explanation": "Product divisible by 9 (both factors divisible by 3); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8530 × 8644",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 8530 × 8644?",
        "options": [
          "73733320",
          "73733319",
          "73733300",
          "73733321"
        ],
        "answer": "73733320",
        "correct_value": 73733320,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9071 × 8363",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 9071 × 8363?",
        "options": [
          "88380773",
          "86000773",
          "80270773",
          "75860773"
        ],
        "answer": "75860773",
        "correct_value": 75860773,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000766",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4077 × 6150",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 4077 × 6150?",
        "options": [
          "25073551",
          "25073552",
          "25073550",
          "25073549"
        ],
        "answer": "25073550",
        "correct_value": 25073550,
        "explanation": "Product divisible by 9 (both factors divisible by 3); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "8240 × 8382",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 8240 × 8382?",
        "options": [
          "69067681",
          "69067679",
          "69067680",
          "69067670"
        ],
        "answer": "69067680",
        "correct_value": 69067680,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6329 × 7169",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6329 × 7169?",
        "options": [
          "53862601",
          "53092601",
          "44992601",
          "45372601"
        ],
        "answer": "45372601",
        "correct_value": 45372601,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000767",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6918 × 8652",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 6918 × 8652?",
        "options": [
          "598545432",
          "125694519",
          "5985450",
          "59854536"
        ],
        "answer": "59854536",
        "correct_value": 59854536,
        "explanation": "Product has 8 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7335 × 4896",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 7335 × 4896?",
        "options": [
          "35912161",
          "35912140",
          "35912159",
          "35912160"
        ],
        "answer": "35912160",
        "correct_value": 35912160,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6129 × 3929",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6129 × 3929?",
        "options": [
          "22120841",
          "24080841",
          "22320841",
          "27220841"
        ],
        "answer": "24080841",
        "correct_value": 24080841,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000768",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4950 × 8282",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 4950 × 8282?",
        "options": [
          "40995903",
          "40995901",
          "40995899",
          "40995900"
        ],
        "answer": "40995900",
        "correct_value": 40995900,
        "explanation": "Product ends in 0 (5 × even); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6270 × 3586",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 6270 × 3586?",
        "options": [
          "22484219",
          "22484221",
          "22484220",
          "22484210"
        ],
        "answer": "22484220",
        "correct_value": 22484220,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1629 × 2035",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 1629 × 2035?",
        "options": [
          "3323015",
          "3315015",
          "3335015",
          "3670015"
        ],
        "answer": "3315015",
        "correct_value": 3315015,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000769",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4071 × 6447",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 4071 × 6447?",
        "options": [
          "2624571",
          "26245737",
          "262457376",
          "262457440"
        ],
        "answer": "26245737",
        "correct_value": 26245737,
        "explanation": "Product has 8 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7835 × 7120",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 7835 × 7120?",
        "options": [
          "55785200",
          "55785199",
          "55785201",
          "55785220"
        ],
        "answer": "55785200",
        "correct_value": 55785200,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3949 × 6659",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 3949 × 6659?",
        "options": [
          "25336391",
          "27986391",
          "23706391",
          "26296391"
        ],
        "answer": "26296391",
        "correct_value": 26296391,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000770",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3282 × 8889",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 3282 × 8889?",
        "options": [
          "29173700",
          "29173697",
          "29173698",
          "29173699"
        ],
        "answer": "29173698",
        "correct_value": 29173698,
        "explanation": "Product divisible by 9 (both factors divisible by 3); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6300 × 3428",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 6300 × 3428?",
        "options": [
          "21596399",
          "21596410",
          "21596401",
          "21596400"
        ],
        "answer": "21596400",
        "correct_value": 21596400,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8573 × 3255",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 8573 × 3255?",
        "options": [
          "27905115",
          "28025115",
          "23195115",
          "30245115"
        ],
        "answer": "27905115",
        "correct_value": 27905115,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000771",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5562 × 7803",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 5562 × 7803?",
        "options": [
          "43400288",
          "43400285",
          "43400286",
          "43400287"
        ],
        "answer": "43400286",
        "correct_value": 43400286,
        "explanation": "Product divisible by 9 (both factors divisible by 3); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3220 × 4794",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 3220 × 4794?",
        "options": [
          "15436679",
          "15436670",
          "15436680",
          "15436681"
        ],
        "answer": "15436680",
        "correct_value": 15436680,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9029 × 4643",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 9029 × 4643?",
        "options": [
          "34681647",
          "41921647",
          "47521647",
          "44771647"
        ],
        "answer": "41921647",
        "correct_value": 41921647,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000772",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2726 × 5890",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 2726 × 5890?",
        "options": [
          "3211228",
          "16056140",
          "1605614",
          "1605614062"
        ],
        "answer": "16056140",
        "correct_value": 16056140,
        "explanation": "Product has 8 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7015 × 8432",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 7015 × 8432?",
        "options": [
          "59150480",
          "59150481",
          "59150460",
          "59150479"
        ],
        "answer": "59150480",
        "correct_value": 59150480,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8137 × 6445",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 8137 × 6445?",
        "options": [
          "51942965",
          "54592965",
          "55742965",
          "52442965"
        ],
        "answer": "52442965",
        "correct_value": 52442965,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000773",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5656 × 1959",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 5656 × 1959?",
        "options": [
          "9972084",
          "1108005",
          "110801089",
          "11080104"
        ],
        "answer": "11080104",
        "correct_value": 11080104,
        "explanation": "Product has 8 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9530 × 7204",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 9530 × 7204?",
        "options": [
          "68654100",
          "68654120",
          "68654121",
          "68654119"
        ],
        "answer": "68654120",
        "correct_value": 68654120,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8843 × 3025",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 8843 × 3025?",
        "options": [
          "26750075",
          "31650075",
          "28600075",
          "31740075"
        ],
        "answer": "26750075",
        "correct_value": 26750075,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000774",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8968 × 8292",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 8968 × 8292?",
        "options": [
          "148725306",
          "156161571",
          "141289041",
          "74362656"
        ],
        "answer": "74362656",
        "correct_value": 74362656,
        "explanation": "Product has 8 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2985 × 6260",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 2985 × 6260?",
        "options": [
          "18686101",
          "18686099",
          "18686090",
          "18686100"
        ],
        "answer": "18686100",
        "correct_value": 18686100,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3359 × 3871",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 3359 × 3871?",
        "options": [
          "11432689",
          "13002689",
          "12312689",
          "14772689"
        ],
        "answer": "13002689",
        "correct_value": 13002689,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000775",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "5559 × 9837",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 5559 × 9837?",
        "options": [
          "54683883",
          "54683882",
          "54683885",
          "54683884"
        ],
        "answer": "54683883",
        "correct_value": 54683883,
        "explanation": "Product divisible by 9 (both factors divisible by 3); only one option matches."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7515 × 6352",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 7515 × 6352?",
        "options": [
          "47735280",
          "47735279",
          "47735281",
          "47735300"
        ],
        "answer": "47735280",
        "correct_value": 47735280,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6763 × 9965",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6763 × 9965?",
        "options": [
          "67833295",
          "67393295",
          "66413295",
          "64953295"
        ],
        "answer": "67393295",
        "correct_value": 67393295,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000776",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6135 × 7717",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 6135 × 7717?",
        "options": [
          "47343795",
          "47343796",
          "47343798",
          "47343794"
        ],
        "answer": "47343795",
        "correct_value": 47343795,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3570 × 1412",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 3570 × 1412?",
        "options": [
          "5040839",
          "5040840",
          "5040850",
          "5040841"
        ],
        "answer": "5040840",
        "correct_value": 5040840,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4761 × 9455",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 4761 × 9455?",
        "options": [
          "39715255",
          "37465255",
          "42125255",
          "45015255"
        ],
        "answer": "45015255",
        "correct_value": 45015255,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000777",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "7521 × 4423",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 7521 × 4423?",
        "options": [
          "33265382",
          "33265386",
          "33265383",
          "33265384"
        ],
        "answer": "33265383",
        "correct_value": 33265383,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2895 × 9642",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 2895 × 9642?",
        "options": [
          "27913591",
          "27913600",
          "27913590",
          "27913589"
        ],
        "answer": "27913590",
        "correct_value": 27913590,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8473 × 6827",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 8473 × 6827?",
        "options": [
          "63685171",
          "58625171",
          "47495171",
          "57845171"
        ],
        "answer": "57845171",
        "correct_value": 57845171,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000778",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1220 × 5134",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 1220 × 5134?",
        "options": [
          "6263483",
          "6263479",
          "6263481",
          "6263480"
        ],
        "answer": "6263480",
        "correct_value": 6263480,
        "explanation": "Product ends in 0 (5 × even); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7810 × 8136",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 7810 × 8136?",
        "options": [
          "63542159",
          "63542160",
          "63542170",
          "63542161"
        ],
        "answer": "63542160",
        "correct_value": 63542160,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3947 × 4463",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 3947 × 4463?",
        "options": [
          "18675461",
          "17615461",
          "14985461",
          "17575461"
        ],
        "answer": "17615461",
        "correct_value": 17615461,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000779",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6325 × 3054",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 6325 × 3054?",
        "options": [
          "19316551",
          "19316550",
          "19316549",
          "19316553"
        ],
        "answer": "19316550",
        "correct_value": 19316550,
        "explanation": "Product ends in 0 (5 × even); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5240 × 2594",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 5240 × 2594?",
        "options": [
          "13592550",
          "13592561",
          "13592560",
          "13592559"
        ],
        "answer": "13592560",
        "correct_value": 13592560,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6361 × 8057",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6361 × 8057?",
        "options": [
          "45500577",
          "47680577",
          "55870577",
          "51250577"
        ],
        "answer": "51250577",
        "correct_value": 51250577,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000780",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8020 × 2628",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 8020 × 2628?",
        "options": [
          "21076560",
          "210765613",
          "2107656056",
          "2107656"
        ],
        "answer": "21076560",
        "correct_value": 21076560,
        "explanation": "Product has 8 digits; only one option matches."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6365 × 6990",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 6365 × 6990?",
        "options": [
          "44491349",
          "44491360",
          "44491351",
          "44491350"
        ],
        "answer": "44491350",
        "correct_value": 44491350,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1475 × 9751",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 1475 × 9751?",
        "options": [
          "15392725",
          "16922725",
          "11932725",
          "14382725"
        ],
        "answer": "14382725",
        "correct_value": 14382725,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000781",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1459 × 1977",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 1459 × 1977?",
        "options": [
          "2884443",
          "2884444",
          "2884442",
          "2884446"
        ],
        "answer": "2884443",
        "correct_value": 2884443,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2115 × 1132",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 2115 × 1132?",
        "options": [
          "2394181",
          "2394179",
          "2394180",
          "2394190"
        ],
        "answer": "2394180",
        "correct_value": 2394180,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1529 × 5743",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 1529 × 5743?",
        "options": [
          "9260047",
          "8781047",
          "9884047",
          "9469047"
        ],
        "answer": "8781047",
        "correct_value": 8781047,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000782",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1133 × 1067",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 1133 × 1067?",
        "options": [
          "241775",
          "1208911",
          "120883",
          "12089157"
        ],
        "answer": "1208911",
        "correct_value": 1208911,
        "explanation": "Product has 7 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2730 × 9160",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 2730 × 9160?",
        "options": [
          "25006801",
          "25006799",
          "25006800",
          "25006780"
        ],
        "answer": "25006800",
        "correct_value": 25006800,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7655 × 6267",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 7655 × 6267?",
        "options": [
          "42983885",
          "57303885",
          "45823885",
          "47973885"
        ],
        "answer": "47973885",
        "correct_value": 47973885,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000783",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2598 × 7416",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 2598 × 7416?",
        "options": [
          "19266770",
          "19266768",
          "19266767",
          "19266769"
        ],
        "answer": "19266768",
        "correct_value": 19266768,
        "explanation": "Product divisible by 9 (both factors divisible by 3); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3345 × 2034",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 3345 × 2034?",
        "options": [
          "6803750",
          "6803730",
          "6803731",
          "6803729"
        ],
        "answer": "6803730",
        "correct_value": 6803730,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2571 × 6841",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 2571 × 6841?",
        "options": [
          "17588211",
          "17758211",
          "15968211",
          "15858211"
        ],
        "answer": "17588211",
        "correct_value": 17588211,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000784",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6660 × 8455",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 6660 × 8455?",
        "options": [
          "101358540",
          "112620600",
          "56310300",
          "118251630"
        ],
        "answer": "56310300",
        "correct_value": 56310300,
        "explanation": "Product has 8 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2330 × 7234",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 2330 × 7234?",
        "options": [
          "16855230",
          "16855221",
          "16855219",
          "16855220"
        ],
        "answer": "16855220",
        "correct_value": 16855220,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3761 × 1059",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 3761 × 1059?",
        "options": [
          "3284899",
          "4549899",
          "3908899",
          "3982899"
        ],
        "answer": "3982899",
        "correct_value": 3982899,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000785",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6056 × 4809",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 6056 × 4809?",
        "options": [
          "2912330471",
          "2912325",
          "2912330441",
          "29123304"
        ],
        "answer": "29123304",
        "correct_value": 29123304,
        "explanation": "Product has 8 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6210 × 8004",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 6210 × 8004?",
        "options": [
          "49704850",
          "49704839",
          "49704841",
          "49704840"
        ],
        "answer": "49704840",
        "correct_value": 49704840,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7127 × 7331",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 7127 × 7331?",
        "options": [
          "59388037",
          "51908037",
          "52248037",
          "58928037"
        ],
        "answer": "52248037",
        "correct_value": 52248037,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000786",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3972 × 8996",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 3972 × 8996?",
        "options": [
          "35732112",
          "3573211248",
          "7146416",
          "357321137"
        ],
        "answer": "35732112",
        "correct_value": 35732112,
        "explanation": "Product has 8 digits; only one option matches."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3600 × 5672",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 3600 × 5672?",
        "options": [
          "20419190",
          "20419199",
          "20419201",
          "20419200"
        ],
        "answer": "20419200",
        "correct_value": 20419200,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "6925 × 7753",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 6925 × 7753?",
        "options": [
          "53689525",
          "58779525",
          "60889525",
          "54819525"
        ],
        "answer": "53689525",
        "correct_value": 53689525,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000787",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3567 × 7987",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 3567 × 7987?",
        "options": [
          "28489629",
          "28489630",
          "28489628",
          "28489632"
        ],
        "answer": "28489629",
        "correct_value": 28489629,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4010 × 6726",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 4010 × 6726?",
        "options": [
          "26971261",
          "26971259",
          "26971260",
          "26971240"
        ],
        "answer": "26971260",
        "correct_value": 26971260,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7953 × 6161",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 7953 × 6161?",
        "options": [
          "39698433",
          "47548433",
          "48998433",
          "39668433"
        ],
        "answer": "48998433",
        "correct_value": 48998433,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000788",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2243 × 8255",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 2243 × 8255?",
        "options": [
          "18515964",
          "18515965",
          "18515966",
          "18515968"
        ],
        "answer": "18515965",
        "correct_value": 18515965,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1875 × 4468",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 1875 × 4468?",
        "options": [
          "8377501",
          "8377520",
          "8377499",
          "8377500"
        ],
        "answer": "8377500",
        "correct_value": 8377500,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7461 × 1355",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 7461 × 1355?",
        "options": [
          "10699655",
          "10109655",
          "11959655",
          "11729655"
        ],
        "answer": "10109655",
        "correct_value": 10109655,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000789",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3121 × 1321",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 3121 × 1321?",
        "options": [
          "4122842",
          "4122840",
          "4122841",
          "4122844"
        ],
        "answer": "4122841",
        "correct_value": 4122841,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9430 × 6180",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 9430 × 6180?",
        "options": [
          "58277400",
          "58277399",
          "58277401",
          "58277390"
        ],
        "answer": "58277400",
        "correct_value": 58277400,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "7373 × 4227",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 7373 × 4227?",
        "options": [
          "30475671",
          "31455671",
          "32725671",
          "31165671"
        ],
        "answer": "31165671",
        "correct_value": 31165671,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000790",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4420 × 5326",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 4420 × 5326?",
        "options": [
          "23540919",
          "23540920",
          "23540921",
          "23540923"
        ],
        "answer": "23540920",
        "correct_value": 23540920,
        "explanation": "Product ends in 0 (5 × even); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1610 × 9938",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 1610 × 9938?",
        "options": [
          "16000179",
          "16000181",
          "16000180",
          "16000200"
        ],
        "answer": "16000180",
        "correct_value": 16000180,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3365 × 2025",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 3365 × 2025?",
        "options": [
          "7273125",
          "6677125",
          "6814125",
          "6075125"
        ],
        "answer": "6814125",
        "correct_value": 6814125,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000791",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4610 × 7330",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 4610 × 7330?",
        "options": [
          "3379130046",
          "33791300",
          "6758260",
          "3379130077"
        ],
        "answer": "33791300",
        "correct_value": 33791300,
        "explanation": "Product has 8 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2605 × 5854",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 2605 × 5854?",
        "options": [
          "15249650",
          "15249670",
          "15249669",
          "15249671"
        ],
        "answer": "15249670",
        "correct_value": 15249670,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "3765 × 6065",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 3765 × 6065?",
        "options": [
          "26494725",
          "22834725",
          "26064725",
          "24244725"
        ],
        "answer": "22834725",
        "correct_value": 22834725,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000792",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "4893 × 1523",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 4893 × 1523?",
        "options": [
          "7452040",
          "7452042",
          "7452038",
          "7452039"
        ],
        "answer": "7452039",
        "correct_value": 7452039,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3210 × 3880",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 3210 × 3880?",
        "options": [
          "12454780",
          "12454799",
          "12454801",
          "12454800"
        ],
        "answer": "12454800",
        "correct_value": 12454800,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "9357 × 5973",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 9357 × 5973?",
        "options": [
          "63209361",
          "55889361",
          "57259361",
          "63039361"
        ],
        "answer": "55889361",
        "correct_value": 55889361,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000793",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "3395 × 6722",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 3395 × 6722?",
        "options": [
          "22821191",
          "22821190",
          "22821189",
          "22821193"
        ],
        "answer": "22821190",
        "correct_value": 22821190,
        "explanation": "Product ends in 0 (5 × even); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9985 × 9804",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 9985 × 9804?",
        "options": [
          "97892941",
          "97892960",
          "97892940",
          "97892939"
        ],
        "answer": "97892940",
        "correct_value": 97892940,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2251 × 9459",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 2251 × 9459?",
        "options": [
          "25332209",
          "23342209",
          "21292209",
          "23812209"
        ],
        "answer": "21292209",
        "correct_value": 21292209,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000794",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2277 × 4068",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 2277 × 4068?",
        "options": [
          "9262835",
          "9262837",
          "9262836",
          "9262838"
        ],
        "answer": "9262836",
        "correct_value": 9262836,
        "explanation": "Product divisible by 9 (both factors divisible by 3); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5415 × 7006",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 5415 × 7006?",
        "options": [
          "37937491",
          "37937490",
          "37937510",
          "37937489"
        ],
        "answer": "37937490",
        "correct_value": 37937490,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "2459 × 1543",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 2459 × 1543?",
        "options": [
          "3907237",
          "3794237",
          "3474237",
          "3604237"
        ],
        "answer": "3794237",
        "correct_value": 3794237,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000795",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9405 × 8910",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 9405 × 8910?",
        "options": [
          "83798551",
          "83798549",
          "83798550",
          "83798552"
        ],
        "answer": "83798550",
        "correct_value": 83798550,
        "explanation": "Product divisible by 9 (both factors divisible by 3); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "4260 × 6314",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 4260 × 6314?",
        "options": [
          "26897620",
          "26897641",
          "26897640",
          "26897639"
        ],
        "answer": "26897640",
        "correct_value": 26897640,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8371 × 2153",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 8371 × 2153?",
        "options": [
          "15482763",
          "16052763",
          "18712763",
          "18022763"
        ],
        "answer": "18022763",
        "correct_value": 18022763,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000796",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6125 × 6048",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 6125 × 6048?",
        "options": [
          "37044000",
          "37043999",
          "37044003",
          "37044001"
        ],
        "answer": "37044000",
        "correct_value": 37044000,
        "explanation": "Product ends in 0 (5 × even); only one option matches."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3560 × 8686",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 3560 × 8686?",
        "options": [
          "30922160",
          "30922159",
          "30922170",
          "30922161"
        ],
        "answer": "30922160",
        "correct_value": 30922160,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8169 × 2525",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 8169 × 2525?",
        "options": [
          "20626725",
          "23906725",
          "23006725",
          "22406725"
        ],
        "answer": "20626725",
        "correct_value": 20626725,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000797",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6777 × 6015",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 6777 × 6015?",
        "options": [
          "4076361",
          "4076365567",
          "40763655",
          "8152727"
        ],
        "answer": "40763655",
        "correct_value": 40763655,
        "explanation": "Product has 8 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3925 × 5618",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 3925 × 5618?",
        "options": [
          "22050670",
          "22050651",
          "22050649",
          "22050650"
        ],
        "answer": "22050650",
        "correct_value": 22050650,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "5275 × 3233",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 5275 × 3233?",
        "options": [
          "17054075",
          "20244075",
          "20144075",
          "16344075"
        ],
        "answer": "17054075",
        "correct_value": 17054075,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000798",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1760 × 7480",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 1760 × 7480?",
        "options": [
          "13164803",
          "13164800",
          "13164801",
          "13164799"
        ],
        "answer": "13164800",
        "correct_value": 13164800,
        "explanation": "Product ends in 0 (5 × even); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "2760 × 5986",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 2760 × 5986?",
        "options": [
          "16521360",
          "16521380",
          "16521361",
          "16521359"
        ],
        "answer": "16521360",
        "correct_value": 16521360,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "8329 × 7465",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 8329 × 7465?",
        "options": [
          "62175985",
          "61435985",
          "68395985",
          "52275985"
        ],
        "answer": "62175985",
        "correct_value": 62175985,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000799",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "1077 × 7895",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 1077 × 7895?",
        "options": [
          "8502918",
          "8502915",
          "8502914",
          "8502916"
        ],
        "answer": "8502915",
        "correct_value": 8502915,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9135 × 5574",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 9135 × 5574?",
        "options": [
          "50918470",
          "50918489",
          "50918490",
          "50918491"
        ],
        "answer": "50918490",
        "correct_value": 50918490,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4975 × 7349",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 4975 × 7349?",
        "options": [
          "36561275",
          "38921275",
          "39561275",
          "34621275"
        ],
        "answer": "36561275",
        "correct_value": 36561275,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000800",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "6809 × 9143",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 6809 × 9143?",
        "options": [
          "62254688",
          "62254686",
          "62254687",
          "62254690"
        ],
        "answer": "62254687",
        "correct_value": 62254687,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "1090 × 5974",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 1090 × 5974?",
        "options": [
          "6511661",
          "6511660",
          "6511640",
          "6511659"
        ],
        "answer": "6511660",
        "correct_value": 6511660,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "4073 × 6239",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 4073 × 6239?",
        "options": [
          "25411447",
          "28471447",
          "23491447",
          "30431447"
        ],
        "answer": "25411447",
        "correct_value": 25411447,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000801",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "2531 × 7515",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 2531 × 7515?",
        "options": [
          "19020468",
          "19020465",
          "19020466",
          "19020464"
        ],
        "answer": "19020465",
        "correct_value": 19020465,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "9035 × 8546",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 9035 × 8546?",
        "options": [
          "77213111",
          "77213100",
          "77213109",
          "77213110"
        ],
        "answer": "77213110",
        "correct_value": 77213110,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "1451 × 9671",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 1451 × 9671?",
        "options": [
          "16752621",
          "11452621",
          "14032621",
          "12302621"
        ],
        "answer": "14032621",
        "correct_value": 14032621,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  }
]