[
  {
    "family_id": "magnitude_estimation_000001",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 98?",
        "options": [
          "9614",
          "9594",
          "9604",
          "9624"
        ],
        "answer": "9604",
        "correct_value": 9604,
        "explanation": "Round to 100: 98≈100, 98≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "99 * 105",
      "ns_shortcut": "Round 99≈100, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 105?",
        "options": [
          "10405",
          "10385",
          "10415",
          "10395"
        ],
        "answer": "10395",
        "correct_value": 10395,
        "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": "57 * 52",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 57 * 52?",
        "options": [
          "2974",
          "2984",
          "2954",
          "2964"
        ],
        "answer": "2964",
        "correct_value": 2964,
        "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_000002",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 99",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 99?",
        "options": [
          "9811",
          "9791",
          "9821",
          "9801"
        ],
        "answer": "9801",
        "correct_value": 9801,
        "explanation": "Round to 100: 99≈100, 99≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "102 * 103",
      "ns_shortcut": "Round 102≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 103?",
        "options": [
          "10506",
          "10516",
          "10526",
          "10496"
        ],
        "answer": "10506",
        "correct_value": 10506,
        "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": "64 * 66",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 64 * 66?",
        "options": [
          "4244",
          "4234",
          "4214",
          "4224"
        ],
        "answer": "4224",
        "correct_value": 4224,
        "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_000003",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 101",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 101?",
        "options": [
          "10221",
          "10191",
          "10201",
          "10211"
        ],
        "answer": "10201",
        "correct_value": 10201,
        "explanation": "Round to 100: 101≈100, 101≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "98 * 103",
      "ns_shortcut": "Round 98≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 103?",
        "options": [
          "10114",
          "10104",
          "10094",
          "10084"
        ],
        "answer": "10094",
        "correct_value": 10094,
        "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": "66 * 50",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 66 * 50?",
        "options": [
          "3290",
          "3310",
          "3300",
          "3320"
        ],
        "answer": "3300",
        "correct_value": 3300,
        "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_000004",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 102",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 102?",
        "options": [
          "9986",
          "10006",
          "10016",
          "9996"
        ],
        "answer": "9996",
        "correct_value": 9996,
        "explanation": "Round to 100: 98≈100, 102≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "101 * 105",
      "ns_shortcut": "Round 101≈100, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 105?",
        "options": [
          "10595",
          "10605",
          "10625",
          "10615"
        ],
        "answer": "10605",
        "correct_value": 10605,
        "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": "40 * 60",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 40 * 60?",
        "options": [
          "2420",
          "2400",
          "2390",
          "2410"
        ],
        "answer": "2400",
        "correct_value": 2400,
        "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_000005",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 98?",
        "options": [
          "9702",
          "9722",
          "9712",
          "9692"
        ],
        "answer": "9702",
        "correct_value": 9702,
        "explanation": "Round to 100: 99≈100, 98≈100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "101 * 103",
      "ns_shortcut": "Round 101≈100, then adjust.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 103?",
        "options": [
          "10393",
          "10403",
          "10413",
          "10423"
        ],
        "answer": "10403",
        "correct_value": 10403,
        "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": "60 * 47",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 60 * 47?",
        "options": [
          "2830",
          "2810",
          "2840",
          "2820"
        ],
        "answer": "2820",
        "correct_value": 2820,
        "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_000006",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 99",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 99?",
        "options": [
          "9801",
          "9821",
          "9811",
          "9791"
        ],
        "answer": "9801",
        "correct_value": 9801,
        "explanation": "Round to 100: 99≈100, 99≈100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "99 * 105",
      "ns_shortcut": "Round 99≈100, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 105?",
        "options": [
          "10405",
          "10385",
          "10395",
          "10415"
        ],
        "answer": "10395",
        "correct_value": 10395,
        "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": "65 * 40",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 65 * 40?",
        "options": [
          "2600",
          "2590",
          "2610",
          "2620"
        ],
        "answer": "2600",
        "correct_value": 2600,
        "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_000007",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 99",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 99?",
        "options": [
          "9692",
          "9712",
          "9702",
          "9722"
        ],
        "answer": "9702",
        "correct_value": 9702,
        "explanation": "Round to 100: 98≈100, 99≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "102 * 105",
      "ns_shortcut": "Round 102≈100, then adjust.",
      "shortcut_strength": 0.965,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 105?",
        "options": [
          "10730",
          "10720",
          "10710",
          "10700"
        ],
        "answer": "10710",
        "correct_value": 10710,
        "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": "43 * 46",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 43 * 46?",
        "options": [
          "1978",
          "1988",
          "1968",
          "1998"
        ],
        "answer": "1978",
        "correct_value": 1978,
        "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_000008",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 101",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 101?",
        "options": [
          "10322",
          "10292",
          "10302",
          "10312"
        ],
        "answer": "10302",
        "correct_value": 10302,
        "explanation": "Round to 100: 102≈100, 101≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "98 * 103",
      "ns_shortcut": "Round 98≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 103?",
        "options": [
          "10104",
          "10114",
          "10084",
          "10094"
        ],
        "answer": "10094",
        "correct_value": 10094,
        "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": "64 * 60",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 64 * 60?",
        "options": [
          "3850",
          "3840",
          "3860",
          "3830"
        ],
        "answer": "3840",
        "correct_value": 3840,
        "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_000009",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 102",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 102?",
        "options": [
          "10404",
          "10414",
          "10424",
          "10394"
        ],
        "answer": "10404",
        "correct_value": 10404,
        "explanation": "Round to 100: 102≈100, 102≈100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "98 * 105",
      "ns_shortcut": "Round 98≈100, then adjust.",
      "shortcut_strength": 0.965,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 105?",
        "options": [
          "10280",
          "10300",
          "10310",
          "10290"
        ],
        "answer": "10290",
        "correct_value": 10290,
        "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": "63 * 59",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 63 * 59?",
        "options": [
          "3707",
          "3727",
          "3717",
          "3737"
        ],
        "answer": "3717",
        "correct_value": 3717,
        "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_000010",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 99",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 99?",
        "options": [
          "10118",
          "10108",
          "10098",
          "10088"
        ],
        "answer": "10098",
        "correct_value": 10098,
        "explanation": "Round to 100: 102≈100, 99≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "99 * 105",
      "ns_shortcut": "Round 99≈100, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 105?",
        "options": [
          "10385",
          "10405",
          "10415",
          "10395"
        ],
        "answer": "10395",
        "correct_value": 10395,
        "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": "65 * 59",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 65 * 59?",
        "options": [
          "3855",
          "3825",
          "3835",
          "3845"
        ],
        "answer": "3835",
        "correct_value": 3835,
        "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_000011",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 98?",
        "options": [
          "9692",
          "9702",
          "9712",
          "9722"
        ],
        "answer": "9702",
        "correct_value": 9702,
        "explanation": "Round to 100: 99≈100, 98≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "98 * 104",
      "ns_shortcut": "Round 98≈100, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 104?",
        "options": [
          "10202",
          "10182",
          "10192",
          "10212"
        ],
        "answer": "10192",
        "correct_value": 10192,
        "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": "46 * 67",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 46 * 67?",
        "options": [
          "3102",
          "3092",
          "3072",
          "3082"
        ],
        "answer": "3082",
        "correct_value": 3082,
        "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_000012",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 99",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 99?",
        "options": [
          "9702",
          "9692",
          "9722",
          "9712"
        ],
        "answer": "9702",
        "correct_value": 9702,
        "explanation": "Round to 100: 98≈100, 99≈100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "99 * 104",
      "ns_shortcut": "Round 99≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 104?",
        "options": [
          "10306",
          "10316",
          "10296",
          "10286"
        ],
        "answer": "10296",
        "correct_value": 10296,
        "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": "61 * 48",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 61 * 48?",
        "options": [
          "2928",
          "2938",
          "2948",
          "2918"
        ],
        "answer": "2928",
        "correct_value": 2928,
        "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_000013",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 102",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 102?",
        "options": [
          "10414",
          "10424",
          "10394",
          "10404"
        ],
        "answer": "10404",
        "correct_value": 10404,
        "explanation": "Round to 100: 102≈100, 102≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "98 * 104",
      "ns_shortcut": "Round 98≈100, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 104?",
        "options": [
          "10202",
          "10182",
          "10212",
          "10192"
        ],
        "answer": "10192",
        "correct_value": 10192,
        "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": "57 * 46",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 57 * 46?",
        "options": [
          "2632",
          "2642",
          "2612",
          "2622"
        ],
        "answer": "2622",
        "correct_value": 2622,
        "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_000014",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 98?",
        "options": [
          "9722",
          "9692",
          "9712",
          "9702"
        ],
        "answer": "9702",
        "correct_value": 9702,
        "explanation": "Round to 100: 99≈100, 98≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "99 * 104",
      "ns_shortcut": "Round 99≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 104?",
        "options": [
          "10306",
          "10316",
          "10296",
          "10286"
        ],
        "answer": "10296",
        "correct_value": 10296,
        "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": "62 * 68",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 62 * 68?",
        "options": [
          "4236",
          "4226",
          "4216",
          "4206"
        ],
        "answer": "4216",
        "correct_value": 4216,
        "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_000015",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 99",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 99?",
        "options": [
          "10118",
          "10108",
          "10088",
          "10098"
        ],
        "answer": "10098",
        "correct_value": 10098,
        "explanation": "Round to 100: 102≈100, 99≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "101 * 104",
      "ns_shortcut": "Round 101≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 104?",
        "options": [
          "10524",
          "10504",
          "10514",
          "10494"
        ],
        "answer": "10504",
        "correct_value": 10504,
        "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": "60 * 59",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 60 * 59?",
        "options": [
          "3560",
          "3550",
          "3530",
          "3540"
        ],
        "answer": "3540",
        "correct_value": 3540,
        "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_000016",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 98?",
        "options": [
          "9888",
          "9918",
          "9898",
          "9908"
        ],
        "answer": "9898",
        "correct_value": 9898,
        "explanation": "Round to 100: 101≈100, 98≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "102 * 103",
      "ns_shortcut": "Round 102≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 103?",
        "options": [
          "10526",
          "10516",
          "10506",
          "10496"
        ],
        "answer": "10506",
        "correct_value": 10506,
        "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": "53 * 46",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 53 * 46?",
        "options": [
          "2458",
          "2428",
          "2448",
          "2438"
        ],
        "answer": "2438",
        "correct_value": 2438,
        "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_000017",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 98?",
        "options": [
          "9614",
          "9624",
          "9594",
          "9604"
        ],
        "answer": "9604",
        "correct_value": 9604,
        "explanation": "Round to 100: 98≈100, 98≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "102 * 104",
      "ns_shortcut": "Round 102≈100, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 104?",
        "options": [
          "10628",
          "10618",
          "10608",
          "10598"
        ],
        "answer": "10608",
        "correct_value": 10608,
        "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": "67 * 40",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 67 * 40?",
        "options": [
          "2700",
          "2680",
          "2670",
          "2690"
        ],
        "answer": "2680",
        "correct_value": 2680,
        "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_000018",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 101",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 101?",
        "options": [
          "10302",
          "10322",
          "10312",
          "10292"
        ],
        "answer": "10302",
        "correct_value": 10302,
        "explanation": "Round to 100: 102≈100, 101≈100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "102 * 103",
      "ns_shortcut": "Round 102≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 103?",
        "options": [
          "10526",
          "10506",
          "10496",
          "10516"
        ],
        "answer": "10506",
        "correct_value": 10506,
        "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": "69 * 40",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 69 * 40?",
        "options": [
          "2750",
          "2770",
          "2780",
          "2760"
        ],
        "answer": "2760",
        "correct_value": 2760,
        "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_000019",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 98?",
        "options": [
          "9614",
          "9604",
          "9624",
          "9594"
        ],
        "answer": "9604",
        "correct_value": 9604,
        "explanation": "Round to 100: 98≈100, 98≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "98 * 105",
      "ns_shortcut": "Round 98≈100, then adjust.",
      "shortcut_strength": 0.965,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 105?",
        "options": [
          "10300",
          "10310",
          "10280",
          "10290"
        ],
        "answer": "10290",
        "correct_value": 10290,
        "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": "58 * 41",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 58 * 41?",
        "options": [
          "2398",
          "2378",
          "2368",
          "2388"
        ],
        "answer": "2378",
        "correct_value": 2378,
        "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_000020",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 98?",
        "options": [
          "9692",
          "9722",
          "9712",
          "9702"
        ],
        "answer": "9702",
        "correct_value": 9702,
        "explanation": "Round to 100: 99≈100, 98≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "101 * 103",
      "ns_shortcut": "Round 101≈100, then adjust.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 103?",
        "options": [
          "10393",
          "10413",
          "10403",
          "10423"
        ],
        "answer": "10403",
        "correct_value": 10403,
        "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": "51 * 43",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 51 * 43?",
        "options": [
          "2193",
          "2183",
          "2203",
          "2213"
        ],
        "answer": "2193",
        "correct_value": 2193,
        "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_000021",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 98?",
        "options": [
          "9614",
          "9604",
          "9624",
          "9594"
        ],
        "answer": "9604",
        "correct_value": 9604,
        "explanation": "Round to 100: 98≈100, 98≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "98 * 105",
      "ns_shortcut": "Round 98≈100, then adjust.",
      "shortcut_strength": 0.965,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 105?",
        "options": [
          "10290",
          "10280",
          "10310",
          "10300"
        ],
        "answer": "10290",
        "correct_value": 10290,
        "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": "43 * 68",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 43 * 68?",
        "options": [
          "2934",
          "2914",
          "2924",
          "2944"
        ],
        "answer": "2924",
        "correct_value": 2924,
        "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_000022",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 101",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 101?",
        "options": [
          "10201",
          "10221",
          "10191",
          "10211"
        ],
        "answer": "10201",
        "correct_value": 10201,
        "explanation": "Round to 100: 101≈100, 101≈100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "98 * 105",
      "ns_shortcut": "Round 98≈100, then adjust.",
      "shortcut_strength": 0.965,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 105?",
        "options": [
          "10300",
          "10290",
          "10280",
          "10310"
        ],
        "answer": "10290",
        "correct_value": 10290,
        "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": "69 * 67",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 69 * 67?",
        "options": [
          "4643",
          "4623",
          "4613",
          "4633"
        ],
        "answer": "4623",
        "correct_value": 4623,
        "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_000023",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 99",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 99?",
        "options": [
          "9692",
          "9702",
          "9712",
          "9722"
        ],
        "answer": "9702",
        "correct_value": 9702,
        "explanation": "Round to 100: 98≈100, 99≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "101 * 103",
      "ns_shortcut": "Round 101≈100, then adjust.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 103?",
        "options": [
          "10403",
          "10413",
          "10393",
          "10423"
        ],
        "answer": "10403",
        "correct_value": 10403,
        "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": "47 * 67",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 47 * 67?",
        "options": [
          "3169",
          "3159",
          "3139",
          "3149"
        ],
        "answer": "3149",
        "correct_value": 3149,
        "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_000024",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 98?",
        "options": [
          "9918",
          "9888",
          "9908",
          "9898"
        ],
        "answer": "9898",
        "correct_value": 9898,
        "explanation": "Round to 100: 101≈100, 98≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "101 * 103",
      "ns_shortcut": "Round 101≈100, then adjust.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 103?",
        "options": [
          "10403",
          "10413",
          "10423",
          "10393"
        ],
        "answer": "10403",
        "correct_value": 10403,
        "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": "56 * 39",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 56 * 39?",
        "options": [
          "2194",
          "2204",
          "2174",
          "2184"
        ],
        "answer": "2184",
        "correct_value": 2184,
        "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_000025",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 101",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 101?",
        "options": [
          "9918",
          "9898",
          "9888",
          "9908"
        ],
        "answer": "9898",
        "correct_value": 9898,
        "explanation": "Round to 100: 98≈100, 101≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "98 * 104",
      "ns_shortcut": "Round 98≈100, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 104?",
        "options": [
          "10182",
          "10202",
          "10192",
          "10212"
        ],
        "answer": "10192",
        "correct_value": 10192,
        "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": "45 * 60",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 45 * 60?",
        "options": [
          "2690",
          "2700",
          "2720",
          "2710"
        ],
        "answer": "2700",
        "correct_value": 2700,
        "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_000026",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 102",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 102?",
        "options": [
          "10292",
          "10322",
          "10302",
          "10312"
        ],
        "answer": "10302",
        "correct_value": 10302,
        "explanation": "Round to 100: 101≈100, 102≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "99 * 104",
      "ns_shortcut": "Round 99≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 104?",
        "options": [
          "10316",
          "10306",
          "10286",
          "10296"
        ],
        "answer": "10296",
        "correct_value": 10296,
        "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": "64 * 68",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 64 * 68?",
        "options": [
          "4362",
          "4352",
          "4372",
          "4342"
        ],
        "answer": "4352",
        "correct_value": 4352,
        "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_000027",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 99",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 99?",
        "options": [
          "10019",
          "9989",
          "10009",
          "9999"
        ],
        "answer": "9999",
        "correct_value": 9999,
        "explanation": "Round to 100: 101≈100, 99≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "102 * 103",
      "ns_shortcut": "Round 102≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 103?",
        "options": [
          "10506",
          "10526",
          "10496",
          "10516"
        ],
        "answer": "10506",
        "correct_value": 10506,
        "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": "48 * 65",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 48 * 65?",
        "options": [
          "3110",
          "3140",
          "3120",
          "3130"
        ],
        "answer": "3120",
        "correct_value": 3120,
        "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_000028",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 102",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 102?",
        "options": [
          "10088",
          "10098",
          "10108",
          "10118"
        ],
        "answer": "10098",
        "correct_value": 10098,
        "explanation": "Round to 100: 99≈100, 102≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "101 * 104",
      "ns_shortcut": "Round 101≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 104?",
        "options": [
          "10504",
          "10514",
          "10524",
          "10494"
        ],
        "answer": "10504",
        "correct_value": 10504,
        "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": "69 * 39",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 69 * 39?",
        "options": [
          "2711",
          "2681",
          "2701",
          "2691"
        ],
        "answer": "2691",
        "correct_value": 2691,
        "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_000029",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 98?",
        "options": [
          "9888",
          "9908",
          "9918",
          "9898"
        ],
        "answer": "9898",
        "correct_value": 9898,
        "explanation": "Round to 100: 101≈100, 98≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "101 * 105",
      "ns_shortcut": "Round 101≈100, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 105?",
        "options": [
          "10595",
          "10605",
          "10615",
          "10625"
        ],
        "answer": "10605",
        "correct_value": 10605,
        "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": "51 * 67",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 51 * 67?",
        "options": [
          "3437",
          "3417",
          "3407",
          "3427"
        ],
        "answer": "3417",
        "correct_value": 3417,
        "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_000030",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 98?",
        "options": [
          "9996",
          "10016",
          "9986",
          "10006"
        ],
        "answer": "9996",
        "correct_value": 9996,
        "explanation": "Round to 100: 102≈100, 98≈100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "98 * 105",
      "ns_shortcut": "Round 98≈100, then adjust.",
      "shortcut_strength": 0.965,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 105?",
        "options": [
          "10290",
          "10300",
          "10280",
          "10310"
        ],
        "answer": "10290",
        "correct_value": 10290,
        "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": "60 * 66",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 60 * 66?",
        "options": [
          "3950",
          "3970",
          "3980",
          "3960"
        ],
        "answer": "3960",
        "correct_value": 3960,
        "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_000031",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 102",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 102?",
        "options": [
          "10302",
          "10292",
          "10312",
          "10322"
        ],
        "answer": "10302",
        "correct_value": 10302,
        "explanation": "Round to 100: 101≈100, 102≈100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "99 * 103",
      "ns_shortcut": "Round 99≈100, then adjust.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 103?",
        "options": [
          "10197",
          "10207",
          "10217",
          "10187"
        ],
        "answer": "10197",
        "correct_value": 10197,
        "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": "60 * 62",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 60 * 62?",
        "options": [
          "3720",
          "3710",
          "3740",
          "3730"
        ],
        "answer": "3720",
        "correct_value": 3720,
        "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_000032",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 98?",
        "options": [
          "9986",
          "9996",
          "10006",
          "10016"
        ],
        "answer": "9996",
        "correct_value": 9996,
        "explanation": "Round to 100: 102≈100, 98≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "102 * 105",
      "ns_shortcut": "Round 102≈100, then adjust.",
      "shortcut_strength": 0.965,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 105?",
        "options": [
          "10710",
          "10700",
          "10720",
          "10730"
        ],
        "answer": "10710",
        "correct_value": 10710,
        "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": "53 * 60",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 53 * 60?",
        "options": [
          "3180",
          "3170",
          "3200",
          "3190"
        ],
        "answer": "3180",
        "correct_value": 3180,
        "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_000033",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 98?",
        "options": [
          "9702",
          "9712",
          "9692",
          "9722"
        ],
        "answer": "9702",
        "correct_value": 9702,
        "explanation": "Round to 100: 99≈100, 98≈100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "98 * 103",
      "ns_shortcut": "Round 98≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 103?",
        "options": [
          "10104",
          "10084",
          "10094",
          "10114"
        ],
        "answer": "10094",
        "correct_value": 10094,
        "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": "43 * 39",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 43 * 39?",
        "options": [
          "1697",
          "1687",
          "1667",
          "1677"
        ],
        "answer": "1677",
        "correct_value": 1677,
        "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_000034",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 102",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 102?",
        "options": [
          "10006",
          "9996",
          "10016",
          "9986"
        ],
        "answer": "9996",
        "correct_value": 9996,
        "explanation": "Round to 100: 98≈100, 102≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "102 * 104",
      "ns_shortcut": "Round 102≈100, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 104?",
        "options": [
          "10618",
          "10628",
          "10608",
          "10598"
        ],
        "answer": "10608",
        "correct_value": 10608,
        "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": "59 * 61",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 59 * 61?",
        "options": [
          "3619",
          "3609",
          "3589",
          "3599"
        ],
        "answer": "3599",
        "correct_value": 3599,
        "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_000035",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 99",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 99?",
        "options": [
          "9811",
          "9821",
          "9801",
          "9791"
        ],
        "answer": "9801",
        "correct_value": 9801,
        "explanation": "Round to 100: 99≈100, 99≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "98 * 104",
      "ns_shortcut": "Round 98≈100, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 104?",
        "options": [
          "10192",
          "10212",
          "10182",
          "10202"
        ],
        "answer": "10192",
        "correct_value": 10192,
        "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": "69 * 63",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 69 * 63?",
        "options": [
          "4347",
          "4357",
          "4367",
          "4337"
        ],
        "answer": "4347",
        "correct_value": 4347,
        "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_000036",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 99",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 99?",
        "options": [
          "10098",
          "10118",
          "10108",
          "10088"
        ],
        "answer": "10098",
        "correct_value": 10098,
        "explanation": "Round to 100: 102≈100, 99≈100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "99 * 105",
      "ns_shortcut": "Round 99≈100, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 105?",
        "options": [
          "10395",
          "10405",
          "10385",
          "10415"
        ],
        "answer": "10395",
        "correct_value": 10395,
        "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": "59 * 46",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 59 * 46?",
        "options": [
          "2704",
          "2714",
          "2724",
          "2734"
        ],
        "answer": "2714",
        "correct_value": 2714,
        "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_000037",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 99",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 99?",
        "options": [
          "9999",
          "9989",
          "10009",
          "10019"
        ],
        "answer": "9999",
        "correct_value": 9999,
        "explanation": "Round to 100: 101≈100, 99≈100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "98 * 103",
      "ns_shortcut": "Round 98≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 103?",
        "options": [
          "10114",
          "10084",
          "10094",
          "10104"
        ],
        "answer": "10094",
        "correct_value": 10094,
        "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": "61 * 43",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 61 * 43?",
        "options": [
          "2643",
          "2613",
          "2623",
          "2633"
        ],
        "answer": "2623",
        "correct_value": 2623,
        "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_000038",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 101",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 101?",
        "options": [
          "10322",
          "10302",
          "10312",
          "10292"
        ],
        "answer": "10302",
        "correct_value": 10302,
        "explanation": "Round to 100: 102≈100, 101≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "99 * 104",
      "ns_shortcut": "Round 99≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 104?",
        "options": [
          "10306",
          "10296",
          "10316",
          "10286"
        ],
        "answer": "10296",
        "correct_value": 10296,
        "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": "66 * 67",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 66 * 67?",
        "options": [
          "4442",
          "4422",
          "4432",
          "4412"
        ],
        "answer": "4422",
        "correct_value": 4422,
        "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_000039",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 101",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 101?",
        "options": [
          "10221",
          "10201",
          "10211",
          "10191"
        ],
        "answer": "10201",
        "correct_value": 10201,
        "explanation": "Round to 100: 101≈100, 101≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "102 * 103",
      "ns_shortcut": "Round 102≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 103?",
        "options": [
          "10506",
          "10496",
          "10516",
          "10526"
        ],
        "answer": "10506",
        "correct_value": 10506,
        "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": "39 * 51",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 39 * 51?",
        "options": [
          "1989",
          "1999",
          "1979",
          "2009"
        ],
        "answer": "1989",
        "correct_value": 1989,
        "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_000040",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 102",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 102?",
        "options": [
          "10088",
          "10098",
          "10118",
          "10108"
        ],
        "answer": "10098",
        "correct_value": 10098,
        "explanation": "Round to 100: 99≈100, 102≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "102 * 105",
      "ns_shortcut": "Round 102≈100, then adjust.",
      "shortcut_strength": 0.965,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 105?",
        "options": [
          "10730",
          "10720",
          "10700",
          "10710"
        ],
        "answer": "10710",
        "correct_value": 10710,
        "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": "43 * 66",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 43 * 66?",
        "options": [
          "2848",
          "2858",
          "2838",
          "2828"
        ],
        "answer": "2838",
        "correct_value": 2838,
        "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_000041",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 102",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 102?",
        "options": [
          "10292",
          "10312",
          "10302",
          "10322"
        ],
        "answer": "10302",
        "correct_value": 10302,
        "explanation": "Round to 100: 101≈100, 102≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "101 * 104",
      "ns_shortcut": "Round 101≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 104?",
        "options": [
          "10504",
          "10524",
          "10514",
          "10494"
        ],
        "answer": "10504",
        "correct_value": 10504,
        "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": "47 * 65",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 47 * 65?",
        "options": [
          "3075",
          "3045",
          "3065",
          "3055"
        ],
        "answer": "3055",
        "correct_value": 3055,
        "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_000042",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 101",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 101?",
        "options": [
          "9888",
          "9898",
          "9918",
          "9908"
        ],
        "answer": "9898",
        "correct_value": 9898,
        "explanation": "Round to 100: 98≈100, 101≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "98 * 103",
      "ns_shortcut": "Round 98≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 103?",
        "options": [
          "10084",
          "10114",
          "10094",
          "10104"
        ],
        "answer": "10094",
        "correct_value": 10094,
        "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": "58 * 43",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 58 * 43?",
        "options": [
          "2514",
          "2484",
          "2494",
          "2504"
        ],
        "answer": "2494",
        "correct_value": 2494,
        "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_000043",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 99",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 99?",
        "options": [
          "9702",
          "9712",
          "9722",
          "9692"
        ],
        "answer": "9702",
        "correct_value": 9702,
        "explanation": "Round to 100: 98≈100, 99≈100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "101 * 103",
      "ns_shortcut": "Round 101≈100, then adjust.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 103?",
        "options": [
          "10423",
          "10413",
          "10393",
          "10403"
        ],
        "answer": "10403",
        "correct_value": 10403,
        "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": "42 * 57",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 42 * 57?",
        "options": [
          "2384",
          "2414",
          "2404",
          "2394"
        ],
        "answer": "2394",
        "correct_value": 2394,
        "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_000044",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 99",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 99?",
        "options": [
          "10108",
          "10088",
          "10118",
          "10098"
        ],
        "answer": "10098",
        "correct_value": 10098,
        "explanation": "Round to 100: 102≈100, 99≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "98 * 105",
      "ns_shortcut": "Round 98≈100, then adjust.",
      "shortcut_strength": 0.965,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 105?",
        "options": [
          "10300",
          "10290",
          "10280",
          "10310"
        ],
        "answer": "10290",
        "correct_value": 10290,
        "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": "64 * 57",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 64 * 57?",
        "options": [
          "3638",
          "3668",
          "3658",
          "3648"
        ],
        "answer": "3648",
        "correct_value": 3648,
        "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_000045",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 98?",
        "options": [
          "9888",
          "9908",
          "9898",
          "9918"
        ],
        "answer": "9898",
        "correct_value": 9898,
        "explanation": "Round to 100: 101≈100, 98≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "102 * 103",
      "ns_shortcut": "Round 102≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 103?",
        "options": [
          "10506",
          "10526",
          "10516",
          "10496"
        ],
        "answer": "10506",
        "correct_value": 10506,
        "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": "61 * 43",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 61 * 43?",
        "options": [
          "2643",
          "2633",
          "2623",
          "2613"
        ],
        "answer": "2623",
        "correct_value": 2623,
        "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_000046",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 102",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 102?",
        "options": [
          "10404",
          "10414",
          "10424",
          "10394"
        ],
        "answer": "10404",
        "correct_value": 10404,
        "explanation": "Round to 100: 102≈100, 102≈100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "101 * 103",
      "ns_shortcut": "Round 101≈100, then adjust.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 103?",
        "options": [
          "10393",
          "10423",
          "10413",
          "10403"
        ],
        "answer": "10403",
        "correct_value": 10403,
        "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": "46 * 63",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 46 * 63?",
        "options": [
          "2898",
          "2908",
          "2918",
          "2888"
        ],
        "answer": "2898",
        "correct_value": 2898,
        "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_000047",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 98?",
        "options": [
          "9918",
          "9898",
          "9908",
          "9888"
        ],
        "answer": "9898",
        "correct_value": 9898,
        "explanation": "Round to 100: 101≈100, 98≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "102 * 103",
      "ns_shortcut": "Round 102≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 103?",
        "options": [
          "10506",
          "10496",
          "10516",
          "10526"
        ],
        "answer": "10506",
        "correct_value": 10506,
        "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": "47 * 67",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 47 * 67?",
        "options": [
          "3159",
          "3149",
          "3139",
          "3169"
        ],
        "answer": "3149",
        "correct_value": 3149,
        "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_000048",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 98",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 98?",
        "options": [
          "9702",
          "9692",
          "9722",
          "9712"
        ],
        "answer": "9702",
        "correct_value": 9702,
        "explanation": "Round to 100: 99≈100, 98≈100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "102 * 105",
      "ns_shortcut": "Round 102≈100, then adjust.",
      "shortcut_strength": 0.965,
      "pure_math": {
        "question": "Which of the following is the best estimate for 102 * 105?",
        "options": [
          "10710",
          "10700",
          "10730",
          "10720"
        ],
        "answer": "10710",
        "correct_value": 10710,
        "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": "59 * 61",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 59 * 61?",
        "options": [
          "3619",
          "3599",
          "3609",
          "3589"
        ],
        "answer": "3599",
        "correct_value": 3599,
        "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_000049",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 101",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.985,
      "pure_math": {
        "question": "Which of the following is the best estimate for 98 * 101?",
        "options": [
          "9918",
          "9898",
          "9888",
          "9908"
        ],
        "answer": "9898",
        "correct_value": 9898,
        "explanation": "Round to 100: 98≈100, 101≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "101 * 105",
      "ns_shortcut": "Round 101≈100, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 105?",
        "options": [
          "10605",
          "10595",
          "10615",
          "10625"
        ],
        "answer": "10605",
        "correct_value": 10605,
        "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": "52 * 62",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 52 * 62?",
        "options": [
          "3224",
          "3214",
          "3234",
          "3244"
        ],
        "answer": "3224",
        "correct_value": 3224,
        "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_000050",
    "category": "magnitude_estimation",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 101",
      "ns_shortcut": "Round both to 100 and multiply.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Which of the following is the best estimate for 101 * 101?",
        "options": [
          "10211",
          "10191",
          "10201",
          "10221"
        ],
        "answer": "10201",
        "correct_value": 10201,
        "explanation": "Round to 100: 101≈100, 101≈100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "99 * 104",
      "ns_shortcut": "Round 99≈100, then adjust.",
      "shortcut_strength": 0.975,
      "pure_math": {
        "question": "Which of the following is the best estimate for 99 * 104?",
        "options": [
          "10306",
          "10286",
          "10316",
          "10296"
        ],
        "answer": "10296",
        "correct_value": 10296,
        "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": "45 * 45",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which of the following is the best estimate for 45 * 45?",
        "options": [
          "2025",
          "2045",
          "2035",
          "2015"
        ],
        "answer": "2025",
        "correct_value": 2025,
        "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": "structural_shortcuts_000051",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 34",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 34?",
        "options": [
          "3322",
          "3342",
          "3332",
          "3352"
        ],
        "answer": "3332",
        "correct_value": 3332,
        "explanation": "Distributive: (100-2)*34 = 100*34 - 2*34."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "96 * 48",
      "ns_shortcut": "Use (100-4)*m, correction is 4*48.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 96 * 48?",
        "options": [
          "4618",
          "4598",
          "4628",
          "4608"
        ],
        "answer": "4608",
        "correct_value": 4608,
        "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": "47 * 40",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 47 * 40?",
        "options": [
          "1870",
          "1890",
          "1900",
          "1880"
        ],
        "answer": "1880",
        "correct_value": 1880,
        "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_000052",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 91",
      "ns_shortcut": "Use (100-1)*m = 100*m - 1*m.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "What is 99 * 91?",
        "options": [
          "9019",
          "9029",
          "9009",
          "8999"
        ],
        "answer": "9009",
        "correct_value": 9009,
        "explanation": "Distributive: (100-1)*91 = 100*91 - 1*91."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "104 * 46",
      "ns_shortcut": "Use (100+4)*m, correction is 4*46.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 104 * 46?",
        "options": [
          "4784",
          "4804",
          "4794",
          "4774"
        ],
        "answer": "4784",
        "correct_value": 4784,
        "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": "49 * 44",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 49 * 44?",
        "options": [
          "2146",
          "2176",
          "2166",
          "2156"
        ],
        "answer": "2156",
        "correct_value": 2156,
        "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_000053",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 18",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 18?",
        "options": [
          "1784",
          "1764",
          "1774",
          "1754"
        ],
        "answer": "1764",
        "correct_value": 1764,
        "explanation": "Distributive: (100-2)*18 = 100*18 - 2*18."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "104 * 90",
      "ns_shortcut": "Use (100+4)*m, correction is 4*90.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 104 * 90?",
        "options": [
          "9370",
          "9380",
          "9350",
          "9360"
        ],
        "answer": "9360",
        "correct_value": 9360,
        "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": "64 * 57",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 64 * 57?",
        "options": [
          "3658",
          "3638",
          "3648",
          "3668"
        ],
        "answer": "3648",
        "correct_value": 3648,
        "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_000054",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 81",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 81?",
        "options": [
          "7948",
          "7938",
          "7958",
          "7928"
        ],
        "answer": "7938",
        "correct_value": 7938,
        "explanation": "Distributive: (100-2)*81 = 100*81 - 2*81."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "104 * 58",
      "ns_shortcut": "Use (100+4)*m, correction is 4*58.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 104 * 58?",
        "options": [
          "6032",
          "6052",
          "6042",
          "6022"
        ],
        "answer": "6032",
        "correct_value": 6032,
        "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": "66 * 57",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 66 * 57?",
        "options": [
          "3782",
          "3762",
          "3772",
          "3752"
        ],
        "answer": "3762",
        "correct_value": 3762,
        "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_000055",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 36",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 36?",
        "options": [
          "3548",
          "3528",
          "3518",
          "3538"
        ],
        "answer": "3528",
        "correct_value": 3528,
        "explanation": "Distributive: (100-2)*36 = 100*36 - 2*36."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "96 * 40",
      "ns_shortcut": "Use (100-4)*m, correction is 4*40.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 96 * 40?",
        "options": [
          "3830",
          "3840",
          "3860",
          "3850"
        ],
        "answer": "3840",
        "correct_value": 3840,
        "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": "44 * 39",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 44 * 39?",
        "options": [
          "1716",
          "1736",
          "1726",
          "1706"
        ],
        "answer": "1716",
        "correct_value": 1716,
        "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_000056",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 14",
      "ns_shortcut": "Use (100+1)*m = 100*m + 1*m.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "What is 101 * 14?",
        "options": [
          "1414",
          "1434",
          "1404",
          "1424"
        ],
        "answer": "1414",
        "correct_value": 1414,
        "explanation": "Distributive: (100+1)*14 = 100*14 + 1*14."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "105 * 68",
      "ns_shortcut": "Use (100+5)*m, correction is 5*68.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "What is 105 * 68?",
        "options": [
          "7150",
          "7130",
          "7160",
          "7140"
        ],
        "answer": "7140",
        "correct_value": 7140,
        "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": "68 * 47",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 68 * 47?",
        "options": [
          "3216",
          "3196",
          "3186",
          "3206"
        ],
        "answer": "3196",
        "correct_value": 3196,
        "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_000057",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 92",
      "ns_shortcut": "Use (100-1)*m = 100*m - 1*m.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "What is 99 * 92?",
        "options": [
          "9128",
          "9108",
          "9098",
          "9118"
        ],
        "answer": "9108",
        "correct_value": 9108,
        "explanation": "Distributive: (100-1)*92 = 100*92 - 1*92."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "95 * 17",
      "ns_shortcut": "Use (100-5)*m, correction is 5*17.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "What is 95 * 17?",
        "options": [
          "1615",
          "1635",
          "1605",
          "1625"
        ],
        "answer": "1615",
        "correct_value": 1615,
        "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": "53 * 42",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 53 * 42?",
        "options": [
          "2226",
          "2236",
          "2246",
          "2216"
        ],
        "answer": "2226",
        "correct_value": 2226,
        "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_000058",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 44",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 44?",
        "options": [
          "4508",
          "4488",
          "4498",
          "4478"
        ],
        "answer": "4488",
        "correct_value": 4488,
        "explanation": "Distributive: (100+2)*44 = 100*44 + 2*44."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "104 * 15",
      "ns_shortcut": "Use (100+4)*m, correction is 4*15.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 104 * 15?",
        "options": [
          "1560",
          "1570",
          "1580",
          "1550"
        ],
        "answer": "1560",
        "correct_value": 1560,
        "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": "58 * 47",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 58 * 47?",
        "options": [
          "2736",
          "2746",
          "2716",
          "2726"
        ],
        "answer": "2726",
        "correct_value": 2726,
        "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_000059",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 96",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 96?",
        "options": [
          "9418",
          "9408",
          "9398",
          "9428"
        ],
        "answer": "9408",
        "correct_value": 9408,
        "explanation": "Distributive: (100-2)*96 = 100*96 - 2*96."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "96 * 70",
      "ns_shortcut": "Use (100-4)*m, correction is 4*70.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 96 * 70?",
        "options": [
          "6740",
          "6720",
          "6730",
          "6710"
        ],
        "answer": "6720",
        "correct_value": 6720,
        "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": "57 * 52",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 57 * 52?",
        "options": [
          "2984",
          "2974",
          "2964",
          "2954"
        ],
        "answer": "2964",
        "correct_value": 2964,
        "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_000060",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 62",
      "ns_shortcut": "Use (100+1)*m = 100*m + 1*m.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "What is 101 * 62?",
        "options": [
          "6252",
          "6262",
          "6272",
          "6282"
        ],
        "answer": "6262",
        "correct_value": 6262,
        "explanation": "Distributive: (100+1)*62 = 100*62 + 1*62."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "96 * 52",
      "ns_shortcut": "Use (100-4)*m, correction is 4*52.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 96 * 52?",
        "options": [
          "4992",
          "5002",
          "5012",
          "4982"
        ],
        "answer": "4992",
        "correct_value": 4992,
        "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": "48 * 60",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 48 * 60?",
        "options": [
          "2890",
          "2880",
          "2900",
          "2870"
        ],
        "answer": "2880",
        "correct_value": 2880,
        "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_000061",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 21",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 21?",
        "options": [
          "2142",
          "2132",
          "2152",
          "2162"
        ],
        "answer": "2142",
        "correct_value": 2142,
        "explanation": "Distributive: (100+2)*21 = 100*21 + 2*21."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "95 * 61",
      "ns_shortcut": "Use (100-5)*m, correction is 5*61.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "What is 95 * 61?",
        "options": [
          "5785",
          "5805",
          "5815",
          "5795"
        ],
        "answer": "5795",
        "correct_value": 5795,
        "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": "52 * 40",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 52 * 40?",
        "options": [
          "2080",
          "2070",
          "2100",
          "2090"
        ],
        "answer": "2080",
        "correct_value": 2080,
        "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_000062",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 90",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 90?",
        "options": [
          "9190",
          "9200",
          "9180",
          "9170"
        ],
        "answer": "9180",
        "correct_value": 9180,
        "explanation": "Distributive: (100+2)*90 = 100*90 + 2*90."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "97 * 80",
      "ns_shortcut": "Use (100-3)*m, correction is 3*80.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "What is 97 * 80?",
        "options": [
          "7760",
          "7780",
          "7750",
          "7770"
        ],
        "answer": "7760",
        "correct_value": 7760,
        "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": "67 * 61",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 67 * 61?",
        "options": [
          "4097",
          "4107",
          "4087",
          "4077"
        ],
        "answer": "4087",
        "correct_value": 4087,
        "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_000063",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 30",
      "ns_shortcut": "Use (100-1)*m = 100*m - 1*m.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "What is 99 * 30?",
        "options": [
          "2980",
          "2970",
          "2960",
          "2990"
        ],
        "answer": "2970",
        "correct_value": 2970,
        "explanation": "Distributive: (100-1)*30 = 100*30 - 1*30."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "104 * 62",
      "ns_shortcut": "Use (100+4)*m, correction is 4*62.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 104 * 62?",
        "options": [
          "6458",
          "6468",
          "6438",
          "6448"
        ],
        "answer": "6448",
        "correct_value": 6448,
        "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": "53 * 69",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 53 * 69?",
        "options": [
          "3667",
          "3647",
          "3677",
          "3657"
        ],
        "answer": "3657",
        "correct_value": 3657,
        "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_000064",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 47",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 47?",
        "options": [
          "4794",
          "4784",
          "4804",
          "4814"
        ],
        "answer": "4794",
        "correct_value": 4794,
        "explanation": "Distributive: (100+2)*47 = 100*47 + 2*47."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "103 * 41",
      "ns_shortcut": "Use (100+3)*m, correction is 3*41.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "What is 103 * 41?",
        "options": [
          "4233",
          "4223",
          "4243",
          "4213"
        ],
        "answer": "4223",
        "correct_value": 4223,
        "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": "51 * 45",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 51 * 45?",
        "options": [
          "2315",
          "2285",
          "2295",
          "2305"
        ],
        "answer": "2295",
        "correct_value": 2295,
        "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_000065",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 53",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 53?",
        "options": [
          "5396",
          "5416",
          "5406",
          "5426"
        ],
        "answer": "5406",
        "correct_value": 5406,
        "explanation": "Distributive: (100+2)*53 = 100*53 + 2*53."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "105 * 48",
      "ns_shortcut": "Use (100+5)*m, correction is 5*48.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "What is 105 * 48?",
        "options": [
          "5060",
          "5050",
          "5040",
          "5030"
        ],
        "answer": "5040",
        "correct_value": 5040,
        "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": "56 * 54",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 56 * 54?",
        "options": [
          "3024",
          "3014",
          "3034",
          "3044"
        ],
        "answer": "3024",
        "correct_value": 3024,
        "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_000066",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 51",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 51?",
        "options": [
          "5192",
          "5202",
          "5222",
          "5212"
        ],
        "answer": "5202",
        "correct_value": 5202,
        "explanation": "Distributive: (100+2)*51 = 100*51 + 2*51."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "104 * 59",
      "ns_shortcut": "Use (100+4)*m, correction is 4*59.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 104 * 59?",
        "options": [
          "6156",
          "6136",
          "6126",
          "6146"
        ],
        "answer": "6136",
        "correct_value": 6136,
        "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": "49 * 62",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 49 * 62?",
        "options": [
          "3038",
          "3048",
          "3058",
          "3028"
        ],
        "answer": "3038",
        "correct_value": 3038,
        "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_000067",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 94",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 94?",
        "options": [
          "9608",
          "9588",
          "9578",
          "9598"
        ],
        "answer": "9588",
        "correct_value": 9588,
        "explanation": "Distributive: (100+2)*94 = 100*94 + 2*94."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "96 * 74",
      "ns_shortcut": "Use (100-4)*m, correction is 4*74.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 96 * 74?",
        "options": [
          "7094",
          "7114",
          "7104",
          "7124"
        ],
        "answer": "7104",
        "correct_value": 7104,
        "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": "42 * 55",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 42 * 55?",
        "options": [
          "2320",
          "2330",
          "2310",
          "2300"
        ],
        "answer": "2310",
        "correct_value": 2310,
        "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_000068",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 93",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 93?",
        "options": [
          "9506",
          "9476",
          "9486",
          "9496"
        ],
        "answer": "9486",
        "correct_value": 9486,
        "explanation": "Distributive: (100+2)*93 = 100*93 + 2*93."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "97 * 53",
      "ns_shortcut": "Use (100-3)*m, correction is 3*53.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "What is 97 * 53?",
        "options": [
          "5151",
          "5141",
          "5161",
          "5131"
        ],
        "answer": "5141",
        "correct_value": 5141,
        "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": "66 * 49",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 66 * 49?",
        "options": [
          "3234",
          "3254",
          "3244",
          "3224"
        ],
        "answer": "3234",
        "correct_value": 3234,
        "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_000069",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 89",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 89?",
        "options": [
          "8742",
          "8732",
          "8712",
          "8722"
        ],
        "answer": "8722",
        "correct_value": 8722,
        "explanation": "Distributive: (100-2)*89 = 100*89 - 2*89."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "96 * 21",
      "ns_shortcut": "Use (100-4)*m, correction is 4*21.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 96 * 21?",
        "options": [
          "2026",
          "2036",
          "2016",
          "2006"
        ],
        "answer": "2016",
        "correct_value": 2016,
        "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": "53 * 44",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 53 * 44?",
        "options": [
          "2342",
          "2322",
          "2332",
          "2352"
        ],
        "answer": "2332",
        "correct_value": 2332,
        "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_000070",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 17",
      "ns_shortcut": "Use (100+1)*m = 100*m + 1*m.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "What is 101 * 17?",
        "options": [
          "1717",
          "1707",
          "1727",
          "1737"
        ],
        "answer": "1717",
        "correct_value": 1717,
        "explanation": "Distributive: (100+1)*17 = 100*17 + 1*17."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "103 * 28",
      "ns_shortcut": "Use (100+3)*m, correction is 3*28.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "What is 103 * 28?",
        "options": [
          "2884",
          "2874",
          "2904",
          "2894"
        ],
        "answer": "2884",
        "correct_value": 2884,
        "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": "57 * 60",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 57 * 60?",
        "options": [
          "3410",
          "3440",
          "3420",
          "3430"
        ],
        "answer": "3420",
        "correct_value": 3420,
        "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_000071",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 88",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 88?",
        "options": [
          "8634",
          "8624",
          "8644",
          "8614"
        ],
        "answer": "8624",
        "correct_value": 8624,
        "explanation": "Distributive: (100-2)*88 = 100*88 - 2*88."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "103 * 84",
      "ns_shortcut": "Use (100+3)*m, correction is 3*84.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "What is 103 * 84?",
        "options": [
          "8672",
          "8642",
          "8652",
          "8662"
        ],
        "answer": "8652",
        "correct_value": 8652,
        "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": "59 * 47",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 59 * 47?",
        "options": [
          "2793",
          "2773",
          "2783",
          "2763"
        ],
        "answer": "2773",
        "correct_value": 2773,
        "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_000072",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 46",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 46?",
        "options": [
          "4712",
          "4682",
          "4692",
          "4702"
        ],
        "answer": "4692",
        "correct_value": 4692,
        "explanation": "Distributive: (100+2)*46 = 100*46 + 2*46."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "97 * 85",
      "ns_shortcut": "Use (100-3)*m, correction is 3*85.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "What is 97 * 85?",
        "options": [
          "8245",
          "8255",
          "8235",
          "8265"
        ],
        "answer": "8245",
        "correct_value": 8245,
        "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": "61 * 47",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 61 * 47?",
        "options": [
          "2887",
          "2867",
          "2877",
          "2857"
        ],
        "answer": "2867",
        "correct_value": 2867,
        "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_000073",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 71",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 71?",
        "options": [
          "7262",
          "7252",
          "7232",
          "7242"
        ],
        "answer": "7242",
        "correct_value": 7242,
        "explanation": "Distributive: (100+2)*71 = 100*71 + 2*71."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "104 * 55",
      "ns_shortcut": "Use (100+4)*m, correction is 4*55.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 104 * 55?",
        "options": [
          "5720",
          "5730",
          "5710",
          "5740"
        ],
        "answer": "5720",
        "correct_value": 5720,
        "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": "39 * 65",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 39 * 65?",
        "options": [
          "2555",
          "2535",
          "2545",
          "2525"
        ],
        "answer": "2535",
        "correct_value": 2535,
        "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_000074",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 87",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 87?",
        "options": [
          "8546",
          "8526",
          "8536",
          "8516"
        ],
        "answer": "8526",
        "correct_value": 8526,
        "explanation": "Distributive: (100-2)*87 = 100*87 - 2*87."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "104 * 55",
      "ns_shortcut": "Use (100+4)*m, correction is 4*55.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 104 * 55?",
        "options": [
          "5710",
          "5720",
          "5740",
          "5730"
        ],
        "answer": "5720",
        "correct_value": 5720,
        "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": "58 * 47",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 58 * 47?",
        "options": [
          "2716",
          "2726",
          "2746",
          "2736"
        ],
        "answer": "2726",
        "correct_value": 2726,
        "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_000075",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 49",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 49?",
        "options": [
          "4822",
          "4812",
          "4802",
          "4792"
        ],
        "answer": "4802",
        "correct_value": 4802,
        "explanation": "Distributive: (100-2)*49 = 100*49 - 2*49."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "105 * 26",
      "ns_shortcut": "Use (100+5)*m, correction is 5*26.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "What is 105 * 26?",
        "options": [
          "2720",
          "2750",
          "2740",
          "2730"
        ],
        "answer": "2730",
        "correct_value": 2730,
        "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": "62 * 52",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 62 * 52?",
        "options": [
          "3214",
          "3244",
          "3224",
          "3234"
        ],
        "answer": "3224",
        "correct_value": 3224,
        "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_000076",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 77",
      "ns_shortcut": "Use (100+1)*m = 100*m + 1*m.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "What is 101 * 77?",
        "options": [
          "7767",
          "7787",
          "7777",
          "7797"
        ],
        "answer": "7777",
        "correct_value": 7777,
        "explanation": "Distributive: (100+1)*77 = 100*77 + 1*77."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "103 * 47",
      "ns_shortcut": "Use (100+3)*m, correction is 3*47.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "What is 103 * 47?",
        "options": [
          "4831",
          "4851",
          "4841",
          "4861"
        ],
        "answer": "4841",
        "correct_value": 4841,
        "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": "69 * 41",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 69 * 41?",
        "options": [
          "2849",
          "2819",
          "2829",
          "2839"
        ],
        "answer": "2829",
        "correct_value": 2829,
        "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_000077",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 21",
      "ns_shortcut": "Use (100+1)*m = 100*m + 1*m.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "What is 101 * 21?",
        "options": [
          "2141",
          "2131",
          "2121",
          "2111"
        ],
        "answer": "2121",
        "correct_value": 2121,
        "explanation": "Distributive: (100+1)*21 = 100*21 + 1*21."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "104 * 25",
      "ns_shortcut": "Use (100+4)*m, correction is 4*25.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 104 * 25?",
        "options": [
          "2600",
          "2620",
          "2610",
          "2590"
        ],
        "answer": "2600",
        "correct_value": 2600,
        "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": "57 * 51",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 57 * 51?",
        "options": [
          "2917",
          "2897",
          "2907",
          "2927"
        ],
        "answer": "2907",
        "correct_value": 2907,
        "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_000078",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 13",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 13?",
        "options": [
          "1336",
          "1326",
          "1316",
          "1346"
        ],
        "answer": "1326",
        "correct_value": 1326,
        "explanation": "Distributive: (100+2)*13 = 100*13 + 2*13."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "105 * 18",
      "ns_shortcut": "Use (100+5)*m, correction is 5*18.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "What is 105 * 18?",
        "options": [
          "1890",
          "1900",
          "1910",
          "1880"
        ],
        "answer": "1890",
        "correct_value": 1890,
        "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": "59 * 52",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 59 * 52?",
        "options": [
          "3078",
          "3088",
          "3058",
          "3068"
        ],
        "answer": "3068",
        "correct_value": 3068,
        "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_000079",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 48",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 48?",
        "options": [
          "4714",
          "4724",
          "4704",
          "4694"
        ],
        "answer": "4704",
        "correct_value": 4704,
        "explanation": "Distributive: (100-2)*48 = 100*48 - 2*48."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "96 * 78",
      "ns_shortcut": "Use (100-4)*m, correction is 4*78.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 96 * 78?",
        "options": [
          "7488",
          "7508",
          "7478",
          "7498"
        ],
        "answer": "7488",
        "correct_value": 7488,
        "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": "50 * 60",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 50 * 60?",
        "options": [
          "3010",
          "3000",
          "3020",
          "2990"
        ],
        "answer": "3000",
        "correct_value": 3000,
        "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_000080",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 93",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 93?",
        "options": [
          "9476",
          "9506",
          "9496",
          "9486"
        ],
        "answer": "9486",
        "correct_value": 9486,
        "explanation": "Distributive: (100+2)*93 = 100*93 + 2*93."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "97 * 14",
      "ns_shortcut": "Use (100-3)*m, correction is 3*14.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "What is 97 * 14?",
        "options": [
          "1348",
          "1368",
          "1358",
          "1378"
        ],
        "answer": "1358",
        "correct_value": 1358,
        "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": "53 * 69",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 53 * 69?",
        "options": [
          "3677",
          "3657",
          "3647",
          "3667"
        ],
        "answer": "3657",
        "correct_value": 3657,
        "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_000081",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 79",
      "ns_shortcut": "Use (100+1)*m = 100*m + 1*m.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "What is 101 * 79?",
        "options": [
          "7969",
          "7989",
          "7979",
          "7999"
        ],
        "answer": "7979",
        "correct_value": 7979,
        "explanation": "Distributive: (100+1)*79 = 100*79 + 1*79."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "97 * 34",
      "ns_shortcut": "Use (100-3)*m, correction is 3*34.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "What is 97 * 34?",
        "options": [
          "3318",
          "3288",
          "3308",
          "3298"
        ],
        "answer": "3298",
        "correct_value": 3298,
        "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": "60 * 45",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 60 * 45?",
        "options": [
          "2720",
          "2710",
          "2690",
          "2700"
        ],
        "answer": "2700",
        "correct_value": 2700,
        "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_000082",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 26",
      "ns_shortcut": "Use (100-1)*m = 100*m - 1*m.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "What is 99 * 26?",
        "options": [
          "2564",
          "2594",
          "2574",
          "2584"
        ],
        "answer": "2574",
        "correct_value": 2574,
        "explanation": "Distributive: (100-1)*26 = 100*26 - 1*26."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "104 * 37",
      "ns_shortcut": "Use (100+4)*m, correction is 4*37.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 104 * 37?",
        "options": [
          "3868",
          "3848",
          "3838",
          "3858"
        ],
        "answer": "3848",
        "correct_value": 3848,
        "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": "64 * 67",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 64 * 67?",
        "options": [
          "4308",
          "4278",
          "4298",
          "4288"
        ],
        "answer": "4288",
        "correct_value": 4288,
        "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_000083",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 79",
      "ns_shortcut": "Use (100-1)*m = 100*m - 1*m.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "What is 99 * 79?",
        "options": [
          "7831",
          "7811",
          "7821",
          "7841"
        ],
        "answer": "7821",
        "correct_value": 7821,
        "explanation": "Distributive: (100-1)*79 = 100*79 - 1*79."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "105 * 13",
      "ns_shortcut": "Use (100+5)*m, correction is 5*13.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "What is 105 * 13?",
        "options": [
          "1385",
          "1355",
          "1365",
          "1375"
        ],
        "answer": "1365",
        "correct_value": 1365,
        "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": "64 * 64",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 64 * 64?",
        "options": [
          "4096",
          "4086",
          "4116",
          "4106"
        ],
        "answer": "4096",
        "correct_value": 4096,
        "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_000084",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 32",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 32?",
        "options": [
          "3146",
          "3126",
          "3136",
          "3156"
        ],
        "answer": "3136",
        "correct_value": 3136,
        "explanation": "Distributive: (100-2)*32 = 100*32 - 2*32."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "105 * 63",
      "ns_shortcut": "Use (100+5)*m, correction is 5*63.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "What is 105 * 63?",
        "options": [
          "6625",
          "6605",
          "6635",
          "6615"
        ],
        "answer": "6615",
        "correct_value": 6615,
        "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": "54 * 53",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 54 * 53?",
        "options": [
          "2872",
          "2862",
          "2852",
          "2882"
        ],
        "answer": "2862",
        "correct_value": 2862,
        "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_000085",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 74",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 74?",
        "options": [
          "7538",
          "7548",
          "7568",
          "7558"
        ],
        "answer": "7548",
        "correct_value": 7548,
        "explanation": "Distributive: (100+2)*74 = 100*74 + 2*74."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "105 * 94",
      "ns_shortcut": "Use (100+5)*m, correction is 5*94.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "What is 105 * 94?",
        "options": [
          "9860",
          "9870",
          "9880",
          "9890"
        ],
        "answer": "9870",
        "correct_value": 9870,
        "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": "40 * 54",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 40 * 54?",
        "options": [
          "2180",
          "2160",
          "2170",
          "2150"
        ],
        "answer": "2160",
        "correct_value": 2160,
        "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_000086",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 66",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 66?",
        "options": [
          "6752",
          "6742",
          "6722",
          "6732"
        ],
        "answer": "6732",
        "correct_value": 6732,
        "explanation": "Distributive: (100+2)*66 = 100*66 + 2*66."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "104 * 28",
      "ns_shortcut": "Use (100+4)*m, correction is 4*28.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 104 * 28?",
        "options": [
          "2932",
          "2922",
          "2902",
          "2912"
        ],
        "answer": "2912",
        "correct_value": 2912,
        "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": "58 * 59",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 58 * 59?",
        "options": [
          "3422",
          "3412",
          "3432",
          "3442"
        ],
        "answer": "3422",
        "correct_value": 3422,
        "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_000087",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 74",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 74?",
        "options": [
          "7558",
          "7568",
          "7548",
          "7538"
        ],
        "answer": "7548",
        "correct_value": 7548,
        "explanation": "Distributive: (100+2)*74 = 100*74 + 2*74."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "105 * 93",
      "ns_shortcut": "Use (100+5)*m, correction is 5*93.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "What is 105 * 93?",
        "options": [
          "9765",
          "9785",
          "9755",
          "9775"
        ],
        "answer": "9765",
        "correct_value": 9765,
        "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": "67 * 46",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 67 * 46?",
        "options": [
          "3082",
          "3102",
          "3092",
          "3072"
        ],
        "answer": "3082",
        "correct_value": 3082,
        "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_000088",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 63",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 63?",
        "options": [
          "6416",
          "6446",
          "6436",
          "6426"
        ],
        "answer": "6426",
        "correct_value": 6426,
        "explanation": "Distributive: (100+2)*63 = 100*63 + 2*63."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "97 * 95",
      "ns_shortcut": "Use (100-3)*m, correction is 3*95.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "What is 97 * 95?",
        "options": [
          "9205",
          "9215",
          "9225",
          "9235"
        ],
        "answer": "9215",
        "correct_value": 9215,
        "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": "60 * 68",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 60 * 68?",
        "options": [
          "4090",
          "4100",
          "4080",
          "4070"
        ],
        "answer": "4080",
        "correct_value": 4080,
        "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_000089",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 21",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 21?",
        "options": [
          "2078",
          "2068",
          "2058",
          "2048"
        ],
        "answer": "2058",
        "correct_value": 2058,
        "explanation": "Distributive: (100-2)*21 = 100*21 - 2*21."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "96 * 81",
      "ns_shortcut": "Use (100-4)*m, correction is 4*81.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 96 * 81?",
        "options": [
          "7766",
          "7786",
          "7796",
          "7776"
        ],
        "answer": "7776",
        "correct_value": 7776,
        "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": "60 * 42",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 60 * 42?",
        "options": [
          "2520",
          "2540",
          "2530",
          "2510"
        ],
        "answer": "2520",
        "correct_value": 2520,
        "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_000090",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 46",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 46?",
        "options": [
          "4498",
          "4508",
          "4518",
          "4528"
        ],
        "answer": "4508",
        "correct_value": 4508,
        "explanation": "Distributive: (100-2)*46 = 100*46 - 2*46."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "104 * 74",
      "ns_shortcut": "Use (100+4)*m, correction is 4*74.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 104 * 74?",
        "options": [
          "7716",
          "7686",
          "7696",
          "7706"
        ],
        "answer": "7696",
        "correct_value": 7696,
        "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": "46 * 66",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 46 * 66?",
        "options": [
          "3026",
          "3056",
          "3046",
          "3036"
        ],
        "answer": "3036",
        "correct_value": 3036,
        "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_000091",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 45",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 45?",
        "options": [
          "4430",
          "4410",
          "4400",
          "4420"
        ],
        "answer": "4410",
        "correct_value": 4410,
        "explanation": "Distributive: (100-2)*45 = 100*45 - 2*45."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "104 * 94",
      "ns_shortcut": "Use (100+4)*m, correction is 4*94.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 104 * 94?",
        "options": [
          "9786",
          "9766",
          "9776",
          "9796"
        ],
        "answer": "9776",
        "correct_value": 9776,
        "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": "47 * 61",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 47 * 61?",
        "options": [
          "2867",
          "2857",
          "2877",
          "2887"
        ],
        "answer": "2867",
        "correct_value": 2867,
        "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_000092",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 33",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 33?",
        "options": [
          "3234",
          "3224",
          "3254",
          "3244"
        ],
        "answer": "3234",
        "correct_value": 3234,
        "explanation": "Distributive: (100-2)*33 = 100*33 - 2*33."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "95 * 28",
      "ns_shortcut": "Use (100-5)*m, correction is 5*28.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "What is 95 * 28?",
        "options": [
          "2670",
          "2680",
          "2650",
          "2660"
        ],
        "answer": "2660",
        "correct_value": 2660,
        "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": "51 * 52",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 51 * 52?",
        "options": [
          "2672",
          "2652",
          "2662",
          "2642"
        ],
        "answer": "2652",
        "correct_value": 2652,
        "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_000093",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 49",
      "ns_shortcut": "Use (100+1)*m = 100*m + 1*m.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "What is 101 * 49?",
        "options": [
          "4959",
          "4949",
          "4939",
          "4969"
        ],
        "answer": "4949",
        "correct_value": 4949,
        "explanation": "Distributive: (100+1)*49 = 100*49 + 1*49."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "95 * 29",
      "ns_shortcut": "Use (100-5)*m, correction is 5*29.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "What is 95 * 29?",
        "options": [
          "2745",
          "2755",
          "2775",
          "2765"
        ],
        "answer": "2755",
        "correct_value": 2755,
        "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": "60 * 41",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 60 * 41?",
        "options": [
          "2460",
          "2450",
          "2470",
          "2480"
        ],
        "answer": "2460",
        "correct_value": 2460,
        "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_000094",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 87",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 87?",
        "options": [
          "8874",
          "8894",
          "8884",
          "8864"
        ],
        "answer": "8874",
        "correct_value": 8874,
        "explanation": "Distributive: (100+2)*87 = 100*87 + 2*87."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "96 * 75",
      "ns_shortcut": "Use (100-4)*m, correction is 4*75.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 96 * 75?",
        "options": [
          "7190",
          "7220",
          "7210",
          "7200"
        ],
        "answer": "7200",
        "correct_value": 7200,
        "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": "42 * 48",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 42 * 48?",
        "options": [
          "2016",
          "2026",
          "2036",
          "2006"
        ],
        "answer": "2016",
        "correct_value": 2016,
        "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_000095",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 38",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 38?",
        "options": [
          "3734",
          "3724",
          "3744",
          "3714"
        ],
        "answer": "3724",
        "correct_value": 3724,
        "explanation": "Distributive: (100-2)*38 = 100*38 - 2*38."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "95 * 36",
      "ns_shortcut": "Use (100-5)*m, correction is 5*36.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "What is 95 * 36?",
        "options": [
          "3430",
          "3410",
          "3420",
          "3440"
        ],
        "answer": "3420",
        "correct_value": 3420,
        "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": "63 * 47",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 63 * 47?",
        "options": [
          "2951",
          "2961",
          "2971",
          "2981"
        ],
        "answer": "2961",
        "correct_value": 2961,
        "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_000096",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 * 73",
      "ns_shortcut": "Use (100-2)*m = 100*m - 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 98 * 73?",
        "options": [
          "7164",
          "7174",
          "7154",
          "7144"
        ],
        "answer": "7154",
        "correct_value": 7154,
        "explanation": "Distributive: (100-2)*73 = 100*73 - 2*73."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "103 * 78",
      "ns_shortcut": "Use (100+3)*m, correction is 3*78.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "What is 103 * 78?",
        "options": [
          "8034",
          "8024",
          "8054",
          "8044"
        ],
        "answer": "8034",
        "correct_value": 8034,
        "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": "41 * 51",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 41 * 51?",
        "options": [
          "2111",
          "2081",
          "2101",
          "2091"
        ],
        "answer": "2091",
        "correct_value": 2091,
        "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_000097",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "102 * 19",
      "ns_shortcut": "Use (100+2)*m = 100*m + 2*m.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "What is 102 * 19?",
        "options": [
          "1938",
          "1948",
          "1928",
          "1958"
        ],
        "answer": "1938",
        "correct_value": 1938,
        "explanation": "Distributive: (100+2)*19 = 100*19 + 2*19."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "104 * 61",
      "ns_shortcut": "Use (100+4)*m, correction is 4*61.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 104 * 61?",
        "options": [
          "6364",
          "6344",
          "6354",
          "6334"
        ],
        "answer": "6344",
        "correct_value": 6344,
        "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": "51 * 39",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 51 * 39?",
        "options": [
          "1979",
          "1999",
          "1989",
          "2009"
        ],
        "answer": "1989",
        "correct_value": 1989,
        "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_000098",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "101 * 21",
      "ns_shortcut": "Use (100+1)*m = 100*m + 1*m.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "What is 101 * 21?",
        "options": [
          "2131",
          "2141",
          "2121",
          "2111"
        ],
        "answer": "2121",
        "correct_value": 2121,
        "explanation": "Distributive: (100+1)*21 = 100*21 + 1*21."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "103 * 85",
      "ns_shortcut": "Use (100+3)*m, correction is 3*85.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "What is 103 * 85?",
        "options": [
          "8765",
          "8755",
          "8775",
          "8745"
        ],
        "answer": "8755",
        "correct_value": 8755,
        "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": "51 * 66",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 51 * 66?",
        "options": [
          "3366",
          "3376",
          "3356",
          "3386"
        ],
        "answer": "3366",
        "correct_value": 3366,
        "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_000099",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 52",
      "ns_shortcut": "Use (100-1)*m = 100*m - 1*m.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "What is 99 * 52?",
        "options": [
          "5138",
          "5168",
          "5148",
          "5158"
        ],
        "answer": "5148",
        "correct_value": 5148,
        "explanation": "Distributive: (100-1)*52 = 100*52 - 1*52."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "104 * 75",
      "ns_shortcut": "Use (100+4)*m, correction is 4*75.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "What is 104 * 75?",
        "options": [
          "7800",
          "7820",
          "7790",
          "7810"
        ],
        "answer": "7800",
        "correct_value": 7800,
        "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": "62 * 69",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 62 * 69?",
        "options": [
          "4268",
          "4298",
          "4278",
          "4288"
        ],
        "answer": "4278",
        "correct_value": 4278,
        "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_000100",
    "category": "structural_shortcuts",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 * 42",
      "ns_shortcut": "Use (100-1)*m = 100*m - 1*m.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "What is 99 * 42?",
        "options": [
          "4148",
          "4178",
          "4158",
          "4168"
        ],
        "answer": "4158",
        "correct_value": 4158,
        "explanation": "Distributive: (100-1)*42 = 100*42 - 1*42."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "105 * 19",
      "ns_shortcut": "Use (100+5)*m, correction is 5*19.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "What is 105 * 19?",
        "options": [
          "1995",
          "1985",
          "2015",
          "2005"
        ],
        "answer": "1995",
        "correct_value": 1995,
        "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": "53 * 63",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 53 * 63?",
        "options": [
          "3339",
          "3349",
          "3359",
          "3329"
        ],
        "answer": "3339",
        "correct_value": 3339,
        "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": "relative_distance_000101",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 42/90 or 27/50?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.07333333333333336,
      "pure_math": {
        "question": "Which is larger: 42/90 or 27/50?",
        "options": [
          "42/90",
          "27/50",
          "35/66",
          "11/18"
        ],
        "answer": "27/50",
        "correct_value": 0.54,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 26/55 or 41/74?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.08132678132678134,
      "pure_math": {
        "question": "Which is larger: 26/55 or 41/74?",
        "options": [
          "8/19",
          "26/55",
          "45/69",
          "41/74"
        ],
        "answer": "41/74",
        "correct_value": 0.5540540540540541,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 26/46 or 12/19?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 26/46 or 12/19?",
        "options": [
          "28/92",
          "12/19",
          "26/46",
          "60/88"
        ],
        "answer": "12/19",
        "correct_value": 0.631578947368421,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000102",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 32/67 or 43/83?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.040460348858119055,
      "pure_math": {
        "question": "Which is larger: 32/67 or 43/83?",
        "options": [
          "31/51",
          "49/70",
          "43/83",
          "32/67"
        ],
        "answer": "43/83",
        "correct_value": 0.5180722891566265,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 11/23 or 29/53?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.0689089417555373,
      "pure_math": {
        "question": "Which is larger: 11/23 or 29/53?",
        "options": [
          "13/20",
          "11/23",
          "34/92",
          "29/53"
        ],
        "answer": "29/53",
        "correct_value": 0.5471698113207547,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 37/66 or 45/77?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 37/66 or 45/77?",
        "options": [
          "45/77",
          "25/56",
          "37/66",
          "29/76"
        ],
        "answer": "45/77",
        "correct_value": 0.5844155844155844,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000103",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 25/53 or 49/96?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.038718553459119454,
      "pure_math": {
        "question": "Which is larger: 25/53 or 49/96?",
        "options": [
          "15/52",
          "25/53",
          "49/96",
          "63/90"
        ],
        "answer": "49/96",
        "correct_value": 0.5104166666666666,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 22/46 or 23/42?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.06935817805383027,
      "pure_math": {
        "question": "Which is larger: 22/46 or 23/42?",
        "options": [
          "22/46",
          "12/29",
          "61/94",
          "23/42"
        ],
        "answer": "23/42",
        "correct_value": 0.5476190476190477,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 30/54 or 29/49?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 30/54 or 29/49?",
        "options": [
          "48/94",
          "29/49",
          "67/93",
          "30/54"
        ],
        "answer": "29/49",
        "correct_value": 0.5918367346938775,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000104",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 22/49 or 44/81?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.09423028470647515,
      "pure_math": {
        "question": "Which is larger: 22/49 or 44/81?",
        "options": [
          "16/26",
          "22/49",
          "39/52",
          "44/81"
        ],
        "answer": "44/81",
        "correct_value": 0.5432098765432098,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 36/75 or 31/56?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07357142857142862,
      "pure_math": {
        "question": "Which is larger: 36/75 or 31/56?",
        "options": [
          "31/56",
          "5/12",
          "17/49",
          "36/75"
        ],
        "answer": "31/56",
        "correct_value": 0.5535714285714286,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 19/34 or 23/38?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 19/34 or 23/38?",
        "options": [
          "19/34",
          "8/19",
          "8/27",
          "23/38"
        ],
        "answer": "23/38",
        "correct_value": 0.6052631578947368,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000105",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 46/94 or 28/53?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.038940184664793265,
      "pure_math": {
        "question": "Which is larger: 46/94 or 28/53?",
        "options": [
          "9/29",
          "28/53",
          "45/86",
          "46/94"
        ],
        "answer": "28/53",
        "correct_value": 0.5283018867924528,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 32/66 or 8/15?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.048484848484848464,
      "pure_math": {
        "question": "Which is larger: 32/66 or 8/15?",
        "options": [
          "8/15",
          "38/62",
          "70/96",
          "32/66"
        ],
        "answer": "8/15",
        "correct_value": 0.5333333333333333,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 37/67 or 23/39?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 37/67 or 23/39?",
        "options": [
          "23/39",
          "34/78",
          "27/49",
          "37/67"
        ],
        "answer": "23/39",
        "correct_value": 0.5897435897435898,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000106",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 32/69 or 26/46?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.10144927536231879,
      "pure_math": {
        "question": "Which is larger: 32/69 or 26/46?",
        "options": [
          "45/77",
          "26/46",
          "13/30",
          "32/69"
        ],
        "answer": "26/46",
        "correct_value": 0.5652173913043478,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 44/92 or 39/71?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07103490508266996,
      "pure_math": {
        "question": "Which is larger: 44/92 or 39/71?",
        "options": [
          "31/57",
          "16/23",
          "44/92",
          "39/71"
        ],
        "answer": "39/71",
        "correct_value": 0.5492957746478874,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 17/30 or 26/44?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 17/30 or 26/44?",
        "options": [
          "17/30",
          "48/67",
          "26/44",
          "20/28"
        ],
        "answer": "26/44",
        "correct_value": 0.5909090909090909,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000107",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 30/67 or 29/54?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.08927584300718633,
      "pure_math": {
        "question": "Which is larger: 30/67 or 29/54?",
        "options": [
          "10/16",
          "29/54",
          "41/74",
          "30/67"
        ],
        "answer": "29/54",
        "correct_value": 0.5370370370370371,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 27/57 or 21/38?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07894736842105271,
      "pure_math": {
        "question": "Which is larger: 27/57 or 21/38?",
        "options": [
          "27/57",
          "16/22",
          "21/38",
          "5/13"
        ],
        "answer": "21/38",
        "correct_value": 0.5526315789473685,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 8/14 or 27/46?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 8/14 or 27/46?",
        "options": [
          "8/14",
          "25/70",
          "45/70",
          "27/46"
        ],
        "answer": "27/46",
        "correct_value": 0.5869565217391305,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000108",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 18/42 or 22/37?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.16602316602316608,
      "pure_math": {
        "question": "Which is larger: 18/42 or 22/37?",
        "options": [
          "23/64",
          "18/42",
          "22/37",
          "54/87"
        ],
        "answer": "22/37",
        "correct_value": 0.5945945945945946,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 12/25 or 9/16?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.08250000000000002,
      "pure_math": {
        "question": "Which is larger: 12/25 or 9/16?",
        "options": [
          "12/25",
          "23/40",
          "9/16",
          "61/91"
        ],
        "answer": "9/16",
        "correct_value": 0.5625,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 41/73 or 50/86?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 41/73 or 50/86?",
        "options": [
          "54/90",
          "50/86",
          "20/78",
          "41/73"
        ],
        "answer": "50/86",
        "correct_value": 0.5813953488372093,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000109",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 20/47 or 35/64?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.12134308510638298,
      "pure_math": {
        "question": "Which is larger: 20/47 or 35/64?",
        "options": [
          "46/83",
          "35/64",
          "20/55",
          "20/47"
        ],
        "answer": "35/64",
        "correct_value": 0.546875,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 37/77 or 31/56?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07305194805194809,
      "pure_math": {
        "question": "Which is larger: 37/77 or 31/56?",
        "options": [
          "51/79",
          "12/18",
          "37/77",
          "31/56"
        ],
        "answer": "31/56",
        "correct_value": 0.5535714285714286,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 9/15 or 53/91?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 9/15 or 53/91?",
        "options": [
          "10/42",
          "53/91",
          "9/15",
          "25/59"
        ],
        "answer": "9/15",
        "correct_value": 0.6,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000110",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 19/40 or 48/94?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.03563829787234041,
      "pure_math": {
        "question": "Which is larger: 19/40 or 48/94?",
        "options": [
          "48/94",
          "19/40",
          "6/27",
          "42/84"
        ],
        "answer": "48/94",
        "correct_value": 0.5106382978723404,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 44/92 or 18/32?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.0842391304347826,
      "pure_math": {
        "question": "Which is larger: 44/92 or 18/32?",
        "options": [
          "54/99",
          "53/97",
          "18/32",
          "44/92"
        ],
        "answer": "18/32",
        "correct_value": 0.5625,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 38/68 or 9/14?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 38/68 or 9/14?",
        "options": [
          "6/15",
          "17/47",
          "38/68",
          "9/14"
        ],
        "answer": "9/14",
        "correct_value": 0.6428571428571429,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000111",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 36/75 or 32/60?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.053333333333333344,
      "pure_math": {
        "question": "Which is larger: 36/75 or 32/60?",
        "options": [
          "35/92",
          "32/60",
          "36/75",
          "11/42"
        ],
        "answer": "32/60",
        "correct_value": 0.5333333333333333,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 45/93 or 29/52?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07382133995037221,
      "pure_math": {
        "question": "Which is larger: 45/93 or 29/52?",
        "options": [
          "29/52",
          "45/93",
          "14/44",
          "27/57"
        ],
        "answer": "29/52",
        "correct_value": 0.5576923076923077,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 33/59 or 31/53?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 33/59 or 31/53?",
        "options": [
          "31/53",
          "33/59",
          "55/98",
          "23/33"
        ],
        "answer": "31/53",
        "correct_value": 0.5849056603773585,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000112",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 7/20 or 34/64?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.18125000000000002,
      "pure_math": {
        "question": "Which is larger: 7/20 or 34/64?",
        "options": [
          "7/20",
          "37/79",
          "34/64",
          "32/87"
        ],
        "answer": "34/64",
        "correct_value": 0.53125,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 24/51 or 52/94?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.08260325406758451,
      "pure_math": {
        "question": "Which is larger: 24/51 or 52/94?",
        "options": [
          "52/94",
          "43/67",
          "20/47",
          "24/51"
        ],
        "answer": "52/94",
        "correct_value": 0.5531914893617021,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 30/54 or 39/67?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 30/54 or 39/67?",
        "options": [
          "30/54",
          "39/67",
          "49/88",
          "8/15"
        ],
        "answer": "39/67",
        "correct_value": 0.582089552238806,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000113",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 8/19 or 50/95?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.10526315789473684,
      "pure_math": {
        "question": "Which is larger: 8/19 or 50/95?",
        "options": [
          "30/56",
          "8/19",
          "34/96",
          "50/95"
        ],
        "answer": "50/95",
        "correct_value": 0.5263157894736842,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 7/14 or 14/26?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.038461538461538436,
      "pure_math": {
        "question": "Which is larger: 7/14 or 14/26?",
        "options": [
          "46/92",
          "14/26",
          "7/14",
          "7/18"
        ],
        "answer": "14/26",
        "correct_value": 0.5384615384615384,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 48/87 or 17/29?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 48/87 or 17/29?",
        "options": [
          "48/87",
          "52/96",
          "17/29",
          "25/57"
        ],
        "answer": "17/29",
        "correct_value": 0.5862068965517241,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000114",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 36/77 or 30/56?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.06818181818181818,
      "pure_math": {
        "question": "Which is larger: 36/77 or 30/56?",
        "options": [
          "36/77",
          "13/41",
          "40/93",
          "30/56"
        ],
        "answer": "30/56",
        "correct_value": 0.5357142857142857,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 35/73 or 42/76?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07317952415284795,
      "pure_math": {
        "question": "Which is larger: 35/73 or 42/76?",
        "options": [
          "42/76",
          "27/81",
          "35/73",
          "43/59"
        ],
        "answer": "42/76",
        "correct_value": 0.5526315789473685,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 21/37 or 52/88?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 21/37 or 52/88?",
        "options": [
          "21/37",
          "33/46",
          "30/72",
          "52/88"
        ],
        "answer": "52/88",
        "correct_value": 0.5909090909090909,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000115",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 32/67 or 18/32?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.08488805970149255,
      "pure_math": {
        "question": "Which is larger: 32/67 or 18/32?",
        "options": [
          "32/67",
          "18/32",
          "33/50",
          "15/21"
        ],
        "answer": "18/32",
        "correct_value": 0.5625,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 38/80 or 43/79?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.06930379746835447,
      "pure_math": {
        "question": "Which is larger: 38/80 or 43/79?",
        "options": [
          "38/80",
          "43/79",
          "12/30",
          "20/47"
        ],
        "answer": "43/79",
        "correct_value": 0.5443037974683544,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 14/25 or 21/35?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 14/25 or 21/35?",
        "options": [
          "21/35",
          "14/25",
          "19/73",
          "9/27"
        ],
        "answer": "21/35",
        "correct_value": 0.6,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000116",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 31/69 or 43/80?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.0882246376811594,
      "pure_math": {
        "question": "Which is larger: 31/69 or 43/80?",
        "options": [
          "43/80",
          "31/69",
          "6/21",
          "24/49"
        ],
        "answer": "43/80",
        "correct_value": 0.5375,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 30/62 or 46/83?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07034589972794403,
      "pure_math": {
        "question": "Which is larger: 30/62 or 46/83?",
        "options": [
          "32/50",
          "6/19",
          "30/62",
          "46/83"
        ],
        "answer": "46/83",
        "correct_value": 0.5542168674698795,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 54/97 or 45/76?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 54/97 or 45/76?",
        "options": [
          "17/54",
          "60/80",
          "45/76",
          "54/97"
        ],
        "answer": "45/76",
        "correct_value": 0.5921052631578947,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000117",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 34/74 or 12/17?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.24642289348171703,
      "pure_math": {
        "question": "Which is larger: 34/74 or 12/17?",
        "options": [
          "34/74",
          "12/17",
          "12/31",
          "11/29"
        ],
        "answer": "12/17",
        "correct_value": 0.7058823529411765,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 26/54 or 42/76?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07115009746588702,
      "pure_math": {
        "question": "Which is larger: 26/54 or 42/76?",
        "options": [
          "16/42",
          "26/54",
          "42/76",
          "13/46"
        ],
        "answer": "42/76",
        "correct_value": 0.5526315789473685,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 49/88 or 46/78?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 49/88 or 46/78?",
        "options": [
          "13/21",
          "33/92",
          "46/78",
          "49/88"
        ],
        "answer": "46/78",
        "correct_value": 0.5897435897435898,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000118",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 38/82 or 9/15?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.1365853658536585,
      "pure_math": {
        "question": "Which is larger: 38/82 or 9/15?",
        "options": [
          "38/82",
          "9/15",
          "7/15",
          "36/93"
        ],
        "answer": "9/15",
        "correct_value": 0.6,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 35/73 or 50/90?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07610350076103506,
      "pure_math": {
        "question": "Which is larger: 35/73 or 50/90?",
        "options": [
          "37/79",
          "35/73",
          "50/90",
          "42/92"
        ],
        "answer": "50/90",
        "correct_value": 0.5555555555555556,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 27/48 or 40/68?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 27/48 or 40/68?",
        "options": [
          "40/68",
          "4/19",
          "27/48",
          "21/30"
        ],
        "answer": "40/68",
        "correct_value": 0.5882352941176471,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000119",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 17/36 or 28/53?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.056079664570230614,
      "pure_math": {
        "question": "Which is larger: 17/36 or 28/53?",
        "options": [
          "35/50",
          "28/53",
          "17/36",
          "34/50"
        ],
        "answer": "28/53",
        "correct_value": 0.5283018867924528,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 27/57 or 41/75?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07298245614035087,
      "pure_math": {
        "question": "Which is larger: 27/57 or 41/75?",
        "options": [
          "26/81",
          "27/57",
          "41/75",
          "19/50"
        ],
        "answer": "41/75",
        "correct_value": 0.5466666666666666,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 37/67 or 24/41?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 37/67 or 24/41?",
        "options": [
          "24/41",
          "37/67",
          "8/28",
          "8/16"
        ],
        "answer": "24/41",
        "correct_value": 0.5853658536585366,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000120",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 18/41 or 18/30?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.16097560975609754,
      "pure_math": {
        "question": "Which is larger: 18/41 or 18/30?",
        "options": [
          "18/30",
          "18/50",
          "18/41",
          "22/30"
        ],
        "answer": "18/30",
        "correct_value": 0.6,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 35/73 or 7/12?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.10388127853881285,
      "pure_math": {
        "question": "Which is larger: 35/73 or 7/12?",
        "options": [
          "11/21",
          "47/74",
          "7/12",
          "35/73"
        ],
        "answer": "7/12",
        "correct_value": 0.5833333333333334,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 9/16 or 10/16?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 9/16 or 10/16?",
        "options": [
          "26/46",
          "10/16",
          "9/16",
          "62/86"
        ],
        "answer": "10/16",
        "correct_value": 0.625,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000121",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 8/23 or 35/65?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.1906354515050167,
      "pure_math": {
        "question": "Which is larger: 8/23 or 35/65?",
        "options": [
          "38/56",
          "26/61",
          "8/23",
          "35/65"
        ],
        "answer": "35/65",
        "correct_value": 0.5384615384615384,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 39/82 or 45/81?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07994579945799463,
      "pure_math": {
        "question": "Which is larger: 39/82 or 45/81?",
        "options": [
          "38/80",
          "19/34",
          "39/82",
          "45/81"
        ],
        "answer": "45/81",
        "correct_value": 0.5555555555555556,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 44/80 or 27/45?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 44/80 or 27/45?",
        "options": [
          "65/89",
          "29/88",
          "27/45",
          "44/80"
        ],
        "answer": "27/45",
        "correct_value": 0.6,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000122",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 27/57 or 29/53?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.07348560079443894,
      "pure_math": {
        "question": "Which is larger: 27/57 or 29/53?",
        "options": [
          "27/57",
          "29/53",
          "10/28",
          "53/87"
        ],
        "answer": "29/53",
        "correct_value": 0.5471698113207547,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 7/15 or 8/14?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.10476190476190472,
      "pure_math": {
        "question": "Which is larger: 7/15 or 8/14?",
        "options": [
          "8/14",
          "7/15",
          "17/27",
          "38/52"
        ],
        "answer": "8/14",
        "correct_value": 0.5714285714285714,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 16/29 or 51/87?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 16/29 or 51/87?",
        "options": [
          "31/51",
          "16/29",
          "51/87",
          "26/75"
        ],
        "answer": "51/87",
        "correct_value": 0.5862068965517241,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000123",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 43/88 or 26/48?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.05303030303030298,
      "pure_math": {
        "question": "Which is larger: 43/88 or 26/48?",
        "options": [
          "50/78",
          "26/48",
          "43/88",
          "50/74"
        ],
        "answer": "26/48",
        "correct_value": 0.5416666666666666,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 27/57 or 29/52?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.08400809716599195,
      "pure_math": {
        "question": "Which is larger: 27/57 or 29/52?",
        "options": [
          "34/63",
          "27/57",
          "31/96",
          "29/52"
        ],
        "answer": "29/52",
        "correct_value": 0.5576923076923077,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 24/43 or 54/93?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 24/43 or 54/93?",
        "options": [
          "57/84",
          "24/43",
          "54/93",
          "10/39"
        ],
        "answer": "54/93",
        "correct_value": 0.5806451612903226,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000124",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 11/28 or 50/97?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.12260677466863029,
      "pure_math": {
        "question": "Which is larger: 11/28 or 50/97?",
        "options": [
          "50/97",
          "27/83",
          "11/28",
          "8/34"
        ],
        "answer": "50/97",
        "correct_value": 0.5154639175257731,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 14/29 or 34/62?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.06562847608453831,
      "pure_math": {
        "question": "Which is larger: 14/29 or 34/62?",
        "options": [
          "14/29",
          "45/62",
          "37/98",
          "34/62"
        ],
        "answer": "34/62",
        "correct_value": 0.5483870967741935,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 42/76 or 21/36?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 42/76 or 21/36?",
        "options": [
          "40/81",
          "21/36",
          "42/76",
          "53/94"
        ],
        "answer": "21/36",
        "correct_value": 0.5833333333333334,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000125",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 32/68 or 42/78?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.0678733031674208,
      "pure_math": {
        "question": "Which is larger: 32/68 or 42/78?",
        "options": [
          "42/78",
          "32/68",
          "65/97",
          "34/55"
        ],
        "answer": "42/78",
        "correct_value": 0.5384615384615384,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 16/34 or 23/41?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.09038737446197997,
      "pure_math": {
        "question": "Which is larger: 16/34 or 23/41?",
        "options": [
          "19/48",
          "23/41",
          "16/34",
          "28/45"
        ],
        "answer": "23/41",
        "correct_value": 0.5609756097560976,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 54/98 or 42/72?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 54/98 or 42/72?",
        "options": [
          "30/54",
          "42/72",
          "54/98",
          "27/50"
        ],
        "answer": "42/72",
        "correct_value": 0.5833333333333334,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000126",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 40/83 or 50/96?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.03890562248995988,
      "pure_math": {
        "question": "Which is larger: 40/83 or 50/96?",
        "options": [
          "41/60",
          "50/96",
          "37/54",
          "40/83"
        ],
        "answer": "50/96",
        "correct_value": 0.5208333333333334,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 22/46 or 11/20?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07173913043478264,
      "pure_math": {
        "question": "Which is larger: 22/46 or 11/20?",
        "options": [
          "22/46",
          "27/54",
          "11/20",
          "39/93"
        ],
        "answer": "11/20",
        "correct_value": 0.55,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 43/78 or 26/44?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 43/78 or 26/44?",
        "options": [
          "7/27",
          "37/81",
          "26/44",
          "43/78"
        ],
        "answer": "26/44",
        "correct_value": 0.5909090909090909,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000127",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 44/95 or 42/77?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.08229665071770331,
      "pure_math": {
        "question": "Which is larger: 44/95 or 42/77?",
        "options": [
          "42/77",
          "44/95",
          "11/22",
          "10/39"
        ],
        "answer": "42/77",
        "correct_value": 0.5454545454545454,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 11/22 or 53/97?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.046391752577319534,
      "pure_math": {
        "question": "Which is larger: 11/22 or 53/97?",
        "options": [
          "53/97",
          "11/22",
          "6/27",
          "30/80"
        ],
        "answer": "53/97",
        "correct_value": 0.5463917525773195,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 40/71 or 54/93?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 40/71 or 54/93?",
        "options": [
          "40/71",
          "17/35",
          "21/51",
          "54/93"
        ],
        "answer": "54/93",
        "correct_value": 0.5806451612903226,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000128",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 36/78 or 9/14?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.18131868131868134,
      "pure_math": {
        "question": "Which is larger: 36/78 or 9/14?",
        "options": [
          "9/32",
          "36/78",
          "9/14",
          "40/60"
        ],
        "answer": "9/14",
        "correct_value": 0.6428571428571429,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 7/14 or 6/11?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.045454545454545414,
      "pure_math": {
        "question": "Which is larger: 7/14 or 6/11?",
        "options": [
          "6/11",
          "27/87",
          "7/14",
          "30/48"
        ],
        "answer": "6/11",
        "correct_value": 0.5454545454545454,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 51/92 or 46/79?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 51/92 or 46/79?",
        "options": [
          "50/77",
          "46/79",
          "51/92",
          "19/27"
        ],
        "answer": "46/79",
        "correct_value": 0.5822784810126582,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000129",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 9/24 or 29/52?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.1826923076923077,
      "pure_math": {
        "question": "Which is larger: 9/24 or 29/52?",
        "options": [
          "8/33",
          "29/52",
          "9/24",
          "33/68"
        ],
        "answer": "29/52",
        "correct_value": 0.5576923076923077,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 15/32 or 48/88?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07670454545454541,
      "pure_math": {
        "question": "Which is larger: 15/32 or 48/88?",
        "options": [
          "48/64",
          "15/32",
          "48/88",
          "47/91"
        ],
        "answer": "48/88",
        "correct_value": 0.5454545454545454,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 53/95 or 13/22?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 53/95 or 13/22?",
        "options": [
          "12/33",
          "37/71",
          "13/22",
          "53/95"
        ],
        "answer": "13/22",
        "correct_value": 0.5909090909090909,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000130",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 27/59 or 22/40?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.09237288135593225,
      "pure_math": {
        "question": "Which is larger: 27/59 or 22/40?",
        "options": [
          "57/84",
          "22/52",
          "27/59",
          "22/40"
        ],
        "answer": "22/40",
        "correct_value": 0.55,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 47/98 or 22/40?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07040816326530619,
      "pure_math": {
        "question": "Which is larger: 47/98 or 22/40?",
        "options": [
          "22/40",
          "5/17",
          "36/69",
          "47/98"
        ],
        "answer": "22/40",
        "correct_value": 0.55,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 54/98 or 15/25?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 54/98 or 15/25?",
        "options": [
          "33/57",
          "40/91",
          "15/25",
          "54/98"
        ],
        "answer": "15/25",
        "correct_value": 0.6,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000131",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 33/71 or 18/29?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.15590092277804762,
      "pure_math": {
        "question": "Which is larger: 33/71 or 18/29?",
        "options": [
          "45/63",
          "44/87",
          "18/29",
          "33/71"
        ],
        "answer": "18/29",
        "correct_value": 0.6206896551724138,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 37/77 or 37/67?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07171932545066878,
      "pure_math": {
        "question": "Which is larger: 37/77 or 37/67?",
        "options": [
          "37/77",
          "42/77",
          "13/19",
          "37/67"
        ],
        "answer": "37/67",
        "correct_value": 0.5522388059701493,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 46/83 or 46/78?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 46/83 or 46/78?",
        "options": [
          "46/83",
          "9/29",
          "46/78",
          "28/51"
        ],
        "answer": "46/78",
        "correct_value": 0.5897435897435898,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000132",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 39/84 or 39/72?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.07738095238095233,
      "pure_math": {
        "question": "Which is larger: 39/84 or 39/72?",
        "options": [
          "19/67",
          "39/72",
          "39/84",
          "25/68"
        ],
        "answer": "39/72",
        "correct_value": 0.5416666666666666,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 39/81 or 38/69?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.06924315619967797,
      "pure_math": {
        "question": "Which is larger: 39/81 or 38/69?",
        "options": [
          "39/81",
          "6/12",
          "38/69",
          "43/96"
        ],
        "answer": "38/69",
        "correct_value": 0.5507246376811594,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 47/84 or 12/19?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 47/84 or 12/19?",
        "options": [
          "47/84",
          "35/54",
          "9/15",
          "12/19"
        ],
        "answer": "12/19",
        "correct_value": 0.631578947368421,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000133",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 6/18 or 37/70?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.19523809523809527,
      "pure_math": {
        "question": "Which is larger: 6/18 or 37/70?",
        "options": [
          "37/70",
          "26/62",
          "6/18",
          "18/27"
        ],
        "answer": "37/70",
        "correct_value": 0.5285714285714286,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 32/67 or 32/58?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07411219763252702,
      "pure_math": {
        "question": "Which is larger: 32/67 or 32/58?",
        "options": [
          "32/58",
          "66/97",
          "16/58",
          "32/67"
        ],
        "answer": "32/58",
        "correct_value": 0.5517241379310345,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 14/25 or 19/32?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 14/25 or 19/32?",
        "options": [
          "27/77",
          "44/78",
          "19/32",
          "14/25"
        ],
        "answer": "19/32",
        "correct_value": 0.59375,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000134",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 23/48 or 38/69?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.07155797101449274,
      "pure_math": {
        "question": "Which is larger: 23/48 or 38/69?",
        "options": [
          "46/79",
          "43/78",
          "38/69",
          "23/48"
        ],
        "answer": "38/69",
        "correct_value": 0.5507246376811594,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 26/54 or 16/29?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07024265644955302,
      "pure_math": {
        "question": "Which is larger: 26/54 or 16/29?",
        "options": [
          "26/54",
          "16/29",
          "17/45",
          "6/24"
        ],
        "answer": "16/29",
        "correct_value": 0.5517241379310345,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 22/40 or 21/36?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 22/40 or 21/36?",
        "options": [
          "22/40",
          "21/36",
          "5/18",
          "23/86"
        ],
        "answer": "21/36",
        "correct_value": 0.5833333333333334,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000135",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 18/41 or 10/15?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.2276422764227642,
      "pure_math": {
        "question": "Which is larger: 18/41 or 10/15?",
        "options": [
          "10/15",
          "10/37",
          "26/39",
          "18/41"
        ],
        "answer": "10/15",
        "correct_value": 0.6666666666666666,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 19/39 or 46/83?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.06703738029039236,
      "pure_math": {
        "question": "Which is larger: 19/39 or 46/83?",
        "options": [
          "64/86",
          "19/39",
          "46/83",
          "30/50"
        ],
        "answer": "46/83",
        "correct_value": 0.5542168674698795,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 16/28 or 55/94?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 16/28 or 55/94?",
        "options": [
          "16/28",
          "34/62",
          "55/94",
          "33/76"
        ],
        "answer": "55/94",
        "correct_value": 0.5851063829787234,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000136",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 43/90 or 51/96?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.0534722222222222,
      "pure_math": {
        "question": "Which is larger: 43/90 or 51/96?",
        "options": [
          "51/96",
          "43/90",
          "21/73",
          "33/54"
        ],
        "answer": "51/96",
        "correct_value": 0.53125,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 48/99 or 35/63?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07070707070707072,
      "pure_math": {
        "question": "Which is larger: 48/99 or 35/63?",
        "options": [
          "35/63",
          "24/48",
          "24/62",
          "48/99"
        ],
        "answer": "35/63",
        "correct_value": 0.5555555555555556,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 22/40 or 23/38?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 22/40 or 23/38?",
        "options": [
          "34/48",
          "22/40",
          "23/38",
          "19/28"
        ],
        "answer": "23/38",
        "correct_value": 0.6052631578947368,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000137",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 30/63 or 42/81?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.042328042328042326,
      "pure_math": {
        "question": "Which is larger: 30/63 or 42/81?",
        "options": [
          "30/63",
          "42/81",
          "16/42",
          "21/59"
        ],
        "answer": "42/81",
        "correct_value": 0.5185185185185185,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 32/67 or 31/57?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.06624770882429959,
      "pure_math": {
        "question": "Which is larger: 32/67 or 31/57?",
        "options": [
          "9/34",
          "31/57",
          "32/67",
          "13/21"
        ],
        "answer": "31/57",
        "correct_value": 0.543859649122807,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 11/19 or 20/34?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 11/19 or 20/34?",
        "options": [
          "63/85",
          "11/19",
          "20/34",
          "33/81"
        ],
        "answer": "20/34",
        "correct_value": 0.5882352941176471,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000138",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 21/48 or 7/11?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.19886363636363635,
      "pure_math": {
        "question": "Which is larger: 21/48 or 7/11?",
        "options": [
          "17/25",
          "7/11",
          "32/71",
          "21/48"
        ],
        "answer": "7/11",
        "correct_value": 0.6363636363636364,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 38/80 or 28/51?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07401960784313732,
      "pure_math": {
        "question": "Which is larger: 38/80 or 28/51?",
        "options": [
          "28/51",
          "51/69",
          "38/80",
          "23/46"
        ],
        "answer": "28/51",
        "correct_value": 0.5490196078431373,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 31/56 or 44/75?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 31/56 or 44/75?",
        "options": [
          "47/73",
          "44/75",
          "31/56",
          "16/22"
        ],
        "answer": "44/75",
        "correct_value": 0.5866666666666667,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000139",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 26/57 or 26/50?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.06385964912280706,
      "pure_math": {
        "question": "Which is larger: 26/57 or 26/50?",
        "options": [
          "26/50",
          "26/57",
          "7/28",
          "34/82"
        ],
        "answer": "26/50",
        "correct_value": 0.52,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 23/47 or 16/29?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.062362435803374916,
      "pure_math": {
        "question": "Which is larger: 23/47 or 16/29?",
        "options": [
          "16/29",
          "18/35",
          "21/39",
          "23/47"
        ],
        "answer": "16/29",
        "correct_value": 0.5517241379310345,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 24/42 or 42/72?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 24/42 or 42/72?",
        "options": [
          "24/42",
          "27/68",
          "42/72",
          "54/92"
        ],
        "answer": "42/72",
        "correct_value": 0.5833333333333334,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000140",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 36/79 or 39/72?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.08597046413502107,
      "pure_math": {
        "question": "Which is larger: 36/79 or 39/72?",
        "options": [
          "36/79",
          "21/77",
          "26/92",
          "39/72"
        ],
        "answer": "39/72",
        "correct_value": 0.5416666666666666,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 5/10 or 34/62?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.048387096774193505,
      "pure_math": {
        "question": "Which is larger: 5/10 or 34/62?",
        "options": [
          "5/10",
          "36/90",
          "19/27",
          "34/62"
        ],
        "answer": "34/62",
        "correct_value": 0.5483870967741935,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 7/11 or 22/37?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 7/11 or 22/37?",
        "options": [
          "7/11",
          "22/37",
          "47/74",
          "15/57"
        ],
        "answer": "7/11",
        "correct_value": 0.6363636363636364,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000141",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 5/12 or 8/10?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.38333333333333336,
      "pure_math": {
        "question": "Which is larger: 5/12 or 8/10?",
        "options": [
          "8/10",
          "5/12",
          "7/12",
          "15/62"
        ],
        "answer": "8/10",
        "correct_value": 0.8,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 6/12 or 41/74?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.05405405405405406,
      "pure_math": {
        "question": "Which is larger: 6/12 or 41/74?",
        "options": [
          "6/12",
          "67/99",
          "27/65",
          "41/74"
        ],
        "answer": "41/74",
        "correct_value": 0.5540540540540541,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 22/40 or 20/34?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 22/40 or 20/34?",
        "options": [
          "21/42",
          "20/34",
          "22/40",
          "55/89"
        ],
        "answer": "20/34",
        "correct_value": 0.5882352941176471,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000142",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 26/57 or 34/61?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.10123669830313486,
      "pure_math": {
        "question": "Which is larger: 26/57 or 34/61?",
        "options": [
          "26/57",
          "33/48",
          "17/41",
          "34/61"
        ],
        "answer": "34/61",
        "correct_value": 0.5573770491803278,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 10/21 or 34/61?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.08118657298985166,
      "pure_math": {
        "question": "Which is larger: 10/21 or 34/61?",
        "options": [
          "10/21",
          "50/80",
          "26/58",
          "34/61"
        ],
        "answer": "34/61",
        "correct_value": 0.5573770491803278,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 55/99 or 18/31?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 55/99 or 18/31?",
        "options": [
          "55/99",
          "37/65",
          "12/20",
          "18/31"
        ],
        "answer": "18/31",
        "correct_value": 0.5806451612903226,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000143",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 18/39 or 22/37?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.13305613305613306,
      "pure_math": {
        "question": "Which is larger: 18/39 or 22/37?",
        "options": [
          "18/39",
          "22/37",
          "4/15",
          "34/70"
        ],
        "answer": "22/37",
        "correct_value": 0.5945945945945946,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 15/32 or 28/50?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.09125000000000005,
      "pure_math": {
        "question": "Which is larger: 15/32 or 28/50?",
        "options": [
          "4/12",
          "15/32",
          "28/50",
          "30/85"
        ],
        "answer": "28/50",
        "correct_value": 0.56,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 17/30 or 48/82?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 17/30 or 48/82?",
        "options": [
          "35/59",
          "48/82",
          "17/30",
          "28/40"
        ],
        "answer": "48/82",
        "correct_value": 0.5853658536585366,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000144",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 48/98 or 13/20?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.1602040816326531,
      "pure_math": {
        "question": "Which is larger: 48/98 or 13/20?",
        "options": [
          "14/54",
          "11/22",
          "13/20",
          "48/98"
        ],
        "answer": "13/20",
        "correct_value": 0.65,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 42/87 or 48/88?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.06269592476489022,
      "pure_math": {
        "question": "Which is larger: 42/87 or 48/88?",
        "options": [
          "48/88",
          "12/51",
          "42/87",
          "46/86"
        ],
        "answer": "48/88",
        "correct_value": 0.5454545454545454,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 22/39 or 32/55?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 22/39 or 32/55?",
        "options": [
          "44/80",
          "22/39",
          "32/55",
          "27/65"
        ],
        "answer": "32/55",
        "correct_value": 0.5818181818181818,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000145",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 17/41 or 12/19?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.21694480102695762,
      "pure_math": {
        "question": "Which is larger: 17/41 or 12/19?",
        "options": [
          "12/19",
          "13/29",
          "17/41",
          "31/91"
        ],
        "answer": "12/19",
        "correct_value": 0.631578947368421,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 11/23 or 12/21?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.09316770186335399,
      "pure_math": {
        "question": "Which is larger: 11/23 or 12/21?",
        "options": [
          "11/23",
          "39/66",
          "12/21",
          "4/10"
        ],
        "answer": "12/21",
        "correct_value": 0.5714285714285714,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 12/21 or 20/33?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 12/21 or 20/33?",
        "options": [
          "12/21",
          "44/65",
          "20/33",
          "55/81"
        ],
        "answer": "20/33",
        "correct_value": 0.6060606060606061,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000146",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 9/21 or 29/55?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.09870129870129868,
      "pure_math": {
        "question": "Which is larger: 9/21 or 29/55?",
        "options": [
          "24/51",
          "59/86",
          "9/21",
          "29/55"
        ],
        "answer": "29/55",
        "correct_value": 0.5272727272727272,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 28/59 or 11/20?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.07542372881355935,
      "pure_math": {
        "question": "Which is larger: 28/59 or 11/20?",
        "options": [
          "11/20",
          "53/83",
          "35/81",
          "28/59"
        ],
        "answer": "11/20",
        "correct_value": 0.55,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 18/31 or 16/27?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 18/31 or 16/27?",
        "options": [
          "26/44",
          "20/44",
          "16/27",
          "18/31"
        ],
        "answer": "16/27",
        "correct_value": 0.5925925925925926,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000147",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 30/65 or 25/45?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.09401709401709402,
      "pure_math": {
        "question": "Which is larger: 30/65 or 25/45?",
        "options": [
          "25/45",
          "22/56",
          "21/71",
          "30/65"
        ],
        "answer": "25/45",
        "correct_value": 0.5555555555555556,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 41/86 or 48/88?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.06871035940803377,
      "pure_math": {
        "question": "Which is larger: 41/86 or 48/88?",
        "options": [
          "7/23",
          "41/86",
          "48/88",
          "22/35"
        ],
        "answer": "48/88",
        "correct_value": 0.5454545454545454,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 29/52 or 52/89?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 29/52 or 52/89?",
        "options": [
          "27/52",
          "52/89",
          "29/52",
          "39/58"
        ],
        "answer": "52/89",
        "correct_value": 0.5842696629213483,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000148",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 23/48 or 29/51?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.08946078431372545,
      "pure_math": {
        "question": "Which is larger: 23/48 or 29/51?",
        "options": [
          "29/51",
          "23/35",
          "23/48",
          "17/50"
        ],
        "answer": "29/51",
        "correct_value": 0.5686274509803921,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 47/98 or 50/91?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.06985871271585564,
      "pure_math": {
        "question": "Which is larger: 47/98 or 50/91?",
        "options": [
          "50/91",
          "54/72",
          "47/98",
          "20/41"
        ],
        "answer": "50/91",
        "correct_value": 0.5494505494505495,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 31/56 or 14/24?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 31/56 or 14/24?",
        "options": [
          "55/85",
          "14/24",
          "32/82",
          "31/56"
        ],
        "answer": "14/24",
        "correct_value": 0.5833333333333334,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000149",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 32/69 or 20/36?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.09178743961352659,
      "pure_math": {
        "question": "Which is larger: 32/69 or 20/36?",
        "options": [
          "20/36",
          "46/62",
          "28/98",
          "32/69"
        ],
        "answer": "20/36",
        "correct_value": 0.5555555555555556,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 19/40 or 23/42?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.0726190476190477,
      "pure_math": {
        "question": "Which is larger: 19/40 or 23/42?",
        "options": [
          "40/64",
          "32/94",
          "19/40",
          "23/42"
        ],
        "answer": "23/42",
        "correct_value": 0.5476190476190477,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 47/84 or 36/61?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 47/84 or 36/61?",
        "options": [
          "51/78",
          "50/98",
          "47/84",
          "36/61"
        ],
        "answer": "36/61",
        "correct_value": 0.5901639344262295,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "relative_distance_000150",
    "category": "relative_distance",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "Which is larger: 10/23 or 24/41?",
      "ns_shortcut": "One is below 1/2, the other above; no computation needed.",
      "shortcut_strength": 0.1505832449628844,
      "pure_math": {
        "question": "Which is larger: 10/23 or 24/41?",
        "options": [
          "62/92",
          "10/23",
          "18/55",
          "24/41"
        ],
        "answer": "24/41",
        "correct_value": 0.5853658536585366,
        "explanation": "Both straddle 1/2; compare to benchmark."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "Which is larger: 25/52 or 36/65?",
      "ns_shortcut": "Compare to 1/2, but margin is tight.",
      "shortcut_strength": 0.0730769230769231,
      "pure_math": {
        "question": "Which is larger: 25/52 or 36/65?",
        "options": [
          "9/22",
          "36/65",
          "5/23",
          "25/52"
        ],
        "answer": "36/65",
        "correct_value": 0.5538461538461539,
        "explanation": "One is very close to 1/2, shortcut harder to apply."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "Which is larger: 37/67 or 34/57?",
      "ns_shortcut": "Both on same side; must cross-multiply.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Which is larger: 37/67 or 34/57?",
        "options": [
          "29/60",
          "34/57",
          "61/96",
          "37/67"
        ],
        "answer": "34/57",
        "correct_value": 0.5964912280701754,
        "explanation": "Both above 1/2; benchmark comparison won't help."
      }
    }
  },
  {
    "family_id": "cancellation_identity_000151",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "71 + 28 - 27",
      "ns_shortcut": "Near-cancellation: 28 - 27 = 1, so answer ≈ 71 + 1.",
      "shortcut_strength": 0.9642857142857143,
      "pure_math": {
        "question": "Evaluate: 71 + 28 - 27",
        "options": [
          "82",
          "92",
          "72",
          "62"
        ],
        "answer": "72",
        "correct_value": 72,
        "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": "71 + 28 - 38",
      "ns_shortcut": "Near-cancellation: 28 - 38 = -10, offset is manageable.",
      "shortcut_strength": 0.6428571428571428,
      "pure_math": {
        "question": "Evaluate: 71 + 28 - 38",
        "options": [
          "61",
          "51",
          "71",
          "81"
        ],
        "answer": "61",
        "correct_value": 61,
        "explanation": "B-C = -10; still a moderate shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "71 + 28 - 118",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 71 + 28 - 118",
        "options": [
          "-19",
          "-1",
          "-11",
          "-31"
        ],
        "answer": "-19",
        "correct_value": -19,
        "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_000152",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "22 + 71 - 69",
      "ns_shortcut": "Near-cancellation: 71 - 69 = 2, so answer ≈ 22 + 2.",
      "shortcut_strength": 0.971830985915493,
      "pure_math": {
        "question": "Evaluate: 22 + 71 - 69",
        "options": [
          "14",
          "34",
          "24",
          "44"
        ],
        "answer": "24",
        "correct_value": 24,
        "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": "22 + 71 - 77",
      "ns_shortcut": "Near-cancellation: 71 - 77 = -6, offset is manageable.",
      "shortcut_strength": 0.9154929577464789,
      "pure_math": {
        "question": "Evaluate: 22 + 71 - 77",
        "options": [
          "36",
          "6",
          "26",
          "16"
        ],
        "answer": "16",
        "correct_value": 16,
        "explanation": "B-C = -6; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "22 + 71 - 154",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 22 + 71 - 154",
        "options": [
          "-79",
          "-61",
          "-49",
          "-59"
        ],
        "answer": "-61",
        "correct_value": -61,
        "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_000153",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "80 + 35 - 34",
      "ns_shortcut": "Near-cancellation: 35 - 34 = 1, so answer ≈ 80 + 1.",
      "shortcut_strength": 0.9714285714285714,
      "pure_math": {
        "question": "Evaluate: 80 + 35 - 34",
        "options": [
          "101",
          "81",
          "91",
          "71"
        ],
        "answer": "81",
        "correct_value": 81,
        "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": "80 + 35 - 20",
      "ns_shortcut": "Near-cancellation: 35 - 20 = 15, offset is manageable.",
      "shortcut_strength": 0.5714285714285714,
      "pure_math": {
        "question": "Evaluate: 80 + 35 - 20",
        "options": [
          "115",
          "85",
          "95",
          "105"
        ],
        "answer": "95",
        "correct_value": 95,
        "explanation": "B-C = 15; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "80 + 35 - 100",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 80 + 35 - 100",
        "options": [
          "15",
          "35",
          "5",
          "25"
        ],
        "answer": "15",
        "correct_value": 15,
        "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_000154",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "59 + 15 - 16",
      "ns_shortcut": "Near-cancellation: 15 - 16 = -1, so answer ≈ 59 + -1.",
      "shortcut_strength": 0.9333333333333333,
      "pure_math": {
        "question": "Evaluate: 59 + 15 - 16",
        "options": [
          "78",
          "58",
          "48",
          "68"
        ],
        "answer": "58",
        "correct_value": 58,
        "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": "59 + 15 - 28",
      "ns_shortcut": "Near-cancellation: 15 - 28 = -13, offset is manageable.",
      "shortcut_strength": 0.1333333333333333,
      "pure_math": {
        "question": "Evaluate: 59 + 15 - 28",
        "options": [
          "46",
          "66",
          "36",
          "56"
        ],
        "answer": "46",
        "correct_value": 46,
        "explanation": "B-C = -13; still a moderate shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "59 + 15 - 67",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 59 + 15 - 67",
        "options": [
          "-3",
          "27",
          "17",
          "7"
        ],
        "answer": "7",
        "correct_value": 7,
        "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_000155",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "77 + 55 - 53",
      "ns_shortcut": "Near-cancellation: 55 - 53 = 2, so answer ≈ 77 + 2.",
      "shortcut_strength": 0.9636363636363636,
      "pure_math": {
        "question": "Evaluate: 77 + 55 - 53",
        "options": [
          "89",
          "79",
          "99",
          "69"
        ],
        "answer": "79",
        "correct_value": 79,
        "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": "77 + 55 - 45",
      "ns_shortcut": "Near-cancellation: 55 - 45 = 10, offset is manageable.",
      "shortcut_strength": 0.8181818181818181,
      "pure_math": {
        "question": "Evaluate: 77 + 55 - 45",
        "options": [
          "97",
          "87",
          "107",
          "77"
        ],
        "answer": "87",
        "correct_value": 87,
        "explanation": "B-C = 10; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "77 + 55 - 138",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 77 + 55 - 138",
        "options": [
          "-4",
          "-24",
          "6",
          "-6"
        ],
        "answer": "-6",
        "correct_value": -6,
        "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_000156",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "50 + 30 - 31",
      "ns_shortcut": "Near-cancellation: 30 - 31 = -1, so answer ≈ 50 + -1.",
      "shortcut_strength": 0.9666666666666667,
      "pure_math": {
        "question": "Evaluate: 50 + 30 - 31",
        "options": [
          "59",
          "39",
          "49",
          "69"
        ],
        "answer": "49",
        "correct_value": 49,
        "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": "50 + 30 - 23",
      "ns_shortcut": "Near-cancellation: 30 - 23 = 7, offset is manageable.",
      "shortcut_strength": 0.7666666666666666,
      "pure_math": {
        "question": "Evaluate: 50 + 30 - 23",
        "options": [
          "77",
          "57",
          "67",
          "47"
        ],
        "answer": "57",
        "correct_value": 57,
        "explanation": "B-C = 7; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "50 + 30 - 106",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 50 + 30 - 106",
        "options": [
          "-14",
          "-24",
          "-26",
          "-44"
        ],
        "answer": "-26",
        "correct_value": -26,
        "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_000157",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "91 + 83 - 84",
      "ns_shortcut": "Near-cancellation: 83 - 84 = -1, so answer ≈ 91 + -1.",
      "shortcut_strength": 0.9879518072289156,
      "pure_math": {
        "question": "Evaluate: 91 + 83 - 84",
        "options": [
          "90",
          "110",
          "80",
          "100"
        ],
        "answer": "90",
        "correct_value": 90,
        "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": "91 + 83 - 90",
      "ns_shortcut": "Near-cancellation: 83 - 90 = -7, offset is manageable.",
      "shortcut_strength": 0.9156626506024097,
      "pure_math": {
        "question": "Evaluate: 91 + 83 - 90",
        "options": [
          "74",
          "84",
          "94",
          "104"
        ],
        "answer": "84",
        "correct_value": 84,
        "explanation": "B-C = -7; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "91 + 83 - 21",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 91 + 83 - 21",
        "options": [
          "163",
          "173",
          "153",
          "143"
        ],
        "answer": "153",
        "correct_value": 153,
        "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_000158",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "59 + 86 - 84",
      "ns_shortcut": "Near-cancellation: 86 - 84 = 2, so answer ≈ 59 + 2.",
      "shortcut_strength": 0.9767441860465116,
      "pure_math": {
        "question": "Evaluate: 59 + 86 - 84",
        "options": [
          "61",
          "71",
          "81",
          "51"
        ],
        "answer": "61",
        "correct_value": 61,
        "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": "59 + 86 - 74",
      "ns_shortcut": "Near-cancellation: 86 - 74 = 12, offset is manageable.",
      "shortcut_strength": 0.8604651162790697,
      "pure_math": {
        "question": "Evaluate: 59 + 86 - 74",
        "options": [
          "81",
          "91",
          "71",
          "61"
        ],
        "answer": "71",
        "correct_value": 71,
        "explanation": "B-C = 12; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "59 + 86 - 10",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 59 + 86 - 10",
        "options": [
          "155",
          "135",
          "125",
          "145"
        ],
        "answer": "135",
        "correct_value": 135,
        "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_000159",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "45 + 43 - 42",
      "ns_shortcut": "Near-cancellation: 43 - 42 = 1, so answer ≈ 45 + 1.",
      "shortcut_strength": 0.9767441860465116,
      "pure_math": {
        "question": "Evaluate: 45 + 43 - 42",
        "options": [
          "46",
          "66",
          "36",
          "56"
        ],
        "answer": "46",
        "correct_value": 46,
        "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": "45 + 43 - 57",
      "ns_shortcut": "Near-cancellation: 43 - 57 = -14, offset is manageable.",
      "shortcut_strength": 0.6744186046511628,
      "pure_math": {
        "question": "Evaluate: 45 + 43 - 57",
        "options": [
          "21",
          "51",
          "41",
          "31"
        ],
        "answer": "31",
        "correct_value": 31,
        "explanation": "B-C = -14; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "45 + 43 - 117",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 45 + 43 - 117",
        "options": [
          "-21",
          "-29",
          "-11",
          "-41"
        ],
        "answer": "-29",
        "correct_value": -29,
        "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_000160",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "64 + 28 - 29",
      "ns_shortcut": "Near-cancellation: 28 - 29 = -1, so answer ≈ 64 + -1.",
      "shortcut_strength": 0.9642857142857143,
      "pure_math": {
        "question": "Evaluate: 64 + 28 - 29",
        "options": [
          "53",
          "73",
          "63",
          "83"
        ],
        "answer": "63",
        "correct_value": 63,
        "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": "64 + 28 - 18",
      "ns_shortcut": "Near-cancellation: 28 - 18 = 10, offset is manageable.",
      "shortcut_strength": 0.6428571428571428,
      "pure_math": {
        "question": "Evaluate: 64 + 28 - 18",
        "options": [
          "94",
          "64",
          "84",
          "74"
        ],
        "answer": "74",
        "correct_value": 74,
        "explanation": "B-C = 10; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "64 + 28 - 117",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 64 + 28 - 117",
        "options": [
          "-25",
          "-35",
          "-5",
          "-15"
        ],
        "answer": "-25",
        "correct_value": -25,
        "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_000161",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "88 + 69 - 70",
      "ns_shortcut": "Near-cancellation: 69 - 70 = -1, so answer ≈ 88 + -1.",
      "shortcut_strength": 0.9855072463768116,
      "pure_math": {
        "question": "Evaluate: 88 + 69 - 70",
        "options": [
          "77",
          "107",
          "87",
          "97"
        ],
        "answer": "87",
        "correct_value": 87,
        "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": "88 + 69 - 83",
      "ns_shortcut": "Near-cancellation: 69 - 83 = -14, offset is manageable.",
      "shortcut_strength": 0.7971014492753623,
      "pure_math": {
        "question": "Evaluate: 88 + 69 - 83",
        "options": [
          "74",
          "84",
          "64",
          "94"
        ],
        "answer": "74",
        "correct_value": 74,
        "explanation": "B-C = -14; still a moderate shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "88 + 69 - 147",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 88 + 69 - 147",
        "options": [
          "10",
          "20",
          "0",
          "30"
        ],
        "answer": "10",
        "correct_value": 10,
        "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_000162",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "47 + 88 - 87",
      "ns_shortcut": "Near-cancellation: 88 - 87 = 1, so answer ≈ 47 + 1.",
      "shortcut_strength": 0.9886363636363636,
      "pure_math": {
        "question": "Evaluate: 47 + 88 - 87",
        "options": [
          "68",
          "58",
          "38",
          "48"
        ],
        "answer": "48",
        "correct_value": 48,
        "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": "47 + 88 - 97",
      "ns_shortcut": "Near-cancellation: 88 - 97 = -9, offset is manageable.",
      "shortcut_strength": 0.8977272727272727,
      "pure_math": {
        "question": "Evaluate: 47 + 88 - 97",
        "options": [
          "28",
          "38",
          "58",
          "48"
        ],
        "answer": "38",
        "correct_value": 38,
        "explanation": "B-C = -9; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "47 + 88 - 33",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 47 + 88 - 33",
        "options": [
          "92",
          "112",
          "102",
          "122"
        ],
        "answer": "102",
        "correct_value": 102,
        "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_000163",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "72 + 33 - 32",
      "ns_shortcut": "Near-cancellation: 33 - 32 = 1, so answer ≈ 72 + 1.",
      "shortcut_strength": 0.9696969696969697,
      "pure_math": {
        "question": "Evaluate: 72 + 33 - 32",
        "options": [
          "73",
          "93",
          "83",
          "63"
        ],
        "answer": "73",
        "correct_value": 73,
        "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": "72 + 33 - 48",
      "ns_shortcut": "Near-cancellation: 33 - 48 = -15, offset is manageable.",
      "shortcut_strength": 0.5454545454545454,
      "pure_math": {
        "question": "Evaluate: 72 + 33 - 48",
        "options": [
          "47",
          "77",
          "67",
          "57"
        ],
        "answer": "57",
        "correct_value": 57,
        "explanation": "B-C = -15; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "72 + 33 - 117",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 72 + 33 - 117",
        "options": [
          "-12",
          "2",
          "-8",
          "-28"
        ],
        "answer": "-12",
        "correct_value": -12,
        "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_000164",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "84 + 15 - 17",
      "ns_shortcut": "Near-cancellation: 15 - 17 = -2, so answer ≈ 84 + -2.",
      "shortcut_strength": 0.8666666666666667,
      "pure_math": {
        "question": "Evaluate: 84 + 15 - 17",
        "options": [
          "82",
          "92",
          "102",
          "72"
        ],
        "answer": "82",
        "correct_value": 82,
        "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": "84 + 15 - 28",
      "ns_shortcut": "Near-cancellation: 15 - 28 = -13, offset is manageable.",
      "shortcut_strength": 0.1333333333333333,
      "pure_math": {
        "question": "Evaluate: 84 + 15 - 28",
        "options": [
          "91",
          "81",
          "71",
          "61"
        ],
        "answer": "71",
        "correct_value": 71,
        "explanation": "B-C = -13; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "84 + 15 - 68",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 84 + 15 - 68",
        "options": [
          "31",
          "21",
          "41",
          "51"
        ],
        "answer": "31",
        "correct_value": 31,
        "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_000165",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "53 + 85 - 86",
      "ns_shortcut": "Near-cancellation: 85 - 86 = -1, so answer ≈ 53 + -1.",
      "shortcut_strength": 0.9882352941176471,
      "pure_math": {
        "question": "Evaluate: 53 + 85 - 86",
        "options": [
          "72",
          "52",
          "62",
          "42"
        ],
        "answer": "52",
        "correct_value": 52,
        "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": "53 + 85 - 91",
      "ns_shortcut": "Near-cancellation: 85 - 91 = -6, offset is manageable.",
      "shortcut_strength": 0.9294117647058824,
      "pure_math": {
        "question": "Evaluate: 53 + 85 - 91",
        "options": [
          "57",
          "67",
          "47",
          "37"
        ],
        "answer": "47",
        "correct_value": 47,
        "explanation": "B-C = -6; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "53 + 85 - 135",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 53 + 85 - 135",
        "options": [
          "23",
          "13",
          "3",
          "-7"
        ],
        "answer": "3",
        "correct_value": 3,
        "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_000166",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "35 + 31 - 30",
      "ns_shortcut": "Near-cancellation: 31 - 30 = 1, so answer ≈ 35 + 1.",
      "shortcut_strength": 0.967741935483871,
      "pure_math": {
        "question": "Evaluate: 35 + 31 - 30",
        "options": [
          "56",
          "36",
          "26",
          "46"
        ],
        "answer": "36",
        "correct_value": 36,
        "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": "35 + 31 - 22",
      "ns_shortcut": "Near-cancellation: 31 - 22 = 9, offset is manageable.",
      "shortcut_strength": 0.7096774193548387,
      "pure_math": {
        "question": "Evaluate: 35 + 31 - 22",
        "options": [
          "64",
          "34",
          "54",
          "44"
        ],
        "answer": "44",
        "correct_value": 44,
        "explanation": "B-C = 9; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "35 + 31 - 74",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 35 + 31 - 74",
        "options": [
          "-2",
          "-8",
          "-22",
          "8"
        ],
        "answer": "-8",
        "correct_value": -8,
        "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_000167",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "64 + 26 - 28",
      "ns_shortcut": "Near-cancellation: 26 - 28 = -2, so answer ≈ 64 + -2.",
      "shortcut_strength": 0.9230769230769231,
      "pure_math": {
        "question": "Evaluate: 64 + 26 - 28",
        "options": [
          "82",
          "72",
          "52",
          "62"
        ],
        "answer": "62",
        "correct_value": 62,
        "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": "64 + 26 - 33",
      "ns_shortcut": "Near-cancellation: 26 - 33 = -7, offset is manageable.",
      "shortcut_strength": 0.7307692307692308,
      "pure_math": {
        "question": "Evaluate: 64 + 26 - 33",
        "options": [
          "57",
          "47",
          "77",
          "67"
        ],
        "answer": "57",
        "correct_value": 57,
        "explanation": "B-C = -7; still a moderate shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "64 + 26 - 66",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 64 + 26 - 66",
        "options": [
          "14",
          "34",
          "24",
          "44"
        ],
        "answer": "24",
        "correct_value": 24,
        "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_000168",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 + 31 - 29",
      "ns_shortcut": "Near-cancellation: 31 - 29 = 2, so answer ≈ 98 + 2.",
      "shortcut_strength": 0.935483870967742,
      "pure_math": {
        "question": "Evaluate: 98 + 31 - 29",
        "options": [
          "120",
          "110",
          "90",
          "100"
        ],
        "answer": "100",
        "correct_value": 100,
        "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": "98 + 31 - 37",
      "ns_shortcut": "Near-cancellation: 31 - 37 = -6, offset is manageable.",
      "shortcut_strength": 0.8064516129032258,
      "pure_math": {
        "question": "Evaluate: 98 + 31 - 37",
        "options": [
          "82",
          "112",
          "102",
          "92"
        ],
        "answer": "92",
        "correct_value": 92,
        "explanation": "B-C = -6; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "98 + 31 - 90",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 98 + 31 - 90",
        "options": [
          "49",
          "59",
          "39",
          "29"
        ],
        "answer": "39",
        "correct_value": 39,
        "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_000169",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "18 + 82 - 84",
      "ns_shortcut": "Near-cancellation: 82 - 84 = -2, so answer ≈ 18 + -2.",
      "shortcut_strength": 0.975609756097561,
      "pure_math": {
        "question": "Evaluate: 18 + 82 - 84",
        "options": [
          "16",
          "36",
          "6",
          "26"
        ],
        "answer": "16",
        "correct_value": 16,
        "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": "18 + 82 - 97",
      "ns_shortcut": "Near-cancellation: 82 - 97 = -15, offset is manageable.",
      "shortcut_strength": 0.8170731707317074,
      "pure_math": {
        "question": "Evaluate: 18 + 82 - 97",
        "options": [
          "3",
          "23",
          "-7",
          "13"
        ],
        "answer": "3",
        "correct_value": 3,
        "explanation": "B-C = -15; still a moderate shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "18 + 82 - 29",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 18 + 82 - 29",
        "options": [
          "81",
          "91",
          "61",
          "71"
        ],
        "answer": "71",
        "correct_value": 71,
        "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_000170",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "85 + 64 - 63",
      "ns_shortcut": "Near-cancellation: 64 - 63 = 1, so answer ≈ 85 + 1.",
      "shortcut_strength": 0.984375,
      "pure_math": {
        "question": "Evaluate: 85 + 64 - 63",
        "options": [
          "106",
          "86",
          "96",
          "76"
        ],
        "answer": "86",
        "correct_value": 86,
        "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": "85 + 64 - 73",
      "ns_shortcut": "Near-cancellation: 64 - 73 = -9, offset is manageable.",
      "shortcut_strength": 0.859375,
      "pure_math": {
        "question": "Evaluate: 85 + 64 - 73",
        "options": [
          "96",
          "86",
          "66",
          "76"
        ],
        "answer": "76",
        "correct_value": 76,
        "explanation": "B-C = -9; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "85 + 64 - 153",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 85 + 64 - 153",
        "options": [
          "4",
          "-16",
          "-4",
          "14"
        ],
        "answer": "-4",
        "correct_value": -4,
        "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_000171",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "60 + 52 - 54",
      "ns_shortcut": "Near-cancellation: 52 - 54 = -2, so answer ≈ 60 + -2.",
      "shortcut_strength": 0.9615384615384616,
      "pure_math": {
        "question": "Evaluate: 60 + 52 - 54",
        "options": [
          "58",
          "78",
          "48",
          "68"
        ],
        "answer": "58",
        "correct_value": 58,
        "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": "60 + 52 - 60",
      "ns_shortcut": "Near-cancellation: 52 - 60 = -8, offset is manageable.",
      "shortcut_strength": 0.8461538461538461,
      "pure_math": {
        "question": "Evaluate: 60 + 52 - 60",
        "options": [
          "62",
          "52",
          "72",
          "42"
        ],
        "answer": "52",
        "correct_value": 52,
        "explanation": "B-C = -8; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "60 + 52 - 125",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 60 + 52 - 125",
        "options": [
          "-27",
          "-13",
          "-7",
          "3"
        ],
        "answer": "-13",
        "correct_value": -13,
        "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_000172",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "59 + 87 - 85",
      "ns_shortcut": "Near-cancellation: 87 - 85 = 2, so answer ≈ 59 + 2.",
      "shortcut_strength": 0.9770114942528736,
      "pure_math": {
        "question": "Evaluate: 59 + 87 - 85",
        "options": [
          "71",
          "61",
          "51",
          "81"
        ],
        "answer": "61",
        "correct_value": 61,
        "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": "59 + 87 - 81",
      "ns_shortcut": "Near-cancellation: 87 - 81 = 6, offset is manageable.",
      "shortcut_strength": 0.9310344827586207,
      "pure_math": {
        "question": "Evaluate: 59 + 87 - 81",
        "options": [
          "75",
          "55",
          "85",
          "65"
        ],
        "answer": "65",
        "correct_value": 65,
        "explanation": "B-C = 6; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "59 + 87 - 127",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 59 + 87 - 127",
        "options": [
          "9",
          "39",
          "19",
          "29"
        ],
        "answer": "19",
        "correct_value": 19,
        "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_000173",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "60 + 79 - 78",
      "ns_shortcut": "Near-cancellation: 79 - 78 = 1, so answer ≈ 60 + 1.",
      "shortcut_strength": 0.9873417721518988,
      "pure_math": {
        "question": "Evaluate: 60 + 79 - 78",
        "options": [
          "61",
          "81",
          "71",
          "51"
        ],
        "answer": "61",
        "correct_value": 61,
        "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": "60 + 79 - 94",
      "ns_shortcut": "Near-cancellation: 79 - 94 = -15, offset is manageable.",
      "shortcut_strength": 0.810126582278481,
      "pure_math": {
        "question": "Evaluate: 60 + 79 - 94",
        "options": [
          "65",
          "45",
          "35",
          "55"
        ],
        "answer": "45",
        "correct_value": 45,
        "explanation": "B-C = -15; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "60 + 79 - 20",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 60 + 79 - 20",
        "options": [
          "139",
          "109",
          "119",
          "129"
        ],
        "answer": "119",
        "correct_value": 119,
        "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_000174",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "60 + 90 - 92",
      "ns_shortcut": "Near-cancellation: 90 - 92 = -2, so answer ≈ 60 + -2.",
      "shortcut_strength": 0.9777777777777777,
      "pure_math": {
        "question": "Evaluate: 60 + 90 - 92",
        "options": [
          "58",
          "68",
          "48",
          "78"
        ],
        "answer": "58",
        "correct_value": 58,
        "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": "60 + 90 - 95",
      "ns_shortcut": "Near-cancellation: 90 - 95 = -5, offset is manageable.",
      "shortcut_strength": 0.9444444444444444,
      "pure_math": {
        "question": "Evaluate: 60 + 90 - 95",
        "options": [
          "75",
          "45",
          "55",
          "65"
        ],
        "answer": "55",
        "correct_value": 55,
        "explanation": "B-C = -5; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "60 + 90 - 137",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 60 + 90 - 137",
        "options": [
          "33",
          "3",
          "23",
          "13"
        ],
        "answer": "13",
        "correct_value": 13,
        "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_000175",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 + 16 - 17",
      "ns_shortcut": "Near-cancellation: 16 - 17 = -1, so answer ≈ 25 + -1.",
      "shortcut_strength": 0.9375,
      "pure_math": {
        "question": "Evaluate: 25 + 16 - 17",
        "options": [
          "44",
          "34",
          "14",
          "24"
        ],
        "answer": "24",
        "correct_value": 24,
        "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": "25 + 16 - 10",
      "ns_shortcut": "Near-cancellation: 16 - 10 = 6, offset is manageable.",
      "shortcut_strength": 0.1875,
      "pure_math": {
        "question": "Evaluate: 25 + 16 - 10",
        "options": [
          "21",
          "41",
          "31",
          "51"
        ],
        "answer": "31",
        "correct_value": 31,
        "explanation": "B-C = 6; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "25 + 16 - 64",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 25 + 16 - 64",
        "options": [
          "-7",
          "-17",
          "-37",
          "-23"
        ],
        "answer": "-23",
        "correct_value": -23,
        "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_000176",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "64 + 49 - 51",
      "ns_shortcut": "Near-cancellation: 49 - 51 = -2, so answer ≈ 64 + -2.",
      "shortcut_strength": 0.9591836734693877,
      "pure_math": {
        "question": "Evaluate: 64 + 49 - 51",
        "options": [
          "72",
          "62",
          "52",
          "82"
        ],
        "answer": "62",
        "correct_value": 62,
        "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": "64 + 49 - 37",
      "ns_shortcut": "Near-cancellation: 49 - 37 = 12, offset is manageable.",
      "shortcut_strength": 0.7551020408163265,
      "pure_math": {
        "question": "Evaluate: 64 + 49 - 37",
        "options": [
          "66",
          "86",
          "76",
          "96"
        ],
        "answer": "76",
        "correct_value": 76,
        "explanation": "B-C = 12; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "64 + 49 - 125",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 64 + 49 - 125",
        "options": [
          "-28",
          "-8",
          "-12",
          "2"
        ],
        "answer": "-12",
        "correct_value": -12,
        "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_000177",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "23 + 88 - 90",
      "ns_shortcut": "Near-cancellation: 88 - 90 = -2, so answer ≈ 23 + -2.",
      "shortcut_strength": 0.9772727272727273,
      "pure_math": {
        "question": "Evaluate: 23 + 88 - 90",
        "options": [
          "11",
          "21",
          "41",
          "31"
        ],
        "answer": "21",
        "correct_value": 21,
        "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": "23 + 88 - 93",
      "ns_shortcut": "Near-cancellation: 88 - 93 = -5, offset is manageable.",
      "shortcut_strength": 0.9431818181818182,
      "pure_math": {
        "question": "Evaluate: 23 + 88 - 93",
        "options": [
          "38",
          "8",
          "18",
          "28"
        ],
        "answer": "18",
        "correct_value": 18,
        "explanation": "B-C = -5; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "23 + 88 - 151",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 23 + 88 - 151",
        "options": [
          "-50",
          "-20",
          "-40",
          "-30"
        ],
        "answer": "-40",
        "correct_value": -40,
        "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_000178",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "80 + 68 - 69",
      "ns_shortcut": "Near-cancellation: 68 - 69 = -1, so answer ≈ 80 + -1.",
      "shortcut_strength": 0.9852941176470589,
      "pure_math": {
        "question": "Evaluate: 80 + 68 - 69",
        "options": [
          "69",
          "89",
          "79",
          "99"
        ],
        "answer": "79",
        "correct_value": 79,
        "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": "80 + 68 - 59",
      "ns_shortcut": "Near-cancellation: 68 - 59 = 9, offset is manageable.",
      "shortcut_strength": 0.8676470588235294,
      "pure_math": {
        "question": "Evaluate: 80 + 68 - 59",
        "options": [
          "79",
          "99",
          "109",
          "89"
        ],
        "answer": "89",
        "correct_value": 89,
        "explanation": "B-C = 9; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "80 + 68 - 21",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 80 + 68 - 21",
        "options": [
          "117",
          "147",
          "127",
          "137"
        ],
        "answer": "127",
        "correct_value": 127,
        "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_000179",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "61 + 23 - 21",
      "ns_shortcut": "Near-cancellation: 23 - 21 = 2, so answer ≈ 61 + 2.",
      "shortcut_strength": 0.9130434782608696,
      "pure_math": {
        "question": "Evaluate: 61 + 23 - 21",
        "options": [
          "63",
          "53",
          "73",
          "83"
        ],
        "answer": "63",
        "correct_value": 63,
        "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": "61 + 23 - 36",
      "ns_shortcut": "Near-cancellation: 23 - 36 = -13, offset is manageable.",
      "shortcut_strength": 0.4347826086956522,
      "pure_math": {
        "question": "Evaluate: 61 + 23 - 36",
        "options": [
          "68",
          "58",
          "48",
          "38"
        ],
        "answer": "48",
        "correct_value": 48,
        "explanation": "B-C = -13; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "61 + 23 - 75",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 61 + 23 - 75",
        "options": [
          "19",
          "9",
          "-1",
          "29"
        ],
        "answer": "9",
        "correct_value": 9,
        "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_000180",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "69 + 62 - 60",
      "ns_shortcut": "Near-cancellation: 62 - 60 = 2, so answer ≈ 69 + 2.",
      "shortcut_strength": 0.967741935483871,
      "pure_math": {
        "question": "Evaluate: 69 + 62 - 60",
        "options": [
          "61",
          "71",
          "91",
          "81"
        ],
        "answer": "71",
        "correct_value": 71,
        "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": "69 + 62 - 67",
      "ns_shortcut": "Near-cancellation: 62 - 67 = -5, offset is manageable.",
      "shortcut_strength": 0.9193548387096774,
      "pure_math": {
        "question": "Evaluate: 69 + 62 - 67",
        "options": [
          "74",
          "84",
          "64",
          "54"
        ],
        "answer": "64",
        "correct_value": 64,
        "explanation": "B-C = -5; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "69 + 62 - 136",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 69 + 62 - 136",
        "options": [
          "15",
          "-15",
          "5",
          "-5"
        ],
        "answer": "-5",
        "correct_value": -5,
        "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_000181",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "94 + 63 - 62",
      "ns_shortcut": "Near-cancellation: 63 - 62 = 1, so answer ≈ 94 + 1.",
      "shortcut_strength": 0.9841269841269842,
      "pure_math": {
        "question": "Evaluate: 94 + 63 - 62",
        "options": [
          "105",
          "115",
          "85",
          "95"
        ],
        "answer": "95",
        "correct_value": 95,
        "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": "94 + 63 - 51",
      "ns_shortcut": "Near-cancellation: 63 - 51 = 12, offset is manageable.",
      "shortcut_strength": 0.8095238095238095,
      "pure_math": {
        "question": "Evaluate: 94 + 63 - 51",
        "options": [
          "126",
          "116",
          "96",
          "106"
        ],
        "answer": "106",
        "correct_value": 106,
        "explanation": "B-C = 12; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "94 + 63 - 18",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 94 + 63 - 18",
        "options": [
          "139",
          "129",
          "159",
          "149"
        ],
        "answer": "139",
        "correct_value": 139,
        "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_000182",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 + 62 - 60",
      "ns_shortcut": "Near-cancellation: 62 - 60 = 2, so answer ≈ 99 + 2.",
      "shortcut_strength": 0.967741935483871,
      "pure_math": {
        "question": "Evaluate: 99 + 62 - 60",
        "options": [
          "111",
          "91",
          "121",
          "101"
        ],
        "answer": "101",
        "correct_value": 101,
        "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": "99 + 62 - 77",
      "ns_shortcut": "Near-cancellation: 62 - 77 = -15, offset is manageable.",
      "shortcut_strength": 0.7580645161290323,
      "pure_math": {
        "question": "Evaluate: 99 + 62 - 77",
        "options": [
          "94",
          "104",
          "84",
          "74"
        ],
        "answer": "84",
        "correct_value": 84,
        "explanation": "B-C = -15; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "99 + 62 - 129",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 99 + 62 - 129",
        "options": [
          "32",
          "52",
          "22",
          "42"
        ],
        "answer": "32",
        "correct_value": 32,
        "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_000183",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "50 + 65 - 64",
      "ns_shortcut": "Near-cancellation: 65 - 64 = 1, so answer ≈ 50 + 1.",
      "shortcut_strength": 0.9846153846153847,
      "pure_math": {
        "question": "Evaluate: 50 + 65 - 64",
        "options": [
          "51",
          "41",
          "61",
          "71"
        ],
        "answer": "51",
        "correct_value": 51,
        "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": "50 + 65 - 71",
      "ns_shortcut": "Near-cancellation: 65 - 71 = -6, offset is manageable.",
      "shortcut_strength": 0.9076923076923077,
      "pure_math": {
        "question": "Evaluate: 50 + 65 - 71",
        "options": [
          "34",
          "64",
          "44",
          "54"
        ],
        "answer": "44",
        "correct_value": 44,
        "explanation": "B-C = -6; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "50 + 65 - 16",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 50 + 65 - 16",
        "options": [
          "99",
          "119",
          "89",
          "109"
        ],
        "answer": "99",
        "correct_value": 99,
        "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_000184",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "50 + 67 - 69",
      "ns_shortcut": "Near-cancellation: 67 - 69 = -2, so answer ≈ 50 + -2.",
      "shortcut_strength": 0.9701492537313433,
      "pure_math": {
        "question": "Evaluate: 50 + 67 - 69",
        "options": [
          "38",
          "58",
          "48",
          "68"
        ],
        "answer": "48",
        "correct_value": 48,
        "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": "50 + 67 - 55",
      "ns_shortcut": "Near-cancellation: 67 - 55 = 12, offset is manageable.",
      "shortcut_strength": 0.8208955223880597,
      "pure_math": {
        "question": "Evaluate: 50 + 67 - 55",
        "options": [
          "72",
          "52",
          "62",
          "82"
        ],
        "answer": "62",
        "correct_value": 62,
        "explanation": "B-C = 12; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "50 + 67 - 117",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 50 + 67 - 117",
        "options": [
          "20",
          "10",
          "-10",
          "0"
        ],
        "answer": "0",
        "correct_value": 0,
        "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_000185",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "28 + 26 - 27",
      "ns_shortcut": "Near-cancellation: 26 - 27 = -1, so answer ≈ 28 + -1.",
      "shortcut_strength": 0.9615384615384616,
      "pure_math": {
        "question": "Evaluate: 28 + 26 - 27",
        "options": [
          "17",
          "27",
          "37",
          "47"
        ],
        "answer": "27",
        "correct_value": 27,
        "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": "28 + 26 - 17",
      "ns_shortcut": "Near-cancellation: 26 - 17 = 9, offset is manageable.",
      "shortcut_strength": 0.6538461538461539,
      "pure_math": {
        "question": "Evaluate: 28 + 26 - 17",
        "options": [
          "57",
          "27",
          "37",
          "47"
        ],
        "answer": "37",
        "correct_value": 37,
        "explanation": "B-C = 9; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "28 + 26 - 94",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 28 + 26 - 94",
        "options": [
          "-20",
          "-50",
          "-30",
          "-40"
        ],
        "answer": "-40",
        "correct_value": -40,
        "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_000186",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "27 + 30 - 32",
      "ns_shortcut": "Near-cancellation: 30 - 32 = -2, so answer ≈ 27 + -2.",
      "shortcut_strength": 0.9333333333333333,
      "pure_math": {
        "question": "Evaluate: 27 + 30 - 32",
        "options": [
          "35",
          "45",
          "15",
          "25"
        ],
        "answer": "25",
        "correct_value": 25,
        "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": "27 + 30 - 41",
      "ns_shortcut": "Near-cancellation: 30 - 41 = -11, offset is manageable.",
      "shortcut_strength": 0.6333333333333333,
      "pure_math": {
        "question": "Evaluate: 27 + 30 - 41",
        "options": [
          "26",
          "16",
          "6",
          "36"
        ],
        "answer": "16",
        "correct_value": 16,
        "explanation": "B-C = -11; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "27 + 30 - 107",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 27 + 30 - 107",
        "options": [
          "-40",
          "-30",
          "-60",
          "-50"
        ],
        "answer": "-50",
        "correct_value": -50,
        "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_000187",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "35 + 71 - 72",
      "ns_shortcut": "Near-cancellation: 71 - 72 = -1, so answer ≈ 35 + -1.",
      "shortcut_strength": 0.9859154929577465,
      "pure_math": {
        "question": "Evaluate: 35 + 71 - 72",
        "options": [
          "54",
          "24",
          "44",
          "34"
        ],
        "answer": "34",
        "correct_value": 34,
        "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": "35 + 71 - 83",
      "ns_shortcut": "Near-cancellation: 71 - 83 = -12, offset is manageable.",
      "shortcut_strength": 0.8309859154929577,
      "pure_math": {
        "question": "Evaluate: 35 + 71 - 83",
        "options": [
          "43",
          "33",
          "13",
          "23"
        ],
        "answer": "23",
        "correct_value": 23,
        "explanation": "B-C = -12; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "35 + 71 - 157",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 35 + 71 - 157",
        "options": [
          "-39",
          "-49",
          "-51",
          "-69"
        ],
        "answer": "-51",
        "correct_value": -51,
        "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_000188",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "97 + 69 - 70",
      "ns_shortcut": "Near-cancellation: 69 - 70 = -1, so answer ≈ 97 + -1.",
      "shortcut_strength": 0.9855072463768116,
      "pure_math": {
        "question": "Evaluate: 97 + 69 - 70",
        "options": [
          "106",
          "86",
          "96",
          "116"
        ],
        "answer": "96",
        "correct_value": 96,
        "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": "97 + 69 - 60",
      "ns_shortcut": "Near-cancellation: 69 - 60 = 9, offset is manageable.",
      "shortcut_strength": 0.8695652173913043,
      "pure_math": {
        "question": "Evaluate: 97 + 69 - 60",
        "options": [
          "116",
          "126",
          "106",
          "96"
        ],
        "answer": "106",
        "correct_value": 106,
        "explanation": "B-C = 9; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "97 + 69 - 148",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 97 + 69 - 148",
        "options": [
          "18",
          "8",
          "28",
          "38"
        ],
        "answer": "18",
        "correct_value": 18,
        "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_000189",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "80 + 76 - 78",
      "ns_shortcut": "Near-cancellation: 76 - 78 = -2, so answer ≈ 80 + -2.",
      "shortcut_strength": 0.9736842105263158,
      "pure_math": {
        "question": "Evaluate: 80 + 76 - 78",
        "options": [
          "68",
          "98",
          "88",
          "78"
        ],
        "answer": "78",
        "correct_value": 78,
        "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": "80 + 76 - 87",
      "ns_shortcut": "Near-cancellation: 76 - 87 = -11, offset is manageable.",
      "shortcut_strength": 0.8552631578947368,
      "pure_math": {
        "question": "Evaluate: 80 + 76 - 87",
        "options": [
          "59",
          "69",
          "89",
          "79"
        ],
        "answer": "69",
        "correct_value": 69,
        "explanation": "B-C = -11; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "80 + 76 - 156",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 80 + 76 - 156",
        "options": [
          "0",
          "10",
          "20",
          "-10"
        ],
        "answer": "0",
        "correct_value": 0,
        "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_000190",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "71 + 84 - 82",
      "ns_shortcut": "Near-cancellation: 84 - 82 = 2, so answer ≈ 71 + 2.",
      "shortcut_strength": 0.9761904761904762,
      "pure_math": {
        "question": "Evaluate: 71 + 84 - 82",
        "options": [
          "73",
          "83",
          "63",
          "93"
        ],
        "answer": "73",
        "correct_value": 73,
        "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": "71 + 84 - 75",
      "ns_shortcut": "Near-cancellation: 84 - 75 = 9, offset is manageable.",
      "shortcut_strength": 0.8928571428571429,
      "pure_math": {
        "question": "Evaluate: 71 + 84 - 75",
        "options": [
          "100",
          "70",
          "80",
          "90"
        ],
        "answer": "80",
        "correct_value": 80,
        "explanation": "B-C = 9; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "71 + 84 - 162",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 71 + 84 - 162",
        "options": [
          "7",
          "-23",
          "-3",
          "-7"
        ],
        "answer": "-7",
        "correct_value": -7,
        "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_000191",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "70 + 82 - 81",
      "ns_shortcut": "Near-cancellation: 82 - 81 = 1, so answer ≈ 70 + 1.",
      "shortcut_strength": 0.9878048780487805,
      "pure_math": {
        "question": "Evaluate: 70 + 82 - 81",
        "options": [
          "61",
          "91",
          "71",
          "81"
        ],
        "answer": "71",
        "correct_value": 71,
        "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": "70 + 82 - 97",
      "ns_shortcut": "Near-cancellation: 82 - 97 = -15, offset is manageable.",
      "shortcut_strength": 0.8170731707317074,
      "pure_math": {
        "question": "Evaluate: 70 + 82 - 97",
        "options": [
          "75",
          "55",
          "45",
          "65"
        ],
        "answer": "55",
        "correct_value": 55,
        "explanation": "B-C = -15; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "70 + 82 - 170",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 70 + 82 - 170",
        "options": [
          "-2",
          "-18",
          "-12",
          "-32"
        ],
        "answer": "-18",
        "correct_value": -18,
        "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_000192",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "32 + 45 - 44",
      "ns_shortcut": "Near-cancellation: 45 - 44 = 1, so answer ≈ 32 + 1.",
      "shortcut_strength": 0.9777777777777777,
      "pure_math": {
        "question": "Evaluate: 32 + 45 - 44",
        "options": [
          "43",
          "33",
          "23",
          "53"
        ],
        "answer": "33",
        "correct_value": 33,
        "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": "32 + 45 - 31",
      "ns_shortcut": "Near-cancellation: 45 - 31 = 14, offset is manageable.",
      "shortcut_strength": 0.6888888888888889,
      "pure_math": {
        "question": "Evaluate: 32 + 45 - 31",
        "options": [
          "36",
          "46",
          "66",
          "56"
        ],
        "answer": "46",
        "correct_value": 46,
        "explanation": "B-C = 14; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "32 + 45 - 116",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 32 + 45 - 116",
        "options": [
          "-21",
          "-39",
          "-51",
          "-31"
        ],
        "answer": "-39",
        "correct_value": -39,
        "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_000193",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "21 + 22 - 23",
      "ns_shortcut": "Near-cancellation: 22 - 23 = -1, so answer ≈ 21 + -1.",
      "shortcut_strength": 0.9545454545454546,
      "pure_math": {
        "question": "Evaluate: 21 + 22 - 23",
        "options": [
          "40",
          "10",
          "20",
          "30"
        ],
        "answer": "20",
        "correct_value": 20,
        "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": "21 + 22 - 32",
      "ns_shortcut": "Near-cancellation: 22 - 32 = -10, offset is manageable.",
      "shortcut_strength": 0.5454545454545454,
      "pure_math": {
        "question": "Evaluate: 21 + 22 - 32",
        "options": [
          "31",
          "1",
          "11",
          "21"
        ],
        "answer": "11",
        "correct_value": 11,
        "explanation": "B-C = -10; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "21 + 22 - 107",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 21 + 22 - 107",
        "options": [
          "-56",
          "-76",
          "-64",
          "-46"
        ],
        "answer": "-64",
        "correct_value": -64,
        "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_000194",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "28 + 90 - 91",
      "ns_shortcut": "Near-cancellation: 90 - 91 = -1, so answer ≈ 28 + -1.",
      "shortcut_strength": 0.9888888888888889,
      "pure_math": {
        "question": "Evaluate: 28 + 90 - 91",
        "options": [
          "17",
          "37",
          "47",
          "27"
        ],
        "answer": "27",
        "correct_value": 27,
        "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": "28 + 90 - 99",
      "ns_shortcut": "Near-cancellation: 90 - 99 = -9, offset is manageable.",
      "shortcut_strength": 0.8888888888888888,
      "pure_math": {
        "question": "Evaluate: 28 + 90 - 99",
        "options": [
          "29",
          "19",
          "39",
          "9"
        ],
        "answer": "19",
        "correct_value": 19,
        "explanation": "B-C = -9; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "28 + 90 - 151",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 28 + 90 - 151",
        "options": [
          "-27",
          "-47",
          "-33",
          "-17"
        ],
        "answer": "-33",
        "correct_value": -33,
        "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_000195",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "65 + 77 - 76",
      "ns_shortcut": "Near-cancellation: 77 - 76 = 1, so answer ≈ 65 + 1.",
      "shortcut_strength": 0.987012987012987,
      "pure_math": {
        "question": "Evaluate: 65 + 77 - 76",
        "options": [
          "66",
          "56",
          "86",
          "76"
        ],
        "answer": "66",
        "correct_value": 66,
        "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": "65 + 77 - 92",
      "ns_shortcut": "Near-cancellation: 77 - 92 = -15, offset is manageable.",
      "shortcut_strength": 0.8051948051948052,
      "pure_math": {
        "question": "Evaluate: 65 + 77 - 92",
        "options": [
          "50",
          "70",
          "40",
          "60"
        ],
        "answer": "50",
        "correct_value": 50,
        "explanation": "B-C = -15; still a moderate shortcut."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "65 + 77 - 163",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 65 + 77 - 163",
        "options": [
          "-39",
          "-9",
          "-21",
          "-19"
        ],
        "answer": "-21",
        "correct_value": -21,
        "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_000196",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "99 + 88 - 86",
      "ns_shortcut": "Near-cancellation: 88 - 86 = 2, so answer ≈ 99 + 2.",
      "shortcut_strength": 0.9772727272727273,
      "pure_math": {
        "question": "Evaluate: 99 + 88 - 86",
        "options": [
          "121",
          "111",
          "91",
          "101"
        ],
        "answer": "101",
        "correct_value": 101,
        "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": "99 + 88 - 99",
      "ns_shortcut": "Near-cancellation: 88 - 99 = -11, offset is manageable.",
      "shortcut_strength": 0.8295454545454546,
      "pure_math": {
        "question": "Evaluate: 99 + 88 - 99",
        "options": [
          "108",
          "78",
          "98",
          "88"
        ],
        "answer": "88",
        "correct_value": 88,
        "explanation": "B-C = -11; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "99 + 88 - 27",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 99 + 88 - 27",
        "options": [
          "160",
          "180",
          "150",
          "170"
        ],
        "answer": "160",
        "correct_value": 160,
        "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_000197",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "31 + 26 - 25",
      "ns_shortcut": "Near-cancellation: 26 - 25 = 1, so answer ≈ 31 + 1.",
      "shortcut_strength": 0.9615384615384616,
      "pure_math": {
        "question": "Evaluate: 31 + 26 - 25",
        "options": [
          "52",
          "42",
          "32",
          "22"
        ],
        "answer": "32",
        "correct_value": 32,
        "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": "31 + 26 - 34",
      "ns_shortcut": "Near-cancellation: 26 - 34 = -8, offset is manageable.",
      "shortcut_strength": 0.6923076923076923,
      "pure_math": {
        "question": "Evaluate: 31 + 26 - 34",
        "options": [
          "13",
          "43",
          "33",
          "23"
        ],
        "answer": "23",
        "correct_value": 23,
        "explanation": "B-C = -8; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "31 + 26 - 116",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 31 + 26 - 116",
        "options": [
          "-41",
          "-51",
          "-71",
          "-59"
        ],
        "answer": "-59",
        "correct_value": -59,
        "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_000198",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "66 + 68 - 69",
      "ns_shortcut": "Near-cancellation: 68 - 69 = -1, so answer ≈ 66 + -1.",
      "shortcut_strength": 0.9852941176470589,
      "pure_math": {
        "question": "Evaluate: 66 + 68 - 69",
        "options": [
          "65",
          "85",
          "75",
          "55"
        ],
        "answer": "65",
        "correct_value": 65,
        "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": "66 + 68 - 55",
      "ns_shortcut": "Near-cancellation: 68 - 55 = 13, offset is manageable.",
      "shortcut_strength": 0.8088235294117647,
      "pure_math": {
        "question": "Evaluate: 66 + 68 - 55",
        "options": [
          "99",
          "89",
          "79",
          "69"
        ],
        "answer": "79",
        "correct_value": 79,
        "explanation": "B-C = 13; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "66 + 68 - 158",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 66 + 68 - 158",
        "options": [
          "-6",
          "-24",
          "-36",
          "-16"
        ],
        "answer": "-24",
        "correct_value": -24,
        "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_000199",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "14 + 52 - 54",
      "ns_shortcut": "Near-cancellation: 52 - 54 = -2, so answer ≈ 14 + -2.",
      "shortcut_strength": 0.9615384615384616,
      "pure_math": {
        "question": "Evaluate: 14 + 52 - 54",
        "options": [
          "2",
          "12",
          "22",
          "32"
        ],
        "answer": "12",
        "correct_value": 12,
        "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": "14 + 52 - 62",
      "ns_shortcut": "Near-cancellation: 52 - 62 = -10, offset is manageable.",
      "shortcut_strength": 0.8076923076923077,
      "pure_math": {
        "question": "Evaluate: 14 + 52 - 62",
        "options": [
          "24",
          "4",
          "-6",
          "14"
        ],
        "answer": "4",
        "correct_value": 4,
        "explanation": "B-C = -10; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "14 + 52 - 138",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 14 + 52 - 138",
        "options": [
          "-88",
          "-58",
          "-68",
          "-72"
        ],
        "answer": "-72",
        "correct_value": -72,
        "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_000200",
    "category": "cancellation_identity",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "13 + 70 - 71",
      "ns_shortcut": "Near-cancellation: 70 - 71 = -1, so answer ≈ 13 + -1.",
      "shortcut_strength": 0.9857142857142858,
      "pure_math": {
        "question": "Evaluate: 13 + 70 - 71",
        "options": [
          "22",
          "32",
          "12",
          "2"
        ],
        "answer": "12",
        "correct_value": 12,
        "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": "13 + 70 - 80",
      "ns_shortcut": "Near-cancellation: 70 - 80 = -10, offset is manageable.",
      "shortcut_strength": 0.8571428571428572,
      "pure_math": {
        "question": "Evaluate: 13 + 70 - 80",
        "options": [
          "23",
          "-7",
          "3",
          "13"
        ],
        "answer": "3",
        "correct_value": 3,
        "explanation": "B-C = -10; still a moderate shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "13 + 70 - 154",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Evaluate: 13 + 70 - 154",
        "options": [
          "-89",
          "-71",
          "-69",
          "-59"
        ],
        "answer": "-71",
        "correct_value": -71,
        "explanation": "Large gap between B and C; no cancellation shortcut."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "compatible_numbers_000201",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "24 * 4",
      "ns_shortcut": "Round to 25×4 for easy mental computation.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Estimate 24 × 4.",
        "options": [
          "116",
          "86",
          "106",
          "96"
        ],
        "answer": "96",
        "correct_value": 96,
        "explanation": "Round to compatible pair 25×4 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 6",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.75,
      "pure_math": {
        "question": "Estimate 25 × 6.",
        "options": [
          "140",
          "170",
          "150",
          "160"
        ],
        "answer": "150",
        "correct_value": 150,
        "explanation": "One number rounds to 25, other is farther from 4."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "29 * 6",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 29 × 6.",
        "options": [
          "164",
          "184",
          "174",
          "194"
        ],
        "answer": "174",
        "correct_value": 174,
        "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_000202",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26 * 5",
      "ns_shortcut": "Round to 25×4 for easy mental computation.",
      "shortcut_strength": 0.855,
      "pure_math": {
        "question": "Estimate 26 × 5.",
        "options": [
          "120",
          "140",
          "130",
          "150"
        ],
        "answer": "130",
        "correct_value": 130,
        "explanation": "Round to compatible pair 25×4 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "24 * 6",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.73,
      "pure_math": {
        "question": "Estimate 24 × 6.",
        "options": [
          "164",
          "144",
          "134",
          "154"
        ],
        "answer": "144",
        "correct_value": 144,
        "explanation": "One number rounds to 25, other is farther from 4."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "30 * 7",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 30 × 7.",
        "options": [
          "230",
          "210",
          "220",
          "200"
        ],
        "answer": "210",
        "correct_value": 210,
        "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_000203",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "50 * 2",
      "ns_shortcut": "Round to 50×2 for easy mental computation.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Estimate 50 × 2.",
        "options": [
          "100",
          "110",
          "90",
          "120"
        ],
        "answer": "100",
        "correct_value": 100,
        "explanation": "Round to compatible pair 50×2 = 100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "50 * 4",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "Estimate 50 × 4.",
        "options": [
          "210",
          "200",
          "220",
          "190"
        ],
        "answer": "200",
        "correct_value": 200,
        "explanation": "One number rounds to 50, other is farther from 2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "62 * 5",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 62 × 5.",
        "options": [
          "330",
          "300",
          "320",
          "310"
        ],
        "answer": "310",
        "correct_value": 310,
        "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_000204",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 8",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Estimate 25 × 8.",
        "options": [
          "190",
          "220",
          "200",
          "210"
        ],
        "answer": "200",
        "correct_value": 200,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 9",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.9375,
      "pure_math": {
        "question": "Estimate 25 × 9.",
        "options": [
          "235",
          "245",
          "225",
          "215"
        ],
        "answer": "225",
        "correct_value": 225,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "30 * 11",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 30 × 11.",
        "options": [
          "350",
          "340",
          "320",
          "330"
        ],
        "answer": "330",
        "correct_value": 330,
        "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_000205",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26 * 9",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 0.9175,
      "pure_math": {
        "question": "Estimate 26 × 9.",
        "options": [
          "224",
          "244",
          "254",
          "234"
        ],
        "answer": "234",
        "correct_value": 234,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "24 * 7",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.9175,
      "pure_math": {
        "question": "Estimate 24 × 7.",
        "options": [
          "178",
          "188",
          "158",
          "168"
        ],
        "answer": "168",
        "correct_value": 168,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "30 * 12",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 30 × 12.",
        "options": [
          "360",
          "350",
          "370",
          "380"
        ],
        "answer": "360",
        "correct_value": 360,
        "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_000206",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "51 * 2",
      "ns_shortcut": "Round to 50×2 for easy mental computation.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Estimate 51 × 2.",
        "options": [
          "92",
          "102",
          "112",
          "122"
        ],
        "answer": "102",
        "correct_value": 102,
        "explanation": "Round to compatible pair 50×2 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "50 * 4",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "Estimate 50 × 4.",
        "options": [
          "220",
          "190",
          "200",
          "210"
        ],
        "answer": "200",
        "correct_value": 200,
        "explanation": "One number rounds to 50, other is farther from 2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "59 * 5",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 59 × 5.",
        "options": [
          "285",
          "315",
          "305",
          "295"
        ],
        "answer": "295",
        "correct_value": 295,
        "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_000207",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "51 * 2",
      "ns_shortcut": "Round to 50×2 for easy mental computation.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Estimate 51 × 2.",
        "options": [
          "102",
          "122",
          "92",
          "112"
        ],
        "answer": "102",
        "correct_value": 102,
        "explanation": "Round to compatible pair 50×2 = 100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "51 * 3",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.74,
      "pure_math": {
        "question": "Estimate 51 × 3.",
        "options": [
          "173",
          "153",
          "143",
          "163"
        ],
        "answer": "153",
        "correct_value": 153,
        "explanation": "One number rounds to 50, other is farther from 2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "61 * 5",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 61 × 5.",
        "options": [
          "315",
          "295",
          "305",
          "325"
        ],
        "answer": "305",
        "correct_value": 305,
        "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_000208",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26 * 4",
      "ns_shortcut": "Round to 25×4 for easy mental computation.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Estimate 26 × 4.",
        "options": [
          "94",
          "124",
          "104",
          "114"
        ],
        "answer": "104",
        "correct_value": 104,
        "explanation": "Round to compatible pair 25×4 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 2",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.75,
      "pure_math": {
        "question": "Estimate 25 × 2.",
        "options": [
          "70",
          "40",
          "60",
          "50"
        ],
        "answer": "50",
        "correct_value": 50,
        "explanation": "One number rounds to 25, other is farther from 4."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "30 * 7",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 30 × 7.",
        "options": [
          "210",
          "220",
          "230",
          "200"
        ],
        "answer": "210",
        "correct_value": 210,
        "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_000209",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 7",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 0.9375,
      "pure_math": {
        "question": "Estimate 25 × 7.",
        "options": [
          "175",
          "185",
          "195",
          "165"
        ],
        "answer": "175",
        "correct_value": 175,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "24 * 10",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.855,
      "pure_math": {
        "question": "Estimate 24 × 10.",
        "options": [
          "260",
          "240",
          "230",
          "250"
        ],
        "answer": "240",
        "correct_value": 240,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "30 * 10",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 30 × 10.",
        "options": [
          "310",
          "320",
          "300",
          "290"
        ],
        "answer": "300",
        "correct_value": 300,
        "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_000210",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 8",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Estimate 25 × 8.",
        "options": [
          "200",
          "210",
          "190",
          "220"
        ],
        "answer": "200",
        "correct_value": 200,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 9",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.9375,
      "pure_math": {
        "question": "Estimate 25 × 9.",
        "options": [
          "215",
          "225",
          "245",
          "235"
        ],
        "answer": "225",
        "correct_value": 225,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "29 * 11",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 29 × 11.",
        "options": [
          "319",
          "329",
          "309",
          "339"
        ],
        "answer": "319",
        "correct_value": 319,
        "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_000211",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "51 * 3",
      "ns_shortcut": "Round to 50×2 for easy mental computation.",
      "shortcut_strength": 0.74,
      "pure_math": {
        "question": "Estimate 51 × 3.",
        "options": [
          "153",
          "173",
          "143",
          "163"
        ],
        "answer": "153",
        "correct_value": 153,
        "explanation": "Round to compatible pair 50×2 = 100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "50 * 0",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "Estimate 50 × 0.",
        "options": [
          "-10",
          "0",
          "10",
          "20"
        ],
        "answer": "0",
        "correct_value": 0,
        "explanation": "One number rounds to 50, other is farther from 2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "62 * 4",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 62 × 4.",
        "options": [
          "248",
          "238",
          "258",
          "268"
        ],
        "answer": "248",
        "correct_value": 248,
        "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_000212",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "51 * 2",
      "ns_shortcut": "Round to 50×2 for easy mental computation.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Estimate 51 × 2.",
        "options": [
          "122",
          "92",
          "102",
          "112"
        ],
        "answer": "102",
        "correct_value": 102,
        "explanation": "Round to compatible pair 50×2 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "50 * 0",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "Estimate 50 × 0.",
        "options": [
          "0",
          "-10",
          "10",
          "20"
        ],
        "answer": "0",
        "correct_value": 0,
        "explanation": "One number rounds to 50, other is farther from 2."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "61 * 5",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 61 × 5.",
        "options": [
          "315",
          "295",
          "325",
          "305"
        ],
        "answer": "305",
        "correct_value": 305,
        "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_000213",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "49 * 3",
      "ns_shortcut": "Round to 50×2 for easy mental computation.",
      "shortcut_strength": 0.74,
      "pure_math": {
        "question": "Estimate 49 × 3.",
        "options": [
          "137",
          "147",
          "167",
          "157"
        ],
        "answer": "147",
        "correct_value": 147,
        "explanation": "Round to compatible pair 50×2 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "50 * 3",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.75,
      "pure_math": {
        "question": "Estimate 50 × 3.",
        "options": [
          "160",
          "150",
          "140",
          "170"
        ],
        "answer": "150",
        "correct_value": 150,
        "explanation": "One number rounds to 50, other is farther from 2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "60 * 4",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 60 × 4.",
        "options": [
          "260",
          "240",
          "230",
          "250"
        ],
        "answer": "240",
        "correct_value": 240,
        "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_000214",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26 * 9",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 0.9175,
      "pure_math": {
        "question": "Estimate 26 × 9.",
        "options": [
          "234",
          "244",
          "224",
          "254"
        ],
        "answer": "234",
        "correct_value": 234,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 9",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.9375,
      "pure_math": {
        "question": "Estimate 25 × 9.",
        "options": [
          "245",
          "215",
          "235",
          "225"
        ],
        "answer": "225",
        "correct_value": 225,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "28 * 12",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 28 × 12.",
        "options": [
          "336",
          "346",
          "356",
          "326"
        ],
        "answer": "336",
        "correct_value": 336,
        "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_000215",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "50 * 2",
      "ns_shortcut": "Round to 50×2 for easy mental computation.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Estimate 50 × 2.",
        "options": [
          "100",
          "90",
          "110",
          "120"
        ],
        "answer": "100",
        "correct_value": 100,
        "explanation": "Round to compatible pair 50×2 = 100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "49 * 1",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.74,
      "pure_math": {
        "question": "Estimate 49 × 1.",
        "options": [
          "69",
          "49",
          "59",
          "39"
        ],
        "answer": "49",
        "correct_value": 49,
        "explanation": "One number rounds to 50, other is farther from 2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "60 * 4",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 60 × 4.",
        "options": [
          "230",
          "260",
          "250",
          "240"
        ],
        "answer": "240",
        "correct_value": 240,
        "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_000216",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 4",
      "ns_shortcut": "Round to 25×4 for easy mental computation.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Estimate 25 × 4.",
        "options": [
          "100",
          "90",
          "120",
          "110"
        ],
        "answer": "100",
        "correct_value": 100,
        "explanation": "Round to compatible pair 25×4 = 100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "26 * 6",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.73,
      "pure_math": {
        "question": "Estimate 26 × 6.",
        "options": [
          "166",
          "176",
          "156",
          "146"
        ],
        "answer": "156",
        "correct_value": 156,
        "explanation": "One number rounds to 25, other is farther from 4."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "29 * 7",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 29 × 7.",
        "options": [
          "223",
          "193",
          "213",
          "203"
        ],
        "answer": "203",
        "correct_value": 203,
        "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_000217",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 3",
      "ns_shortcut": "Round to 25×4 for easy mental computation.",
      "shortcut_strength": 0.875,
      "pure_math": {
        "question": "Estimate 25 × 3.",
        "options": [
          "85",
          "65",
          "75",
          "95"
        ],
        "answer": "75",
        "correct_value": 75,
        "explanation": "Round to compatible pair 25×4 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "26 * 3",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.855,
      "pure_math": {
        "question": "Estimate 26 × 3.",
        "options": [
          "68",
          "98",
          "88",
          "78"
        ],
        "answer": "78",
        "correct_value": 78,
        "explanation": "One number rounds to 25, other is farther from 4."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "31 * 7",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 31 × 7.",
        "options": [
          "227",
          "217",
          "237",
          "207"
        ],
        "answer": "217",
        "correct_value": 217,
        "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_000218",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "51 * 2",
      "ns_shortcut": "Round to 50×2 for easy mental computation.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Estimate 51 × 2.",
        "options": [
          "112",
          "122",
          "102",
          "92"
        ],
        "answer": "102",
        "correct_value": 102,
        "explanation": "Round to compatible pair 50×2 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "50 * 1",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.75,
      "pure_math": {
        "question": "Estimate 50 × 1.",
        "options": [
          "70",
          "40",
          "50",
          "60"
        ],
        "answer": "50",
        "correct_value": 50,
        "explanation": "One number rounds to 50, other is farther from 2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "55 * 5",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 55 × 5.",
        "options": [
          "285",
          "275",
          "265",
          "295"
        ],
        "answer": "275",
        "correct_value": 275,
        "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_000219",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 8",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Estimate 25 × 8.",
        "options": [
          "190",
          "220",
          "210",
          "200"
        ],
        "answer": "200",
        "correct_value": 200,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 10",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.875,
      "pure_math": {
        "question": "Estimate 25 × 10.",
        "options": [
          "240",
          "270",
          "250",
          "260"
        ],
        "answer": "250",
        "correct_value": 250,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "30 * 11",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 30 × 11.",
        "options": [
          "320",
          "340",
          "350",
          "330"
        ],
        "answer": "330",
        "correct_value": 330,
        "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_000220",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "24 * 8",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Estimate 24 × 8.",
        "options": [
          "202",
          "182",
          "192",
          "212"
        ],
        "answer": "192",
        "correct_value": 192,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 6",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.875,
      "pure_math": {
        "question": "Estimate 25 × 6.",
        "options": [
          "150",
          "170",
          "140",
          "160"
        ],
        "answer": "150",
        "correct_value": 150,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "30 * 10",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 30 × 10.",
        "options": [
          "290",
          "310",
          "320",
          "300"
        ],
        "answer": "300",
        "correct_value": 300,
        "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_000221",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26 * 4",
      "ns_shortcut": "Round to 25×4 for easy mental computation.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Estimate 26 × 4.",
        "options": [
          "114",
          "94",
          "124",
          "104"
        ],
        "answer": "104",
        "correct_value": 104,
        "explanation": "Round to compatible pair 25×4 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "24 * 3",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.855,
      "pure_math": {
        "question": "Estimate 24 × 3.",
        "options": [
          "82",
          "62",
          "92",
          "72"
        ],
        "answer": "72",
        "correct_value": 72,
        "explanation": "One number rounds to 25, other is farther from 4."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "30 * 6",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 30 × 6.",
        "options": [
          "180",
          "200",
          "190",
          "170"
        ],
        "answer": "180",
        "correct_value": 180,
        "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_000222",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "50 * 2",
      "ns_shortcut": "Round to 50×2 for easy mental computation.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Estimate 50 × 2.",
        "options": [
          "100",
          "90",
          "110",
          "120"
        ],
        "answer": "100",
        "correct_value": 100,
        "explanation": "Round to compatible pair 50×2 = 100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "50 * 1",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.75,
      "pure_math": {
        "question": "Estimate 50 × 1.",
        "options": [
          "60",
          "70",
          "40",
          "50"
        ],
        "answer": "50",
        "correct_value": 50,
        "explanation": "One number rounds to 50, other is farther from 2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "60 * 5",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 60 × 5.",
        "options": [
          "300",
          "310",
          "320",
          "290"
        ],
        "answer": "300",
        "correct_value": 300,
        "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_000223",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "24 * 8",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Estimate 24 × 8.",
        "options": [
          "182",
          "212",
          "202",
          "192"
        ],
        "answer": "192",
        "correct_value": 192,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "26 * 10",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.855,
      "pure_math": {
        "question": "Estimate 26 × 10.",
        "options": [
          "270",
          "260",
          "280",
          "250"
        ],
        "answer": "260",
        "correct_value": 260,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "28 * 10",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 28 × 10.",
        "options": [
          "290",
          "300",
          "270",
          "280"
        ],
        "answer": "280",
        "correct_value": 280,
        "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_000224",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "51 * 1",
      "ns_shortcut": "Round to 50×2 for easy mental computation.",
      "shortcut_strength": 0.74,
      "pure_math": {
        "question": "Estimate 51 × 1.",
        "options": [
          "61",
          "51",
          "41",
          "71"
        ],
        "answer": "51",
        "correct_value": 51,
        "explanation": "Round to compatible pair 50×2 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "49 * 3",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.74,
      "pure_math": {
        "question": "Estimate 49 × 3.",
        "options": [
          "167",
          "147",
          "157",
          "137"
        ],
        "answer": "147",
        "correct_value": 147,
        "explanation": "One number rounds to 50, other is farther from 2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "56 * 5",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 56 × 5.",
        "options": [
          "290",
          "270",
          "280",
          "300"
        ],
        "answer": "280",
        "correct_value": 280,
        "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_000225",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 8",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Estimate 25 × 8.",
        "options": [
          "200",
          "220",
          "210",
          "190"
        ],
        "answer": "200",
        "correct_value": 200,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 7",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.9375,
      "pure_math": {
        "question": "Estimate 25 × 7.",
        "options": [
          "195",
          "175",
          "185",
          "165"
        ],
        "answer": "175",
        "correct_value": 175,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "28 * 11",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 28 × 11.",
        "options": [
          "298",
          "318",
          "308",
          "328"
        ],
        "answer": "308",
        "correct_value": 308,
        "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_000226",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "50 * 3",
      "ns_shortcut": "Round to 50×2 for easy mental computation.",
      "shortcut_strength": 0.75,
      "pure_math": {
        "question": "Estimate 50 × 3.",
        "options": [
          "170",
          "140",
          "150",
          "160"
        ],
        "answer": "150",
        "correct_value": 150,
        "explanation": "Round to compatible pair 50×2 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "51 * 0",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.49,
      "pure_math": {
        "question": "Estimate 51 × 0.",
        "options": [
          "20",
          "0",
          "10",
          "-10"
        ],
        "answer": "0",
        "correct_value": 0,
        "explanation": "One number rounds to 50, other is farther from 2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "62 * 4",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 62 × 4.",
        "options": [
          "238",
          "268",
          "258",
          "248"
        ],
        "answer": "248",
        "correct_value": 248,
        "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_000227",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 4",
      "ns_shortcut": "Round to 25×4 for easy mental computation.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Estimate 25 × 4.",
        "options": [
          "100",
          "120",
          "110",
          "90"
        ],
        "answer": "100",
        "correct_value": 100,
        "explanation": "Round to compatible pair 25×4 = 100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 6",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.75,
      "pure_math": {
        "question": "Estimate 25 × 6.",
        "options": [
          "150",
          "160",
          "170",
          "140"
        ],
        "answer": "150",
        "correct_value": 150,
        "explanation": "One number rounds to 25, other is farther from 4."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "31 * 6",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 31 × 6.",
        "options": [
          "196",
          "176",
          "206",
          "186"
        ],
        "answer": "186",
        "correct_value": 186,
        "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_000228",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26 * 5",
      "ns_shortcut": "Round to 25×4 for easy mental computation.",
      "shortcut_strength": 0.855,
      "pure_math": {
        "question": "Estimate 26 × 5.",
        "options": [
          "140",
          "150",
          "120",
          "130"
        ],
        "answer": "130",
        "correct_value": 130,
        "explanation": "Round to compatible pair 25×4 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 5",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.875,
      "pure_math": {
        "question": "Estimate 25 × 5.",
        "options": [
          "135",
          "125",
          "115",
          "145"
        ],
        "answer": "125",
        "correct_value": 125,
        "explanation": "One number rounds to 25, other is farther from 4."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "29 * 6",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 29 × 6.",
        "options": [
          "194",
          "184",
          "174",
          "164"
        ],
        "answer": "174",
        "correct_value": 174,
        "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_000229",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 4",
      "ns_shortcut": "Round to 25×4 for easy mental computation.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Estimate 25 × 4.",
        "options": [
          "90",
          "120",
          "110",
          "100"
        ],
        "answer": "100",
        "correct_value": 100,
        "explanation": "Round to compatible pair 25×4 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "24 * 3",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.855,
      "pure_math": {
        "question": "Estimate 24 × 3.",
        "options": [
          "72",
          "82",
          "92",
          "62"
        ],
        "answer": "72",
        "correct_value": 72,
        "explanation": "One number rounds to 25, other is farther from 4."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "29 * 6",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 29 × 6.",
        "options": [
          "194",
          "164",
          "174",
          "184"
        ],
        "answer": "174",
        "correct_value": 174,
        "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_000230",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26 * 8",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Estimate 26 × 8.",
        "options": [
          "208",
          "198",
          "218",
          "228"
        ],
        "answer": "208",
        "correct_value": 208,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "26 * 7",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.9175,
      "pure_math": {
        "question": "Estimate 26 × 7.",
        "options": [
          "182",
          "192",
          "202",
          "172"
        ],
        "answer": "182",
        "correct_value": 182,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "30 * 12",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 30 × 12.",
        "options": [
          "350",
          "380",
          "360",
          "370"
        ],
        "answer": "360",
        "correct_value": 360,
        "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_000231",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26 * 8",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Estimate 26 × 8.",
        "options": [
          "218",
          "208",
          "198",
          "228"
        ],
        "answer": "208",
        "correct_value": 208,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "26 * 10",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.855,
      "pure_math": {
        "question": "Estimate 26 × 10.",
        "options": [
          "270",
          "280",
          "260",
          "250"
        ],
        "answer": "260",
        "correct_value": 260,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "28 * 11",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 28 × 11.",
        "options": [
          "298",
          "328",
          "308",
          "318"
        ],
        "answer": "308",
        "correct_value": 308,
        "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_000232",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 5",
      "ns_shortcut": "Round to 25×4 for easy mental computation.",
      "shortcut_strength": 0.875,
      "pure_math": {
        "question": "Estimate 25 × 5.",
        "options": [
          "145",
          "115",
          "125",
          "135"
        ],
        "answer": "125",
        "correct_value": 125,
        "explanation": "Round to compatible pair 25×4 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 6",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.75,
      "pure_math": {
        "question": "Estimate 25 × 6.",
        "options": [
          "160",
          "140",
          "170",
          "150"
        ],
        "answer": "150",
        "correct_value": 150,
        "explanation": "One number rounds to 25, other is farther from 4."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "31 * 6",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 31 × 6.",
        "options": [
          "196",
          "186",
          "176",
          "206"
        ],
        "answer": "186",
        "correct_value": 186,
        "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_000233",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "51 * 2",
      "ns_shortcut": "Round to 50×2 for easy mental computation.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Estimate 51 × 2.",
        "options": [
          "92",
          "112",
          "122",
          "102"
        ],
        "answer": "102",
        "correct_value": 102,
        "explanation": "Round to compatible pair 50×2 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "49 * 0",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.49,
      "pure_math": {
        "question": "Estimate 49 × 0.",
        "options": [
          "-10",
          "0",
          "20",
          "10"
        ],
        "answer": "0",
        "correct_value": 0,
        "explanation": "One number rounds to 50, other is farther from 2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "59 * 5",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 59 × 5.",
        "options": [
          "285",
          "295",
          "315",
          "305"
        ],
        "answer": "295",
        "correct_value": 295,
        "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_000234",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 4",
      "ns_shortcut": "Round to 25×4 for easy mental computation.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Estimate 25 × 4.",
        "options": [
          "100",
          "120",
          "110",
          "90"
        ],
        "answer": "100",
        "correct_value": 100,
        "explanation": "Round to compatible pair 25×4 = 100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 5",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.875,
      "pure_math": {
        "question": "Estimate 25 × 5.",
        "options": [
          "115",
          "125",
          "135",
          "145"
        ],
        "answer": "125",
        "correct_value": 125,
        "explanation": "One number rounds to 25, other is farther from 4."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "28 * 6",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 28 × 6.",
        "options": [
          "178",
          "168",
          "158",
          "188"
        ],
        "answer": "168",
        "correct_value": 168,
        "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_000235",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26 * 8",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Estimate 26 × 8.",
        "options": [
          "218",
          "208",
          "198",
          "228"
        ],
        "answer": "208",
        "correct_value": 208,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 6",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.875,
      "pure_math": {
        "question": "Estimate 25 × 6.",
        "options": [
          "170",
          "160",
          "150",
          "140"
        ],
        "answer": "150",
        "correct_value": 150,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "29 * 10",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 29 × 10.",
        "options": [
          "290",
          "280",
          "300",
          "310"
        ],
        "answer": "290",
        "correct_value": 290,
        "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_000236",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "49 * 2",
      "ns_shortcut": "Round to 50×2 for easy mental computation.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Estimate 49 × 2.",
        "options": [
          "88",
          "98",
          "108",
          "118"
        ],
        "answer": "98",
        "correct_value": 98,
        "explanation": "Round to compatible pair 50×2 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "50 * 4",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "Estimate 50 × 4.",
        "options": [
          "190",
          "220",
          "210",
          "200"
        ],
        "answer": "200",
        "correct_value": 200,
        "explanation": "One number rounds to 50, other is farther from 2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "59 * 4",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 59 × 4.",
        "options": [
          "236",
          "246",
          "226",
          "256"
        ],
        "answer": "236",
        "correct_value": 236,
        "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_000237",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "49 * 1",
      "ns_shortcut": "Round to 50×2 for easy mental computation.",
      "shortcut_strength": 0.74,
      "pure_math": {
        "question": "Estimate 49 × 1.",
        "options": [
          "59",
          "69",
          "39",
          "49"
        ],
        "answer": "49",
        "correct_value": 49,
        "explanation": "Round to compatible pair 50×2 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "50 * 1",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.75,
      "pure_math": {
        "question": "Estimate 50 × 1.",
        "options": [
          "60",
          "70",
          "50",
          "40"
        ],
        "answer": "50",
        "correct_value": 50,
        "explanation": "One number rounds to 50, other is farther from 2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "61 * 4",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 61 × 4.",
        "options": [
          "264",
          "234",
          "244",
          "254"
        ],
        "answer": "244",
        "correct_value": 244,
        "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_000238",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 8",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Estimate 25 × 8.",
        "options": [
          "220",
          "210",
          "190",
          "200"
        ],
        "answer": "200",
        "correct_value": 200,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 10",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.875,
      "pure_math": {
        "question": "Estimate 25 × 10.",
        "options": [
          "250",
          "270",
          "260",
          "240"
        ],
        "answer": "250",
        "correct_value": 250,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "31 * 11",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 31 × 11.",
        "options": [
          "361",
          "331",
          "351",
          "341"
        ],
        "answer": "341",
        "correct_value": 341,
        "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_000239",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 8",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Estimate 25 × 8.",
        "options": [
          "210",
          "200",
          "190",
          "220"
        ],
        "answer": "200",
        "correct_value": 200,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "26 * 6",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.855,
      "pure_math": {
        "question": "Estimate 26 × 6.",
        "options": [
          "156",
          "176",
          "166",
          "146"
        ],
        "answer": "156",
        "correct_value": 156,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "28 * 11",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 28 × 11.",
        "options": [
          "298",
          "308",
          "328",
          "318"
        ],
        "answer": "308",
        "correct_value": 308,
        "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_000240",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26 * 3",
      "ns_shortcut": "Round to 25×4 for easy mental computation.",
      "shortcut_strength": 0.855,
      "pure_math": {
        "question": "Estimate 26 × 3.",
        "options": [
          "88",
          "68",
          "78",
          "98"
        ],
        "answer": "78",
        "correct_value": 78,
        "explanation": "Round to compatible pair 25×4 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 2",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.75,
      "pure_math": {
        "question": "Estimate 25 × 2.",
        "options": [
          "70",
          "40",
          "60",
          "50"
        ],
        "answer": "50",
        "correct_value": 50,
        "explanation": "One number rounds to 25, other is farther from 4."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "30 * 6",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 30 × 6.",
        "options": [
          "190",
          "180",
          "200",
          "170"
        ],
        "answer": "180",
        "correct_value": 180,
        "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_000241",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 4",
      "ns_shortcut": "Round to 25×4 for easy mental computation.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Estimate 25 × 4.",
        "options": [
          "110",
          "120",
          "90",
          "100"
        ],
        "answer": "100",
        "correct_value": 100,
        "explanation": "Round to compatible pair 25×4 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 5",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.875,
      "pure_math": {
        "question": "Estimate 25 × 5.",
        "options": [
          "135",
          "115",
          "125",
          "145"
        ],
        "answer": "125",
        "correct_value": 125,
        "explanation": "One number rounds to 25, other is farther from 4."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "31 * 7",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 31 × 7.",
        "options": [
          "227",
          "207",
          "217",
          "237"
        ],
        "answer": "217",
        "correct_value": 217,
        "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_000242",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 3",
      "ns_shortcut": "Round to 25×4 for easy mental computation.",
      "shortcut_strength": 0.875,
      "pure_math": {
        "question": "Estimate 25 × 3.",
        "options": [
          "75",
          "95",
          "85",
          "65"
        ],
        "answer": "75",
        "correct_value": 75,
        "explanation": "Round to compatible pair 25×4 = 100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 6",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.75,
      "pure_math": {
        "question": "Estimate 25 × 6.",
        "options": [
          "160",
          "170",
          "150",
          "140"
        ],
        "answer": "150",
        "correct_value": 150,
        "explanation": "One number rounds to 25, other is farther from 4."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "30 * 6",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 30 × 6.",
        "options": [
          "180",
          "170",
          "200",
          "190"
        ],
        "answer": "180",
        "correct_value": 180,
        "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_000243",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "50 * 3",
      "ns_shortcut": "Round to 50×2 for easy mental computation.",
      "shortcut_strength": 0.75,
      "pure_math": {
        "question": "Estimate 50 × 3.",
        "options": [
          "150",
          "170",
          "160",
          "140"
        ],
        "answer": "150",
        "correct_value": 150,
        "explanation": "Round to compatible pair 50×2 = 100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "51 * 1",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.74,
      "pure_math": {
        "question": "Estimate 51 × 1.",
        "options": [
          "71",
          "41",
          "61",
          "51"
        ],
        "answer": "51",
        "correct_value": 51,
        "explanation": "One number rounds to 50, other is farther from 2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "58 * 5",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 58 × 5.",
        "options": [
          "300",
          "280",
          "310",
          "290"
        ],
        "answer": "290",
        "correct_value": 290,
        "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_000244",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "24 * 4",
      "ns_shortcut": "Round to 25×4 for easy mental computation.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Estimate 24 × 4.",
        "options": [
          "96",
          "106",
          "86",
          "116"
        ],
        "answer": "96",
        "correct_value": 96,
        "explanation": "Round to compatible pair 25×4 = 100."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "24 * 5",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.855,
      "pure_math": {
        "question": "Estimate 24 × 5.",
        "options": [
          "110",
          "130",
          "120",
          "140"
        ],
        "answer": "120",
        "correct_value": 120,
        "explanation": "One number rounds to 25, other is farther from 4."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "28 * 7",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 28 × 7.",
        "options": [
          "206",
          "196",
          "186",
          "216"
        ],
        "answer": "196",
        "correct_value": 196,
        "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_000245",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 7",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 0.9375,
      "pure_math": {
        "question": "Estimate 25 × 7.",
        "options": [
          "165",
          "195",
          "175",
          "185"
        ],
        "answer": "175",
        "correct_value": 175,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "26 * 7",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.9175,
      "pure_math": {
        "question": "Estimate 26 × 7.",
        "options": [
          "192",
          "202",
          "182",
          "172"
        ],
        "answer": "182",
        "correct_value": 182,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "30 * 11",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 30 × 11.",
        "options": [
          "320",
          "350",
          "330",
          "340"
        ],
        "answer": "330",
        "correct_value": 330,
        "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_000246",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26 * 9",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 0.9175,
      "pure_math": {
        "question": "Estimate 26 × 9.",
        "options": [
          "254",
          "244",
          "224",
          "234"
        ],
        "answer": "234",
        "correct_value": 234,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "24 * 9",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.9175,
      "pure_math": {
        "question": "Estimate 24 × 9.",
        "options": [
          "216",
          "226",
          "236",
          "206"
        ],
        "answer": "216",
        "correct_value": 216,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "30 * 12",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 30 × 12.",
        "options": [
          "350",
          "370",
          "380",
          "360"
        ],
        "answer": "360",
        "correct_value": 360,
        "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_000247",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "49 * 3",
      "ns_shortcut": "Round to 50×2 for easy mental computation.",
      "shortcut_strength": 0.74,
      "pure_math": {
        "question": "Estimate 49 × 3.",
        "options": [
          "167",
          "147",
          "157",
          "137"
        ],
        "answer": "147",
        "correct_value": 147,
        "explanation": "Round to compatible pair 50×2 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "49 * 1",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.74,
      "pure_math": {
        "question": "Estimate 49 × 1.",
        "options": [
          "39",
          "59",
          "69",
          "49"
        ],
        "answer": "49",
        "correct_value": 49,
        "explanation": "One number rounds to 50, other is farther from 2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "58 * 4",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 58 × 4.",
        "options": [
          "252",
          "222",
          "232",
          "242"
        ],
        "answer": "232",
        "correct_value": 232,
        "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_000248",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 9",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 0.9375,
      "pure_math": {
        "question": "Estimate 25 × 9.",
        "options": [
          "215",
          "245",
          "235",
          "225"
        ],
        "answer": "225",
        "correct_value": 225,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 * 6",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.875,
      "pure_math": {
        "question": "Estimate 25 × 6.",
        "options": [
          "160",
          "170",
          "140",
          "150"
        ],
        "answer": "150",
        "correct_value": 150,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "29 * 12",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 29 × 12.",
        "options": [
          "338",
          "368",
          "348",
          "358"
        ],
        "answer": "348",
        "correct_value": 348,
        "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_000249",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 * 7",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 0.9375,
      "pure_math": {
        "question": "Estimate 25 × 7.",
        "options": [
          "175",
          "165",
          "195",
          "185"
        ],
        "answer": "175",
        "correct_value": 175,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "24 * 7",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.9175,
      "pure_math": {
        "question": "Estimate 24 × 7.",
        "options": [
          "168",
          "178",
          "188",
          "158"
        ],
        "answer": "168",
        "correct_value": 168,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "31 * 10",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 31 × 10.",
        "options": [
          "330",
          "310",
          "300",
          "320"
        ],
        "answer": "310",
        "correct_value": 310,
        "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_000250",
    "category": "compatible_numbers",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "24 * 7",
      "ns_shortcut": "Round to 25×8 for easy mental computation.",
      "shortcut_strength": 0.9175,
      "pure_math": {
        "question": "Estimate 24 × 7.",
        "options": [
          "178",
          "168",
          "188",
          "158"
        ],
        "answer": "168",
        "correct_value": 168,
        "explanation": "Round to compatible pair 25×8 = 200."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "24 * 9",
      "ns_shortcut": "Compatible pair shortcut works but less precise.",
      "shortcut_strength": 0.9175,
      "pure_math": {
        "question": "Estimate 24 × 9.",
        "options": [
          "226",
          "236",
          "206",
          "216"
        ],
        "answer": "216",
        "correct_value": 216,
        "explanation": "One number rounds to 25, other is farther from 8."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "31 * 10",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Estimate 31 × 10.",
        "options": [
          "330",
          "320",
          "300",
          "310"
        ],
        "answer": "310",
        "correct_value": 310,
        "explanation": "Not near any compatible pair; full multiplication needed."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "landmark_comparison_000251",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10% of 880 vs 195",
      "ns_shortcut": "Use 10% as landmark: 10% of 880 = 88.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 10% of 880 greater than 195?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 88.0,
        "explanation": "10% ≈ 10%. 10% of 880 = 88. Compare to 195."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "14% of 880 vs 195",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 14% of 880 greater than 195?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 123.2,
        "explanation": "14% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 880 vs 195",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 880 greater than 195?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 730.4,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000252",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "52% of 790 vs 369",
      "ns_shortcut": "Use 50% as landmark: 50% of 790 = 395.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 52% of 790 greater than 369?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 410.8,
        "explanation": "52% ≈ 50%. 50% of 790 = 395. Compare to 369."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "55% of 790 vs 369",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 55% of 790 greater than 369?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 434.5,
        "explanation": "55% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 790 vs 369",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 790 greater than 369?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 292.3,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000253",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "24% of 990 vs 469",
      "ns_shortcut": "Use 25% as landmark: 25% of 990 = 247.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 24% of 990 greater than 469?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 237.6,
        "explanation": "24% ≈ 25%. 25% of 990 = 247. Compare to 469."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "30% of 990 vs 469",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 30% of 990 greater than 469?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 297.0,
        "explanation": "30% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 990 vs 469",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 990 greater than 469?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 821.7,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000254",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "50% of 990 vs 492",
      "ns_shortcut": "Use 50% as landmark: 50% of 990 = 495.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 50% of 990 greater than 492?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 495.0,
        "explanation": "50% ≈ 50%. 50% of 990 = 495. Compare to 492."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "56% of 990 vs 492",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 56% of 990 greater than 492?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 554.4,
        "explanation": "56% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "43% of 990 vs 492",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 43% of 990 greater than 492?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 425.7,
        "explanation": "43% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000255",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "11% of 200 vs 58",
      "ns_shortcut": "Use 10% as landmark: 10% of 200 = 20.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 11% of 200 greater than 58?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 22.0,
        "explanation": "11% ≈ 10%. 10% of 200 = 20. Compare to 58."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7% of 200 vs 58",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Is 7% of 200 greater than 58?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 14.0,
        "explanation": "7% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 200 vs 58",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 200 greater than 58?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 74.0,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000256",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "49% of 830 vs 299",
      "ns_shortcut": "Use 50% as landmark: 50% of 830 = 415.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 49% of 830 greater than 299?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 406.7,
        "explanation": "49% ≈ 50%. 50% of 830 = 415. Compare to 299."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "45% of 830 vs 299",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 45% of 830 greater than 299?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 373.5,
        "explanation": "45% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 830 vs 299",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 830 greater than 299?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 605.9,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000257",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "52% of 560 vs 139",
      "ns_shortcut": "Use 50% as landmark: 50% of 560 = 280.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 52% of 560 greater than 139?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 291.2,
        "explanation": "52% ≈ 50%. 50% of 560 = 280. Compare to 139."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "55% of 560 vs 139",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 55% of 560 greater than 139?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 308.0,
        "explanation": "55% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 560 vs 139",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 560 greater than 139?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 464.8,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000258",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "27% of 640 vs 272",
      "ns_shortcut": "Use 25% as landmark: 25% of 640 = 160.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 27% of 640 greater than 272?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 172.8,
        "explanation": "27% ≈ 25%. 25% of 640 = 160. Compare to 272."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "29% of 640 vs 272",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 29% of 640 greater than 272?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 185.6,
        "explanation": "29% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 640 vs 272",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 640 greater than 272?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 467.2,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000259",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10% of 800 vs 360",
      "ns_shortcut": "Use 10% as landmark: 10% of 800 = 80.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 10% of 800 greater than 360?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 80.0,
        "explanation": "10% ≈ 10%. 10% of 800 = 80. Compare to 360."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "17% of 800 vs 360",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.9299999999999999,
      "pure_math": {
        "question": "Is 17% of 800 greater than 360?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 136.0,
        "explanation": "17% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 800 vs 360",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 800 greater than 360?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 664.0,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000260",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "27% of 710 vs 206",
      "ns_shortcut": "Use 25% as landmark: 25% of 710 = 177.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 27% of 710 greater than 206?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 191.7,
        "explanation": "27% ≈ 25%. 25% of 710 = 177. Compare to 206."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "29% of 710 vs 206",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 29% of 710 greater than 206?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 205.9,
        "explanation": "29% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 710 vs 206",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 710 greater than 206?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 262.7,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000261",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10% of 390 vs 135",
      "ns_shortcut": "Use 10% as landmark: 10% of 390 = 39.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 10% of 390 greater than 135?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 39.0,
        "explanation": "10% ≈ 10%. 10% of 390 = 39. Compare to 135."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3% of 390 vs 135",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.9299999999999999,
      "pure_math": {
        "question": "Is 3% of 390 greater than 135?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 11.7,
        "explanation": "3% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 390 vs 135",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 390 greater than 135?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 284.7,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000262",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10% of 530 vs 246",
      "ns_shortcut": "Use 10% as landmark: 10% of 530 = 53.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 10% of 530 greater than 246?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 53.0,
        "explanation": "10% ≈ 10%. 10% of 530 = 53. Compare to 246."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "13% of 530 vs 246",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Is 13% of 530 greater than 246?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 68.9,
        "explanation": "13% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 530 vs 246",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 530 greater than 246?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 196.1,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000263",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10% of 280 vs 116",
      "ns_shortcut": "Use 10% as landmark: 10% of 280 = 28.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 10% of 280 greater than 116?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 28.0,
        "explanation": "10% ≈ 10%. 10% of 280 = 28. Compare to 116."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "5% of 280 vs 116",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 5% of 280 greater than 116?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 14.0,
        "explanation": "5% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "43% of 280 vs 116",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 43% of 280 greater than 116?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 120.4,
        "explanation": "43% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000264",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8% of 570 vs 134",
      "ns_shortcut": "Use 10% as landmark: 10% of 570 = 57.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 8% of 570 greater than 134?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 45.6,
        "explanation": "8% ≈ 10%. 10% of 570 = 57. Compare to 134."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "16% of 570 vs 134",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 16% of 570 greater than 134?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 91.2,
        "explanation": "16% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 570 vs 134",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 570 greater than 134?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 473.1,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000265",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25% of 930 vs 452",
      "ns_shortcut": "Use 25% as landmark: 25% of 930 = 232.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 25% of 930 greater than 452?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 232.5,
        "explanation": "25% ≈ 25%. 25% of 930 = 232. Compare to 452."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "31% of 930 vs 452",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 31% of 930 greater than 452?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 288.3,
        "explanation": "31% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 930 vs 452",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 930 greater than 452?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 344.1,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000266",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10% of 350 vs 154",
      "ns_shortcut": "Use 10% as landmark: 10% of 350 = 35.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 10% of 350 greater than 154?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 35.0,
        "explanation": "10% ≈ 10%. 10% of 350 = 35. Compare to 154."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3% of 350 vs 154",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.9299999999999999,
      "pure_math": {
        "question": "Is 3% of 350 greater than 154?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 10.5,
        "explanation": "3% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 350 vs 154",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 350 greater than 154?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 290.5,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000267",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "48% of 760 vs 330",
      "ns_shortcut": "Use 50% as landmark: 50% of 760 = 380.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 48% of 760 greater than 330?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 364.8,
        "explanation": "48% ≈ 50%. 50% of 760 = 380. Compare to 330."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "45% of 760 vs 330",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 45% of 760 greater than 330?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 342.0,
        "explanation": "45% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "43% of 760 vs 330",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 43% of 760 greater than 330?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 326.8,
        "explanation": "43% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000268",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "49% of 930 vs 186",
      "ns_shortcut": "Use 50% as landmark: 50% of 930 = 465.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 49% of 930 greater than 186?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 455.7,
        "explanation": "49% ≈ 50%. 50% of 930 = 465. Compare to 186."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "55% of 930 vs 186",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 55% of 930 greater than 186?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 511.5,
        "explanation": "55% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 930 vs 186",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 930 greater than 186?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 678.9,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000269",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "48% of 610 vs 272",
      "ns_shortcut": "Use 50% as landmark: 50% of 610 = 305.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 48% of 610 greater than 272?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 292.8,
        "explanation": "48% ≈ 50%. 50% of 610 = 305. Compare to 272."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "47% of 610 vs 272",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Is 47% of 610 greater than 272?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 286.7,
        "explanation": "47% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 610 vs 272",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 610 greater than 272?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 506.3,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000270",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25% of 460 vs 181",
      "ns_shortcut": "Use 25% as landmark: 25% of 460 = 115.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 25% of 460 greater than 181?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 115.0,
        "explanation": "25% ≈ 25%. 25% of 460 = 115. Compare to 181."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "19% of 460 vs 181",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 19% of 460 greater than 181?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 87.4,
        "explanation": "19% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 460 vs 181",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 460 greater than 181?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 335.8,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000271",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "24% of 830 vs 167",
      "ns_shortcut": "Use 25% as landmark: 25% of 830 = 207.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 24% of 830 greater than 167?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 199.2,
        "explanation": "24% ≈ 25%. 25% of 830 = 207. Compare to 167."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "18% of 830 vs 167",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.9299999999999999,
      "pure_math": {
        "question": "Is 18% of 830 greater than 167?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 149.4,
        "explanation": "18% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 830 vs 167",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 830 greater than 167?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 307.1,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000272",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "23% of 740 vs 223",
      "ns_shortcut": "Use 25% as landmark: 25% of 740 = 185.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 23% of 740 greater than 223?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 170.2,
        "explanation": "23% ≈ 25%. 25% of 740 = 185. Compare to 223."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "32% of 740 vs 223",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.9299999999999999,
      "pure_math": {
        "question": "Is 32% of 740 greater than 223?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 236.8,
        "explanation": "32% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 740 vs 223",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 740 greater than 223?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 614.2,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000273",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "27% of 420 vs 172",
      "ns_shortcut": "Use 25% as landmark: 25% of 420 = 105.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 27% of 420 greater than 172?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 113.4,
        "explanation": "27% ≈ 25%. 25% of 420 = 105. Compare to 172."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "29% of 420 vs 172",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 29% of 420 greater than 172?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 121.8,
        "explanation": "29% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "67% of 420 vs 172",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 67% of 420 greater than 172?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 281.4,
        "explanation": "67% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000274",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "24% of 680 vs 310",
      "ns_shortcut": "Use 25% as landmark: 25% of 680 = 170.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 24% of 680 greater than 310?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 163.2,
        "explanation": "24% ≈ 25%. 25% of 680 = 170. Compare to 310."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "20% of 680 vs 310",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 20% of 680 greater than 310?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 136.0,
        "explanation": "20% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 680 vs 310",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 680 greater than 310?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 251.6,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000275",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "49% of 580 vs 278",
      "ns_shortcut": "Use 50% as landmark: 50% of 580 = 290.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 49% of 580 greater than 278?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 284.2,
        "explanation": "49% ≈ 50%. 50% of 580 = 290. Compare to 278."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "55% of 580 vs 278",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 55% of 580 greater than 278?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 319.0,
        "explanation": "55% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 580 vs 278",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 580 greater than 278?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 481.4,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000276",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10% of 780 vs 158",
      "ns_shortcut": "Use 10% as landmark: 10% of 780 = 78.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 10% of 780 greater than 158?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 78.0,
        "explanation": "10% ≈ 10%. 10% of 780 = 78. Compare to 158."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "13% of 780 vs 158",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Is 13% of 780 greater than 158?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 101.4,
        "explanation": "13% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 780 vs 158",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 780 greater than 158?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 569.4,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000277",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "49% of 960 vs 367",
      "ns_shortcut": "Use 50% as landmark: 50% of 960 = 480.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 49% of 960 greater than 367?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 470.4,
        "explanation": "49% ≈ 50%. 50% of 960 = 480. Compare to 367."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "55% of 960 vs 367",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 55% of 960 greater than 367?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 528.0,
        "explanation": "55% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "43% of 960 vs 367",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 43% of 960 greater than 367?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 412.8,
        "explanation": "43% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000278",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "49% of 830 vs 234",
      "ns_shortcut": "Use 50% as landmark: 50% of 830 = 415.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 49% of 830 greater than 234?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 406.7,
        "explanation": "49% ≈ 50%. 50% of 830 = 415. Compare to 234."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "46% of 830 vs 234",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 46% of 830 greater than 234?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 381.8,
        "explanation": "46% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "43% of 830 vs 234",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 43% of 830 greater than 234?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 356.9,
        "explanation": "43% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000279",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "50% of 430 vs 138",
      "ns_shortcut": "Use 50% as landmark: 50% of 430 = 215.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 50% of 430 greater than 138?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 215.0,
        "explanation": "50% ≈ 50%. 50% of 430 = 215. Compare to 138."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "54% of 430 vs 138",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 54% of 430 greater than 138?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 232.2,
        "explanation": "54% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 430 vs 138",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 430 greater than 138?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 159.1,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000280",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "12% of 250 vs 60",
      "ns_shortcut": "Use 10% as landmark: 10% of 250 = 25.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 12% of 250 greater than 60?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 30.0,
        "explanation": "12% ≈ 10%. 10% of 250 = 25. Compare to 60."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "3% of 250 vs 60",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.9299999999999999,
      "pure_math": {
        "question": "Is 3% of 250 greater than 60?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 7.5,
        "explanation": "3% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 250 vs 60",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 250 greater than 60?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 92.5,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000281",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "11% of 710 vs 237",
      "ns_shortcut": "Use 10% as landmark: 10% of 710 = 71.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 11% of 710 greater than 237?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 78.1,
        "explanation": "11% ≈ 10%. 10% of 710 = 71. Compare to 237."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "16% of 710 vs 237",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 16% of 710 greater than 237?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 113.6,
        "explanation": "16% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "43% of 710 vs 237",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 43% of 710 greater than 237?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 305.3,
        "explanation": "43% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000282",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "23% of 750 vs 221",
      "ns_shortcut": "Use 25% as landmark: 25% of 750 = 187.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 23% of 750 greater than 221?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 172.5,
        "explanation": "23% ≈ 25%. 25% of 750 = 187. Compare to 221."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "22% of 750 vs 221",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Is 22% of 750 greater than 221?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 165.0,
        "explanation": "22% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 750 vs 221",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 750 greater than 221?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 622.5,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000283",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "8% of 640 vs 250",
      "ns_shortcut": "Use 10% as landmark: 10% of 640 = 64.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 8% of 640 greater than 250?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 51.2,
        "explanation": "8% ≈ 10%. 10% of 640 = 64. Compare to 250."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "16% of 640 vs 250",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 16% of 640 greater than 250?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 102.4,
        "explanation": "16% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "43% of 640 vs 250",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 43% of 640 greater than 250?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 275.2,
        "explanation": "43% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000284",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "11% of 680 vs 166",
      "ns_shortcut": "Use 10% as landmark: 10% of 680 = 68.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 11% of 680 greater than 166?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 74.8,
        "explanation": "11% ≈ 10%. 10% of 680 = 68. Compare to 166."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "7% of 680 vs 166",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Is 7% of 680 greater than 166?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 47.6,
        "explanation": "7% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "43% of 680 vs 166",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 43% of 680 greater than 166?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 292.4,
        "explanation": "43% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000285",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "51% of 580 vs 264",
      "ns_shortcut": "Use 50% as landmark: 50% of 580 = 290.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 51% of 580 greater than 264?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 295.8,
        "explanation": "51% ≈ 50%. 50% of 580 = 290. Compare to 264."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "54% of 580 vs 264",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 54% of 580 greater than 264?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 313.2,
        "explanation": "54% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 580 vs 264",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 580 greater than 264?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 481.4,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000286",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "27% of 430 vs 146",
      "ns_shortcut": "Use 25% as landmark: 25% of 430 = 107.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 27% of 430 greater than 146?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 116.1,
        "explanation": "27% ≈ 25%. 25% of 430 = 107. Compare to 146."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "30% of 430 vs 146",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 30% of 430 greater than 146?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 129.0,
        "explanation": "30% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "43% of 430 vs 146",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 43% of 430 greater than 146?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 184.9,
        "explanation": "43% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000287",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "52% of 730 vs 254",
      "ns_shortcut": "Use 50% as landmark: 50% of 730 = 365.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 52% of 730 greater than 254?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 379.6,
        "explanation": "52% ≈ 50%. 50% of 730 = 365. Compare to 254."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "55% of 730 vs 254",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 55% of 730 greater than 254?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 401.5,
        "explanation": "55% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 730 vs 254",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 730 greater than 254?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 532.9,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000288",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "48% of 450 vs 205",
      "ns_shortcut": "Use 50% as landmark: 50% of 450 = 225.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 48% of 450 greater than 205?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 216.0,
        "explanation": "48% ≈ 50%. 50% of 450 = 225. Compare to 205."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "47% of 450 vs 205",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.97,
      "pure_math": {
        "question": "Is 47% of 450 greater than 205?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 211.5,
        "explanation": "47% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "67% of 450 vs 205",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 67% of 450 greater than 205?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 301.5,
        "explanation": "67% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000289",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25% of 400 vs 151",
      "ns_shortcut": "Use 25% as landmark: 25% of 400 = 100.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 25% of 400 greater than 151?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 100.0,
        "explanation": "25% ≈ 25%. 25% of 400 = 100. Compare to 151."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "21% of 400 vs 151",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 21% of 400 greater than 151?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 84.0,
        "explanation": "21% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 400 vs 151",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 400 greater than 151?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 292.0,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000290",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25% of 110 vs 33",
      "ns_shortcut": "Use 25% as landmark: 25% of 110 = 27.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 25% of 110 greater than 33?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 27.5,
        "explanation": "25% ≈ 25%. 25% of 110 = 27. Compare to 33."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "31% of 110 vs 33",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 31% of 110 greater than 33?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 34.1,
        "explanation": "31% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "67% of 110 vs 33",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 67% of 110 greater than 33?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 73.7,
        "explanation": "67% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000291",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "9% of 420 vs 155",
      "ns_shortcut": "Use 10% as landmark: 10% of 420 = 42.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 9% of 420 greater than 155?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 37.8,
        "explanation": "9% ≈ 10%. 10% of 420 = 42. Compare to 155."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6% of 420 vs 155",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 6% of 420 greater than 155?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 25.2,
        "explanation": "6% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 420 vs 155",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 420 greater than 155?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 155.4,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000292",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "27% of 370 vs 178",
      "ns_shortcut": "Use 25% as landmark: 25% of 370 = 92.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 27% of 370 greater than 178?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 99.9,
        "explanation": "27% ≈ 25%. 25% of 370 = 92. Compare to 178."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "19% of 370 vs 178",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 19% of 370 greater than 178?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 70.3,
        "explanation": "19% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "67% of 370 vs 178",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 67% of 370 greater than 178?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 247.9,
        "explanation": "67% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000293",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26% of 430 vs 178",
      "ns_shortcut": "Use 25% as landmark: 25% of 430 = 107.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 26% of 430 greater than 178?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 111.8,
        "explanation": "26% ≈ 25%. 25% of 430 = 107. Compare to 178."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "19% of 430 vs 178",
      "ns_shortcut": "Use 25% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 19% of 430 greater than 178?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 81.7,
        "explanation": "19% is near 25% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 430 vs 178",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 430 greater than 178?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 159.1,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000294",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "49% of 540 vs 263",
      "ns_shortcut": "Use 50% as landmark: 50% of 540 = 270.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 49% of 540 greater than 263?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 264.6,
        "explanation": "49% ≈ 50%. 50% of 540 = 270. Compare to 263."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "55% of 540 vs 263",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 55% of 540 greater than 263?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 297.0,
        "explanation": "55% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 540 vs 263",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 540 greater than 263?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 448.2,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000295",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10% of 720 vs 342",
      "ns_shortcut": "Use 10% as landmark: 10% of 720 = 72.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 10% of 720 greater than 342?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 72.0,
        "explanation": "10% ≈ 10%. 10% of 720 = 72. Compare to 342."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "17% of 720 vs 342",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.9299999999999999,
      "pure_math": {
        "question": "Is 17% of 720 greater than 342?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 122.4,
        "explanation": "17% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "67% of 720 vs 342",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 67% of 720 greater than 342?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 482.4,
        "explanation": "67% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000296",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "48% of 690 vs 299",
      "ns_shortcut": "Use 50% as landmark: 50% of 690 = 345.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 48% of 690 greater than 299?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 331.2,
        "explanation": "48% ≈ 50%. 50% of 690 = 345. Compare to 299."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "56% of 690 vs 299",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.94,
      "pure_math": {
        "question": "Is 56% of 690 greater than 299?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 386.4,
        "explanation": "56% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "83% of 690 vs 299",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 83% of 690 greater than 299?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 572.7,
        "explanation": "83% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000297",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "50% of 830 vs 269",
      "ns_shortcut": "Use 50% as landmark: 50% of 830 = 415.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "Is 50% of 830 greater than 269?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 415.0,
        "explanation": "50% ≈ 50%. 50% of 830 = 415. Compare to 269."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "54% of 830 vs 269",
      "ns_shortcut": "Use 50% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 54% of 830 greater than 269?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 448.2,
        "explanation": "54% is near 50% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "67% of 830 vs 269",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 67% of 830 greater than 269?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 556.1,
        "explanation": "67% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000298",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "12% of 500 vs 174",
      "ns_shortcut": "Use 10% as landmark: 10% of 500 = 50.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 12% of 500 greater than 174?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 60.0,
        "explanation": "12% ≈ 10%. 10% of 500 = 50. Compare to 174."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "15% of 500 vs 174",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.95,
      "pure_math": {
        "question": "Is 15% of 500 greater than 174?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 75.0,
        "explanation": "15% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "73% of 500 vs 174",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 73% of 500 greater than 174?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 365.0,
        "explanation": "73% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000299",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "11% of 560 vs 262",
      "ns_shortcut": "Use 10% as landmark: 10% of 560 = 56.",
      "shortcut_strength": 0.99,
      "pure_math": {
        "question": "Is 11% of 560 greater than 262?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 61.6,
        "explanation": "11% ≈ 10%. 10% of 560 = 56. Compare to 262."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6% of 560 vs 262",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 6% of 560 greater than 262?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 33.6,
        "explanation": "6% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "37% of 560 vs 262",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 37% of 560 greater than 262?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 207.2,
        "explanation": "37% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "landmark_comparison_000300",
    "category": "landmark_comparison",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "12% of 260 vs 82",
      "ns_shortcut": "Use 10% as landmark: 10% of 260 = 26.",
      "shortcut_strength": 0.98,
      "pure_math": {
        "question": "Is 12% of 260 greater than 82?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 31.2,
        "explanation": "12% ≈ 10%. 10% of 260 = 26. Compare to 82."
      }
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "6% of 260 vs 82",
      "ns_shortcut": "Use 10% as approximate anchor, then adjust.",
      "shortcut_strength": 0.96,
      "pure_math": {
        "question": "Is 6% of 260 greater than 82?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "No",
        "correct_value": 15.6,
        "explanation": "6% is near 10% but requires adjustment."
      }
    },
    "control": {
      "task_type": "control",
      "math_expression": "43% of 260 vs 82",
      "ns_shortcut": "No clean shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "Is 43% of 260 greater than 82?",
        "options": [
          "Yes",
          "No",
          "Cannot be determined",
          "Need more information"
        ],
        "answer": "Yes",
        "correct_value": 111.8,
        "explanation": "43% is not near any standard landmark; compute directly."
      }
    }
  },
  {
    "family_id": "equation_reasoning_000301",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "23 + 22 = ___ + 18",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  23 + 22 = ___ + 18",
        "options": [
          "37",
          "27",
          "47",
          "17"
        ],
        "answer": "27",
        "correct_value": 27,
        "explanation": "Blank = A + B − C = 23 + 22 − 18 = 27."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "13 + 60 + ___ = 60 + 77 + 20",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  13 + 60 + ___ = 60 + 77 + 20",
        "options": [
          "104",
          "74",
          "94",
          "84"
        ],
        "answer": "84",
        "correct_value": 84,
        "explanation": "B cancels; blank = C + D − A = 77 + 20 − 13 = 84."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "20 + 93 + ___ = 59 + 49",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  20 + 93 + ___ = 59 + 49",
        "options": [
          "15",
          "-15",
          "-5",
          "5"
        ],
        "answer": "-5",
        "correct_value": -5,
        "explanation": "No matching terms; blank = 59 + 49 − 20 − 93 = -5."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000302",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "90 + 26 = ___ + 26",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  90 + 26 = ___ + 26",
        "options": [
          "80",
          "110",
          "90",
          "100"
        ],
        "answer": "90",
        "correct_value": 90,
        "explanation": "Blank = A + B − C = 90 + 26 − 26 = 90."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "94 + 55 + ___ = 55 + 51 + 70",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  94 + 55 + ___ = 55 + 51 + 70",
        "options": [
          "27",
          "37",
          "47",
          "17"
        ],
        "answer": "27",
        "correct_value": 27,
        "explanation": "B cancels; blank = C + D − A = 51 + 70 − 94 = 27."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "80 + 66 + ___ = 27 + 99",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  80 + 66 + ___ = 27 + 99",
        "options": [
          "-20",
          "-30",
          "0",
          "-10"
        ],
        "answer": "-20",
        "correct_value": -20,
        "explanation": "No matching terms; blank = 27 + 99 − 80 − 66 = -20."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000303",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "77 + 91 = ___ + 91",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  77 + 91 = ___ + 91",
        "options": [
          "77",
          "67",
          "87",
          "97"
        ],
        "answer": "77",
        "correct_value": 77,
        "explanation": "Blank = A + B − C = 77 + 91 − 91 = 77."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "79 + 39 + ___ = 39 + 21 + 66",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  79 + 39 + ___ = 39 + 21 + 66",
        "options": [
          "8",
          "-2",
          "18",
          "28"
        ],
        "answer": "8",
        "correct_value": 8,
        "explanation": "B cancels; blank = C + D − A = 21 + 66 − 79 = 8."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "43 + 29 + ___ = 48 + 11",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  43 + 29 + ___ = 48 + 11",
        "options": [
          "-7",
          "-27",
          "3",
          "-13"
        ],
        "answer": "-13",
        "correct_value": -13,
        "explanation": "No matching terms; blank = 48 + 11 − 43 − 29 = -13."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000304",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "46 × (70 + 78) = 46 × ___ + 46 × 78",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  46 × (70 + 78) = 46 × ___ + 46 × 78",
        "options": [
          "60",
          "80",
          "90",
          "70"
        ],
        "answer": "70",
        "correct_value": 70,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 70."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "71 + 48 + ___ = 48 + 11 + 65",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  71 + 48 + ___ = 48 + 11 + 65",
        "options": [
          "15",
          "5",
          "-5",
          "25"
        ],
        "answer": "5",
        "correct_value": 5,
        "explanation": "B cancels; blank = C + D − A = 11 + 65 − 71 = 5."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "10 + 80 + ___ = 57 + 34",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  10 + 80 + ___ = 57 + 34",
        "options": [
          "1",
          "11",
          "21",
          "-9"
        ],
        "answer": "1",
        "correct_value": 1,
        "explanation": "No matching terms; blank = 57 + 34 − 10 − 80 = 1."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000305",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "41 + 30 = ___ + 92",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  41 + 30 = ___ + 92",
        "options": [
          "-9",
          "-21",
          "-19",
          "-39"
        ],
        "answer": "-21",
        "correct_value": -21,
        "explanation": "Blank = A + B − C = 41 + 30 − 92 = -21."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "43 + 20 + ___ = 20 + 64 + 90",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  43 + 20 + ___ = 20 + 64 + 90",
        "options": [
          "111",
          "101",
          "131",
          "121"
        ],
        "answer": "111",
        "correct_value": 111,
        "explanation": "B cancels; blank = C + D − A = 64 + 90 − 43 = 111."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "46 + 93 + ___ = 78 + 44",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  46 + 93 + ___ = 78 + 44",
        "options": [
          "-13",
          "-3",
          "-17",
          "-33"
        ],
        "answer": "-17",
        "correct_value": -17,
        "explanation": "No matching terms; blank = 78 + 44 − 46 − 93 = -17."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000306",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "27 × 47 × 24 = ___ × 24 × 27",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  27 × 47 × 24 = ___ × 24 × 27",
        "options": [
          "47",
          "57",
          "67",
          "37"
        ],
        "answer": "47",
        "correct_value": 47,
        "explanation": "A and C appear on both sides; blank = B = 47."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "44 + 99 + ___ = 99 + 89 + 72",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  44 + 99 + ___ = 99 + 89 + 72",
        "options": [
          "137",
          "117",
          "107",
          "127"
        ],
        "answer": "117",
        "correct_value": 117,
        "explanation": "B cancels; blank = C + D − A = 89 + 72 − 44 = 117."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "29 + 16 + ___ = 78 + 12",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  29 + 16 + ___ = 78 + 12",
        "options": [
          "65",
          "35",
          "45",
          "55"
        ],
        "answer": "45",
        "correct_value": 45,
        "explanation": "No matching terms; blank = 78 + 12 − 29 − 16 = 45."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000307",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "26 × (66 + 11) = 26 × ___ + 26 × 11",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  26 × (66 + 11) = 26 × ___ + 26 × 11",
        "options": [
          "56",
          "86",
          "66",
          "76"
        ],
        "answer": "66",
        "correct_value": 66,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 66."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "11 + 73 + ___ = 73 + 37 + 53",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  11 + 73 + ___ = 73 + 37 + 53",
        "options": [
          "79",
          "99",
          "89",
          "69"
        ],
        "answer": "79",
        "correct_value": 79,
        "explanation": "B cancels; blank = C + D − A = 37 + 53 − 11 = 79."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "57 + 69 + ___ = 99 + 14",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  57 + 69 + ___ = 99 + 14",
        "options": [
          "-7",
          "-27",
          "-13",
          "3"
        ],
        "answer": "-13",
        "correct_value": -13,
        "explanation": "No matching terms; blank = 99 + 14 − 57 − 69 = -13."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000308",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "44 + 60 + ___ = 60 + 19 + 44",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  44 + 60 + ___ = 60 + 19 + 44",
        "options": [
          "29",
          "39",
          "19",
          "9"
        ],
        "answer": "19",
        "correct_value": 19,
        "explanation": "A and B appear on both sides and cancel; blank = C = 19."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "42 + 58 + ___ = 58 + 11 + 25",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  42 + 58 + ___ = 58 + 11 + 25",
        "options": [
          "-6",
          "6",
          "-24",
          "-4"
        ],
        "answer": "-6",
        "correct_value": -6,
        "explanation": "B cancels; blank = C + D − A = 11 + 25 − 42 = -6."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "41 + 14 + ___ = 35 + 68",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  41 + 14 + ___ = 35 + 68",
        "options": [
          "58",
          "38",
          "68",
          "48"
        ],
        "answer": "48",
        "correct_value": 48,
        "explanation": "No matching terms; blank = 35 + 68 − 41 − 14 = 48."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000309",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "59 + 97 = ___ + 49",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  59 + 97 = ___ + 49",
        "options": [
          "117",
          "97",
          "107",
          "127"
        ],
        "answer": "107",
        "correct_value": 107,
        "explanation": "Blank = A + B − C = 59 + 97 − 49 = 107."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "80 + 76 + ___ = 76 + 25 + 42",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  80 + 76 + ___ = 76 + 25 + 42",
        "options": [
          "-13",
          "-7",
          "3",
          "-27"
        ],
        "answer": "-13",
        "correct_value": -13,
        "explanation": "B cancels; blank = C + D − A = 25 + 42 − 80 = -13."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "35 + 56 + ___ = 16 + 95",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  35 + 56 + ___ = 16 + 95",
        "options": [
          "10",
          "40",
          "20",
          "30"
        ],
        "answer": "20",
        "correct_value": 20,
        "explanation": "No matching terms; blank = 16 + 95 − 35 − 56 = 20."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000310",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "51 + 11 = ___ + 31",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  51 + 11 = ___ + 31",
        "options": [
          "41",
          "31",
          "21",
          "51"
        ],
        "answer": "31",
        "correct_value": 31,
        "explanation": "Blank = A + B − C = 51 + 11 − 31 = 31."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "60 + 41 + ___ = 41 + 11 + 15",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  60 + 41 + ___ = 41 + 11 + 15",
        "options": [
          "-26",
          "-34",
          "-16",
          "-46"
        ],
        "answer": "-34",
        "correct_value": -34,
        "explanation": "B cancels; blank = C + D − A = 11 + 15 − 60 = -34."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "57 + 21 + ___ = 41 + 30",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  57 + 21 + ___ = 41 + 30",
        "options": [
          "7",
          "-3",
          "-7",
          "-23"
        ],
        "answer": "-7",
        "correct_value": -7,
        "explanation": "No matching terms; blank = 41 + 30 − 57 − 21 = -7."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000311",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "17 + 55 + ___ = 55 + 92 + 17",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  17 + 55 + ___ = 55 + 92 + 17",
        "options": [
          "82",
          "92",
          "112",
          "102"
        ],
        "answer": "92",
        "correct_value": 92,
        "explanation": "A and B appear on both sides and cancel; blank = C = 92."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "26 + 72 + ___ = 72 + 39 + 50",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  26 + 72 + ___ = 72 + 39 + 50",
        "options": [
          "53",
          "63",
          "73",
          "83"
        ],
        "answer": "63",
        "correct_value": 63,
        "explanation": "B cancels; blank = C + D − A = 39 + 50 − 26 = 63."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "12 + 98 + ___ = 58 + 55",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  12 + 98 + ___ = 58 + 55",
        "options": [
          "23",
          "3",
          "-7",
          "13"
        ],
        "answer": "3",
        "correct_value": 3,
        "explanation": "No matching terms; blank = 58 + 55 − 12 − 98 = 3."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000312",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "66 + 81 = ___ + 47",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  66 + 81 = ___ + 47",
        "options": [
          "110",
          "120",
          "100",
          "90"
        ],
        "answer": "100",
        "correct_value": 100,
        "explanation": "Blank = A + B − C = 66 + 81 − 47 = 100."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "79 + 54 + ___ = 54 + 51 + 69",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  79 + 54 + ___ = 54 + 51 + 69",
        "options": [
          "51",
          "41",
          "31",
          "61"
        ],
        "answer": "41",
        "correct_value": 41,
        "explanation": "B cancels; blank = C + D − A = 51 + 69 − 79 = 41."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "18 + 77 + ___ = 29 + 67",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  18 + 77 + ___ = 29 + 67",
        "options": [
          "1",
          "-9",
          "11",
          "21"
        ],
        "answer": "1",
        "correct_value": 1,
        "explanation": "No matching terms; blank = 29 + 67 − 18 − 77 = 1."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000313",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10 + 91 = ___ + 74",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  10 + 91 = ___ + 74",
        "options": [
          "37",
          "27",
          "47",
          "17"
        ],
        "answer": "27",
        "correct_value": 27,
        "explanation": "Blank = A + B − C = 10 + 91 − 74 = 27."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "12 + 89 + ___ = 89 + 56 + 89",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  12 + 89 + ___ = 89 + 56 + 89",
        "options": [
          "153",
          "133",
          "123",
          "143"
        ],
        "answer": "133",
        "correct_value": 133,
        "explanation": "B cancels; blank = C + D − A = 56 + 89 − 12 = 133."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "94 + 78 + ___ = 59 + 34",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  94 + 78 + ___ = 59 + 34",
        "options": [
          "-71",
          "-79",
          "-61",
          "-91"
        ],
        "answer": "-79",
        "correct_value": -79,
        "explanation": "No matching terms; blank = 59 + 34 − 94 − 78 = -79."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000314",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "51 × (62 + 92) = 51 × ___ + 51 × 92",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  51 × (62 + 92) = 51 × ___ + 51 × 92",
        "options": [
          "72",
          "52",
          "62",
          "82"
        ],
        "answer": "62",
        "correct_value": 62,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 62."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "76 + 94 + ___ = 94 + 18 + 15",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  76 + 94 + ___ = 94 + 18 + 15",
        "options": [
          "-57",
          "-27",
          "-43",
          "-37"
        ],
        "answer": "-43",
        "correct_value": -43,
        "explanation": "B cancels; blank = C + D − A = 18 + 15 − 76 = -43."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "35 + 23 + ___ = 72 + 34",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  35 + 23 + ___ = 72 + 34",
        "options": [
          "68",
          "58",
          "38",
          "48"
        ],
        "answer": "48",
        "correct_value": 48,
        "explanation": "No matching terms; blank = 72 + 34 − 35 − 23 = 48."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000315",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "77 + 89 = ___ + 99",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  77 + 89 = ___ + 99",
        "options": [
          "57",
          "77",
          "67",
          "87"
        ],
        "answer": "67",
        "correct_value": 67,
        "explanation": "Blank = A + B − C = 77 + 89 − 99 = 67."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "38 + 87 + ___ = 87 + 19 + 11",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  38 + 87 + ___ = 87 + 19 + 11",
        "options": [
          "-8",
          "-22",
          "8",
          "-2"
        ],
        "answer": "-8",
        "correct_value": -8,
        "explanation": "B cancels; blank = C + D − A = 19 + 11 − 38 = -8."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "20 + 69 + ___ = 91 + 17",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  20 + 69 + ___ = 91 + 17",
        "options": [
          "19",
          "29",
          "9",
          "39"
        ],
        "answer": "19",
        "correct_value": 19,
        "explanation": "No matching terms; blank = 91 + 17 − 20 − 69 = 19."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000316",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "17 × (88 + 44) = 17 × ___ + 17 × 44",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  17 × (88 + 44) = 17 × ___ + 17 × 44",
        "options": [
          "98",
          "78",
          "108",
          "88"
        ],
        "answer": "88",
        "correct_value": 88,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 88."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "48 + 19 + ___ = 19 + 37 + 76",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  48 + 19 + ___ = 19 + 37 + 76",
        "options": [
          "75",
          "85",
          "55",
          "65"
        ],
        "answer": "65",
        "correct_value": 65,
        "explanation": "B cancels; blank = C + D − A = 37 + 76 − 48 = 65."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "78 + 59 + ___ = 34 + 34",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  78 + 59 + ___ = 34 + 34",
        "options": [
          "-81",
          "-69",
          "-51",
          "-61"
        ],
        "answer": "-69",
        "correct_value": -69,
        "explanation": "No matching terms; blank = 34 + 34 − 78 − 59 = -69."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000317",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "23 + 91 = ___ + 83",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  23 + 91 = ___ + 83",
        "options": [
          "31",
          "41",
          "21",
          "51"
        ],
        "answer": "31",
        "correct_value": 31,
        "explanation": "Blank = A + B − C = 23 + 91 − 83 = 31."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "99 + 95 + ___ = 95 + 64 + 23",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  99 + 95 + ___ = 95 + 64 + 23",
        "options": [
          "2",
          "-28",
          "-12",
          "-8"
        ],
        "answer": "-12",
        "correct_value": -12,
        "explanation": "B cancels; blank = C + D − A = 64 + 23 − 99 = -12."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "74 + 53 + ___ = 94 + 30",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  74 + 53 + ___ = 94 + 30",
        "options": [
          "-3",
          "13",
          "3",
          "-17"
        ],
        "answer": "-3",
        "correct_value": -3,
        "explanation": "No matching terms; blank = 94 + 30 − 74 − 53 = -3."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000318",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "57 × (62 + 91) = 57 × ___ + 57 × 91",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  57 × (62 + 91) = 57 × ___ + 57 × 91",
        "options": [
          "62",
          "72",
          "82",
          "52"
        ],
        "answer": "62",
        "correct_value": 62,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 62."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "87 + 40 + ___ = 40 + 82 + 79",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  87 + 40 + ___ = 40 + 82 + 79",
        "options": [
          "74",
          "94",
          "64",
          "84"
        ],
        "answer": "74",
        "correct_value": 74,
        "explanation": "B cancels; blank = C + D − A = 82 + 79 − 87 = 74."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "56 + 67 + ___ = 67 + 60",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  56 + 67 + ___ = 67 + 60",
        "options": [
          "14",
          "-6",
          "24",
          "4"
        ],
        "answer": "4",
        "correct_value": 4,
        "explanation": "No matching terms; blank = 67 + 60 − 56 − 67 = 4."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000319",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "86 × (12 + 76) = 86 × ___ + 86 × 76",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  86 × (12 + 76) = 86 × ___ + 86 × 76",
        "options": [
          "32",
          "12",
          "2",
          "22"
        ],
        "answer": "12",
        "correct_value": 12,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 12."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "48 + 38 + ___ = 38 + 37 + 50",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  48 + 38 + ___ = 38 + 37 + 50",
        "options": [
          "29",
          "49",
          "59",
          "39"
        ],
        "answer": "39",
        "correct_value": 39,
        "explanation": "B cancels; blank = C + D − A = 37 + 50 − 48 = 39."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "80 + 75 + ___ = 81 + 83",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  80 + 75 + ___ = 81 + 83",
        "options": [
          "-1",
          "29",
          "9",
          "19"
        ],
        "answer": "9",
        "correct_value": 9,
        "explanation": "No matching terms; blank = 81 + 83 − 80 − 75 = 9."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000320",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "55 + 29 = ___ + 27",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  55 + 29 = ___ + 27",
        "options": [
          "47",
          "57",
          "67",
          "77"
        ],
        "answer": "57",
        "correct_value": 57,
        "explanation": "Blank = A + B − C = 55 + 29 − 27 = 57."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "39 + 42 + ___ = 42 + 48 + 21",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  39 + 42 + ___ = 42 + 48 + 21",
        "options": [
          "40",
          "30",
          "50",
          "20"
        ],
        "answer": "30",
        "correct_value": 30,
        "explanation": "B cancels; blank = C + D − A = 48 + 21 − 39 = 30."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "19 + 51 + ___ = 71 + 32",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  19 + 51 + ___ = 71 + 32",
        "options": [
          "43",
          "33",
          "53",
          "23"
        ],
        "answer": "33",
        "correct_value": 33,
        "explanation": "No matching terms; blank = 71 + 32 − 19 − 51 = 33."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000321",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "14 × (83 + 58) = 14 × ___ + 14 × 58",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  14 × (83 + 58) = 14 × ___ + 14 × 58",
        "options": [
          "103",
          "93",
          "73",
          "83"
        ],
        "answer": "83",
        "correct_value": 83,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 83."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "54 + 65 + ___ = 65 + 63 + 25",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  54 + 65 + ___ = 65 + 63 + 25",
        "options": [
          "24",
          "34",
          "54",
          "44"
        ],
        "answer": "34",
        "correct_value": 34,
        "explanation": "B cancels; blank = C + D − A = 63 + 25 − 54 = 34."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "91 + 90 + ___ = 58 + 16",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  91 + 90 + ___ = 58 + 16",
        "options": [
          "-103",
          "-107",
          "-123",
          "-93"
        ],
        "answer": "-107",
        "correct_value": -107,
        "explanation": "No matching terms; blank = 58 + 16 − 91 − 90 = -107."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000322",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "79 × (82 + 29) = 79 × ___ + 79 × 29",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  79 × (82 + 29) = 79 × ___ + 79 × 29",
        "options": [
          "92",
          "82",
          "72",
          "102"
        ],
        "answer": "82",
        "correct_value": 82,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 82."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "29 + 16 + ___ = 16 + 96 + 60",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  29 + 16 + ___ = 16 + 96 + 60",
        "options": [
          "137",
          "127",
          "147",
          "117"
        ],
        "answer": "127",
        "correct_value": 127,
        "explanation": "B cancels; blank = C + D − A = 96 + 60 − 29 = 127."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "38 + 65 + ___ = 47 + 60",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  38 + 65 + ___ = 47 + 60",
        "options": [
          "24",
          "-6",
          "4",
          "14"
        ],
        "answer": "4",
        "correct_value": 4,
        "explanation": "No matching terms; blank = 47 + 60 − 38 − 65 = 4."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000323",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "70 + 83 + ___ = 83 + 16 + 70",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  70 + 83 + ___ = 83 + 16 + 70",
        "options": [
          "36",
          "16",
          "26",
          "6"
        ],
        "answer": "16",
        "correct_value": 16,
        "explanation": "A and B appear on both sides and cancel; blank = C = 16."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "61 + 74 + ___ = 74 + 65 + 99",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  61 + 74 + ___ = 74 + 65 + 99",
        "options": [
          "123",
          "93",
          "103",
          "113"
        ],
        "answer": "103",
        "correct_value": 103,
        "explanation": "B cancels; blank = C + D − A = 65 + 99 − 61 = 103."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "81 + 35 + ___ = 72 + 60",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  81 + 35 + ___ = 72 + 60",
        "options": [
          "6",
          "16",
          "36",
          "26"
        ],
        "answer": "16",
        "correct_value": 16,
        "explanation": "No matching terms; blank = 72 + 60 − 81 − 35 = 16."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000324",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "19 × 44 × 65 = ___ × 65 × 19",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  19 × 44 × 65 = ___ × 65 × 19",
        "options": [
          "54",
          "44",
          "34",
          "64"
        ],
        "answer": "44",
        "correct_value": 44,
        "explanation": "A and C appear on both sides; blank = B = 44."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "24 + 95 + ___ = 95 + 62 + 64",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  24 + 95 + ___ = 95 + 62 + 64",
        "options": [
          "92",
          "102",
          "112",
          "122"
        ],
        "answer": "102",
        "correct_value": 102,
        "explanation": "B cancels; blank = C + D − A = 62 + 64 − 24 = 102."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "51 + 54 + ___ = 86 + 93",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  51 + 54 + ___ = 86 + 93",
        "options": [
          "94",
          "64",
          "84",
          "74"
        ],
        "answer": "74",
        "correct_value": 74,
        "explanation": "No matching terms; blank = 86 + 93 − 51 − 54 = 74."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000325",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "88 × (66 + 89) = 88 × ___ + 88 × 89",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  88 × (66 + 89) = 88 × ___ + 88 × 89",
        "options": [
          "86",
          "66",
          "56",
          "76"
        ],
        "answer": "66",
        "correct_value": 66,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 66."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "39 + 35 + ___ = 35 + 97 + 57",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  39 + 35 + ___ = 35 + 97 + 57",
        "options": [
          "105",
          "115",
          "135",
          "125"
        ],
        "answer": "115",
        "correct_value": 115,
        "explanation": "B cancels; blank = C + D − A = 97 + 57 − 39 = 115."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "24 + 16 + ___ = 41 + 89",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  24 + 16 + ___ = 41 + 89",
        "options": [
          "110",
          "90",
          "80",
          "100"
        ],
        "answer": "90",
        "correct_value": 90,
        "explanation": "No matching terms; blank = 41 + 89 − 24 − 16 = 90."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000326",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 × (24 + 49) = 98 × ___ + 98 × 49",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  98 × (24 + 49) = 98 × ___ + 98 × 49",
        "options": [
          "44",
          "24",
          "34",
          "14"
        ],
        "answer": "24",
        "correct_value": 24,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 24."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "52 + 36 + ___ = 36 + 78 + 37",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  52 + 36 + ___ = 36 + 78 + 37",
        "options": [
          "63",
          "53",
          "83",
          "73"
        ],
        "answer": "63",
        "correct_value": 63,
        "explanation": "B cancels; blank = C + D − A = 78 + 37 − 52 = 63."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "80 + 71 + ___ = 89 + 28",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  80 + 71 + ___ = 89 + 28",
        "options": [
          "-16",
          "-46",
          "-26",
          "-34"
        ],
        "answer": "-34",
        "correct_value": -34,
        "explanation": "No matching terms; blank = 89 + 28 − 80 − 71 = -34."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000327",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "31 × (17 + 46) = 31 × ___ + 31 × 46",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  31 × (17 + 46) = 31 × ___ + 31 × 46",
        "options": [
          "17",
          "7",
          "37",
          "27"
        ],
        "answer": "17",
        "correct_value": 17,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 17."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "16 + 69 + ___ = 69 + 93 + 11",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  16 + 69 + ___ = 69 + 93 + 11",
        "options": [
          "78",
          "108",
          "98",
          "88"
        ],
        "answer": "88",
        "correct_value": 88,
        "explanation": "B cancels; blank = C + D − A = 93 + 11 − 16 = 88."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "94 + 94 + ___ = 56 + 23",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  94 + 94 + ___ = 56 + 23",
        "options": [
          "-121",
          "-91",
          "-101",
          "-109"
        ],
        "answer": "-109",
        "correct_value": -109,
        "explanation": "No matching terms; blank = 56 + 23 − 94 − 94 = -109."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000328",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "58 × 75 × 22 = ___ × 22 × 58",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  58 × 75 × 22 = ___ × 22 × 58",
        "options": [
          "65",
          "75",
          "85",
          "95"
        ],
        "answer": "75",
        "correct_value": 75,
        "explanation": "A and C appear on both sides; blank = B = 75."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "33 + 35 + ___ = 35 + 74 + 68",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  33 + 35 + ___ = 35 + 74 + 68",
        "options": [
          "119",
          "129",
          "99",
          "109"
        ],
        "answer": "109",
        "correct_value": 109,
        "explanation": "B cancels; blank = C + D − A = 74 + 68 − 33 = 109."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "77 + 49 + ___ = 52 + 72",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  77 + 49 + ___ = 52 + 72",
        "options": [
          "2",
          "-2",
          "12",
          "-18"
        ],
        "answer": "-2",
        "correct_value": -2,
        "explanation": "No matching terms; blank = 52 + 72 − 77 − 49 = -2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000329",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "54 + 97 + ___ = 97 + 55 + 54",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  54 + 97 + ___ = 97 + 55 + 54",
        "options": [
          "55",
          "65",
          "45",
          "75"
        ],
        "answer": "55",
        "correct_value": 55,
        "explanation": "A and B appear on both sides and cancel; blank = C = 55."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "40 + 74 + ___ = 74 + 45 + 17",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  40 + 74 + ___ = 74 + 45 + 17",
        "options": [
          "12",
          "22",
          "32",
          "42"
        ],
        "answer": "22",
        "correct_value": 22,
        "explanation": "B cancels; blank = C + D − A = 45 + 17 − 40 = 22."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "81 + 45 + ___ = 38 + 29",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  81 + 45 + ___ = 38 + 29",
        "options": [
          "-71",
          "-59",
          "-51",
          "-41"
        ],
        "answer": "-59",
        "correct_value": -59,
        "explanation": "No matching terms; blank = 38 + 29 − 81 − 45 = -59."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000330",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "58 + 76 + ___ = 76 + 96 + 58",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  58 + 76 + ___ = 76 + 96 + 58",
        "options": [
          "116",
          "96",
          "86",
          "106"
        ],
        "answer": "96",
        "correct_value": 96,
        "explanation": "A and B appear on both sides and cancel; blank = C = 96."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "83 + 29 + ___ = 29 + 64 + 49",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  83 + 29 + ___ = 29 + 64 + 49",
        "options": [
          "20",
          "30",
          "40",
          "50"
        ],
        "answer": "30",
        "correct_value": 30,
        "explanation": "B cancels; blank = C + D − A = 64 + 49 − 83 = 30."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "36 + 93 + ___ = 27 + 84",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  36 + 93 + ___ = 27 + 84",
        "options": [
          "-2",
          "-32",
          "-18",
          "-12"
        ],
        "answer": "-18",
        "correct_value": -18,
        "explanation": "No matching terms; blank = 27 + 84 − 36 − 93 = -18."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000331",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "65 × 28 × 93 = ___ × 93 × 65",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  65 × 28 × 93 = ___ × 93 × 65",
        "options": [
          "48",
          "28",
          "18",
          "38"
        ],
        "answer": "28",
        "correct_value": 28,
        "explanation": "A and C appear on both sides; blank = B = 28."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "81 + 78 + ___ = 78 + 25 + 33",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  81 + 78 + ___ = 78 + 25 + 33",
        "options": [
          "-17",
          "-37",
          "-23",
          "-7"
        ],
        "answer": "-23",
        "correct_value": -23,
        "explanation": "B cancels; blank = C + D − A = 25 + 33 − 81 = -23."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "50 + 62 + ___ = 62 + 48",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  50 + 62 + ___ = 62 + 48",
        "options": [
          "-2",
          "2",
          "12",
          "-18"
        ],
        "answer": "-2",
        "correct_value": -2,
        "explanation": "No matching terms; blank = 62 + 48 − 50 − 62 = -2."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000332",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "34 × 23 × 26 = ___ × 26 × 34",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  34 × 23 × 26 = ___ × 26 × 34",
        "options": [
          "43",
          "13",
          "23",
          "33"
        ],
        "answer": "23",
        "correct_value": 23,
        "explanation": "A and C appear on both sides; blank = B = 23."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "87 + 82 + ___ = 82 + 88 + 39",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  87 + 82 + ___ = 82 + 88 + 39",
        "options": [
          "30",
          "60",
          "40",
          "50"
        ],
        "answer": "40",
        "correct_value": 40,
        "explanation": "B cancels; blank = C + D − A = 88 + 39 − 87 = 40."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "55 + 20 + ___ = 98 + 71",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  55 + 20 + ___ = 98 + 71",
        "options": [
          "94",
          "84",
          "114",
          "104"
        ],
        "answer": "94",
        "correct_value": 94,
        "explanation": "No matching terms; blank = 98 + 71 − 55 − 20 = 94."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000333",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "33 × (59 + 72) = 33 × ___ + 33 × 72",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  33 × (59 + 72) = 33 × ___ + 33 × 72",
        "options": [
          "69",
          "79",
          "59",
          "49"
        ],
        "answer": "59",
        "correct_value": 59,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 59."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "34 + 38 + ___ = 38 + 14 + 62",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  34 + 38 + ___ = 38 + 14 + 62",
        "options": [
          "32",
          "62",
          "52",
          "42"
        ],
        "answer": "42",
        "correct_value": 42,
        "explanation": "B cancels; blank = C + D − A = 14 + 62 − 34 = 42."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "38 + 95 + ___ = 35 + 36",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  38 + 95 + ___ = 35 + 36",
        "options": [
          "-48",
          "-58",
          "-78",
          "-62"
        ],
        "answer": "-62",
        "correct_value": -62,
        "explanation": "No matching terms; blank = 35 + 36 − 38 − 95 = -62."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000334",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 + 51 = ___ + 68",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  98 + 51 = ___ + 68",
        "options": [
          "81",
          "101",
          "71",
          "91"
        ],
        "answer": "81",
        "correct_value": 81,
        "explanation": "Blank = A + B − C = 98 + 51 − 68 = 81."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "15 + 87 + ___ = 87 + 58 + 50",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  15 + 87 + ___ = 87 + 58 + 50",
        "options": [
          "103",
          "93",
          "113",
          "83"
        ],
        "answer": "93",
        "correct_value": 93,
        "explanation": "B cancels; blank = C + D − A = 58 + 50 − 15 = 93."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "76 + 23 + ___ = 67 + 68",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  76 + 23 + ___ = 67 + 68",
        "options": [
          "56",
          "46",
          "26",
          "36"
        ],
        "answer": "36",
        "correct_value": 36,
        "explanation": "No matching terms; blank = 67 + 68 − 76 − 23 = 36."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000335",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "81 + 59 + ___ = 59 + 76 + 81",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  81 + 59 + ___ = 59 + 76 + 81",
        "options": [
          "96",
          "86",
          "66",
          "76"
        ],
        "answer": "76",
        "correct_value": 76,
        "explanation": "A and B appear on both sides and cancel; blank = C = 76."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "66 + 60 + ___ = 60 + 48 + 46",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  66 + 60 + ___ = 60 + 48 + 46",
        "options": [
          "48",
          "38",
          "28",
          "18"
        ],
        "answer": "28",
        "correct_value": 28,
        "explanation": "B cancels; blank = C + D − A = 48 + 46 − 66 = 28."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "47 + 88 + ___ = 16 + 98",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  47 + 88 + ___ = 16 + 98",
        "options": [
          "-21",
          "-9",
          "-39",
          "-19"
        ],
        "answer": "-21",
        "correct_value": -21,
        "explanation": "No matching terms; blank = 16 + 98 − 47 − 88 = -21."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000336",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "74 + 24 + ___ = 24 + 33 + 74",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  74 + 24 + ___ = 24 + 33 + 74",
        "options": [
          "33",
          "53",
          "23",
          "43"
        ],
        "answer": "33",
        "correct_value": 33,
        "explanation": "A and B appear on both sides and cancel; blank = C = 33."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "51 + 67 + ___ = 67 + 13 + 32",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  51 + 67 + ___ = 67 + 13 + 32",
        "options": [
          "-4",
          "-6",
          "6",
          "-24"
        ],
        "answer": "-6",
        "correct_value": -6,
        "explanation": "B cancels; blank = C + D − A = 13 + 32 − 51 = -6."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "68 + 21 + ___ = 42 + 51",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  68 + 21 + ___ = 42 + 51",
        "options": [
          "-6",
          "4",
          "24",
          "14"
        ],
        "answer": "4",
        "correct_value": 4,
        "explanation": "No matching terms; blank = 42 + 51 − 68 − 21 = 4."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000337",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "24 + 67 + ___ = 67 + 91 + 24",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  24 + 67 + ___ = 67 + 91 + 24",
        "options": [
          "81",
          "101",
          "91",
          "111"
        ],
        "answer": "91",
        "correct_value": 91,
        "explanation": "A and B appear on both sides and cancel; blank = C = 91."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "75 + 88 + ___ = 88 + 30 + 58",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  75 + 88 + ___ = 88 + 30 + 58",
        "options": [
          "23",
          "33",
          "13",
          "3"
        ],
        "answer": "13",
        "correct_value": 13,
        "explanation": "B cancels; blank = C + D − A = 30 + 58 − 75 = 13."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "52 + 82 + ___ = 94 + 29",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  52 + 82 + ___ = 94 + 29",
        "options": [
          "-29",
          "1",
          "-11",
          "-9"
        ],
        "answer": "-11",
        "correct_value": -11,
        "explanation": "No matching terms; blank = 94 + 29 − 52 − 82 = -11."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000338",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "63 + 49 + ___ = 49 + 49 + 63",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  63 + 49 + ___ = 49 + 49 + 63",
        "options": [
          "69",
          "49",
          "59",
          "39"
        ],
        "answer": "49",
        "correct_value": 49,
        "explanation": "A and B appear on both sides and cancel; blank = C = 49."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "25 + 26 + ___ = 26 + 35 + 10",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  25 + 26 + ___ = 26 + 35 + 10",
        "options": [
          "10",
          "30",
          "20",
          "40"
        ],
        "answer": "20",
        "correct_value": 20,
        "explanation": "B cancels; blank = C + D − A = 35 + 10 − 25 = 20."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "73 + 73 + ___ = 79 + 10",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  73 + 73 + ___ = 79 + 10",
        "options": [
          "-53",
          "-43",
          "-57",
          "-73"
        ],
        "answer": "-57",
        "correct_value": -57,
        "explanation": "No matching terms; blank = 79 + 10 − 73 − 73 = -57."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000339",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "68 + 62 = ___ + 66",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  68 + 62 = ___ + 66",
        "options": [
          "74",
          "54",
          "84",
          "64"
        ],
        "answer": "64",
        "correct_value": 64,
        "explanation": "Blank = A + B − C = 68 + 62 − 66 = 64."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "41 + 80 + ___ = 80 + 45 + 89",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  41 + 80 + ___ = 80 + 45 + 89",
        "options": [
          "83",
          "113",
          "93",
          "103"
        ],
        "answer": "93",
        "correct_value": 93,
        "explanation": "B cancels; blank = C + D − A = 45 + 89 − 41 = 93."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "28 + 17 + ___ = 93 + 54",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  28 + 17 + ___ = 93 + 54",
        "options": [
          "112",
          "122",
          "92",
          "102"
        ],
        "answer": "102",
        "correct_value": 102,
        "explanation": "No matching terms; blank = 93 + 54 − 28 − 17 = 102."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000340",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "52 × (21 + 16) = 52 × ___ + 52 × 16",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  52 × (21 + 16) = 52 × ___ + 52 × 16",
        "options": [
          "41",
          "11",
          "31",
          "21"
        ],
        "answer": "21",
        "correct_value": 21,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 21."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "30 + 96 + ___ = 96 + 46 + 88",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  30 + 96 + ___ = 96 + 46 + 88",
        "options": [
          "104",
          "124",
          "94",
          "114"
        ],
        "answer": "104",
        "correct_value": 104,
        "explanation": "B cancels; blank = C + D − A = 46 + 88 − 30 = 104."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "14 + 21 + ___ = 48 + 51",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  14 + 21 + ___ = 48 + 51",
        "options": [
          "54",
          "64",
          "74",
          "84"
        ],
        "answer": "64",
        "correct_value": 64,
        "explanation": "No matching terms; blank = 48 + 51 − 14 − 21 = 64."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000341",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "80 + 18 = ___ + 47",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  80 + 18 = ___ + 47",
        "options": [
          "61",
          "71",
          "51",
          "41"
        ],
        "answer": "51",
        "correct_value": 51,
        "explanation": "Blank = A + B − C = 80 + 18 − 47 = 51."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "98 + 45 + ___ = 45 + 52 + 77",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  98 + 45 + ___ = 45 + 52 + 77",
        "options": [
          "41",
          "31",
          "51",
          "21"
        ],
        "answer": "31",
        "correct_value": 31,
        "explanation": "B cancels; blank = C + D − A = 52 + 77 − 98 = 31."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "99 + 36 + ___ = 88 + 17",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  99 + 36 + ___ = 88 + 17",
        "options": [
          "-20",
          "-40",
          "-10",
          "-30"
        ],
        "answer": "-30",
        "correct_value": -30,
        "explanation": "No matching terms; blank = 88 + 17 − 99 − 36 = -30."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000342",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 + 87 = ___ + 46",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  98 + 87 = ___ + 46",
        "options": [
          "139",
          "149",
          "159",
          "129"
        ],
        "answer": "139",
        "correct_value": 139,
        "explanation": "Blank = A + B − C = 98 + 87 − 46 = 139."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "43 + 77 + ___ = 77 + 83 + 89",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  43 + 77 + ___ = 77 + 83 + 89",
        "options": [
          "119",
          "139",
          "129",
          "149"
        ],
        "answer": "129",
        "correct_value": 129,
        "explanation": "B cancels; blank = C + D − A = 83 + 89 − 43 = 129."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "76 + 90 + ___ = 73 + 73",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  76 + 90 + ___ = 73 + 73",
        "options": [
          "-30",
          "-20",
          "0",
          "-10"
        ],
        "answer": "-20",
        "correct_value": -20,
        "explanation": "No matching terms; blank = 73 + 73 − 76 − 90 = -20."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000343",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "34 × (10 + 25) = 34 × ___ + 34 × 25",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  34 × (10 + 25) = 34 × ___ + 34 × 25",
        "options": [
          "30",
          "0",
          "20",
          "10"
        ],
        "answer": "10",
        "correct_value": 10,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 10."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "36 + 88 + ___ = 88 + 63 + 62",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  36 + 88 + ___ = 88 + 63 + 62",
        "options": [
          "79",
          "109",
          "99",
          "89"
        ],
        "answer": "89",
        "correct_value": 89,
        "explanation": "B cancels; blank = C + D − A = 63 + 62 − 36 = 89."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "81 + 91 + ___ = 37 + 11",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  81 + 91 + ___ = 37 + 11",
        "options": [
          "-124",
          "-136",
          "-106",
          "-116"
        ],
        "answer": "-124",
        "correct_value": -124,
        "explanation": "No matching terms; blank = 37 + 11 − 81 − 91 = -124."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000344",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "18 × (49 + 48) = 18 × ___ + 18 × 48",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  18 × (49 + 48) = 18 × ___ + 18 × 48",
        "options": [
          "59",
          "39",
          "49",
          "69"
        ],
        "answer": "49",
        "correct_value": 49,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 49."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "97 + 52 + ___ = 52 + 53 + 60",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  97 + 52 + ___ = 52 + 53 + 60",
        "options": [
          "26",
          "36",
          "6",
          "16"
        ],
        "answer": "16",
        "correct_value": 16,
        "explanation": "B cancels; blank = C + D − A = 53 + 60 − 97 = 16."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "52 + 53 + ___ = 96 + 71",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  52 + 53 + ___ = 96 + 71",
        "options": [
          "72",
          "82",
          "62",
          "52"
        ],
        "answer": "62",
        "correct_value": 62,
        "explanation": "No matching terms; blank = 96 + 71 − 52 − 53 = 62."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000345",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "29 + 90 = ___ + 68",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  29 + 90 = ___ + 68",
        "options": [
          "51",
          "41",
          "61",
          "71"
        ],
        "answer": "51",
        "correct_value": 51,
        "explanation": "Blank = A + B − C = 29 + 90 − 68 = 51."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "17 + 76 + ___ = 76 + 48 + 82",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  17 + 76 + ___ = 76 + 48 + 82",
        "options": [
          "123",
          "113",
          "103",
          "133"
        ],
        "answer": "113",
        "correct_value": 113,
        "explanation": "B cancels; blank = C + D − A = 48 + 82 − 17 = 113."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "36 + 83 + ___ = 97 + 52",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  36 + 83 + ___ = 97 + 52",
        "options": [
          "40",
          "20",
          "30",
          "50"
        ],
        "answer": "30",
        "correct_value": 30,
        "explanation": "No matching terms; blank = 97 + 52 − 36 − 83 = 30."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000346",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "13 × (53 + 58) = 13 × ___ + 13 × 58",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  13 × (53 + 58) = 13 × ___ + 13 × 58",
        "options": [
          "53",
          "43",
          "73",
          "63"
        ],
        "answer": "53",
        "correct_value": 53,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 53."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "33 + 86 + ___ = 86 + 24 + 49",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  33 + 86 + ___ = 86 + 24 + 49",
        "options": [
          "50",
          "40",
          "30",
          "60"
        ],
        "answer": "40",
        "correct_value": 40,
        "explanation": "B cancels; blank = C + D − A = 24 + 49 − 33 = 40."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "44 + 62 + ___ = 21 + 73",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  44 + 62 + ___ = 21 + 73",
        "options": [
          "-12",
          "2",
          "-28",
          "-8"
        ],
        "answer": "-12",
        "correct_value": -12,
        "explanation": "No matching terms; blank = 21 + 73 − 44 − 62 = -12."
      },
      "distractor_types": [
        "correct",
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000347",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "37 × (77 + 48) = 37 × ___ + 37 × 48",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  37 × (77 + 48) = 37 × ___ + 37 × 48",
        "options": [
          "97",
          "67",
          "77",
          "87"
        ],
        "answer": "77",
        "correct_value": 77,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 77."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "14 + 35 + ___ = 35 + 21 + 66",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  14 + 35 + ___ = 35 + 21 + 66",
        "options": [
          "93",
          "63",
          "83",
          "73"
        ],
        "answer": "73",
        "correct_value": 73,
        "explanation": "B cancels; blank = C + D − A = 21 + 66 − 14 = 73."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "34 + 53 + ___ = 71 + 77",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  34 + 53 + ___ = 71 + 77",
        "options": [
          "51",
          "61",
          "71",
          "81"
        ],
        "answer": "61",
        "correct_value": 61,
        "explanation": "No matching terms; blank = 71 + 77 − 34 − 53 = 61."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000348",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "76 + 96 + ___ = 96 + 26 + 76",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  76 + 96 + ___ = 96 + 26 + 76",
        "options": [
          "16",
          "26",
          "46",
          "36"
        ],
        "answer": "26",
        "correct_value": 26,
        "explanation": "A and B appear on both sides and cancel; blank = C = 26."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "68 + 59 + ___ = 59 + 76 + 24",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  68 + 59 + ___ = 59 + 76 + 24",
        "options": [
          "52",
          "22",
          "42",
          "32"
        ],
        "answer": "32",
        "correct_value": 32,
        "explanation": "B cancels; blank = C + D − A = 76 + 24 − 68 = 32."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "97 + 86 + ___ = 21 + 52",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  97 + 86 + ___ = 21 + 52",
        "options": [
          "-100",
          "-90",
          "-110",
          "-120"
        ],
        "answer": "-110",
        "correct_value": -110,
        "explanation": "No matching terms; blank = 21 + 52 − 97 − 86 = -110."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "correct",
        "nearby_same_digit"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000349",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "12 × (83 + 49) = 12 × ___ + 12 × 49",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  12 × (83 + 49) = 12 × ___ + 12 × 49",
        "options": [
          "103",
          "83",
          "73",
          "93"
        ],
        "answer": "83",
        "correct_value": 83,
        "explanation": "Distributive law: A×(B+C) = A×B + A×C; blank = B = 83."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "34 + 46 + ___ = 46 + 45 + 78",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  34 + 46 + ___ = 46 + 45 + 78",
        "options": [
          "79",
          "89",
          "99",
          "109"
        ],
        "answer": "89",
        "correct_value": 89,
        "explanation": "B cancels; blank = C + D − A = 45 + 78 − 34 = 89."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "44 + 29 + ___ = 30 + 45",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  44 + 29 + ___ = 30 + 45",
        "options": [
          "12",
          "22",
          "-8",
          "2"
        ],
        "answer": "2",
        "correct_value": 2,
        "explanation": "No matching terms; blank = 30 + 45 − 44 − 29 = 2."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "equation_reasoning_000350",
    "category": "equation_reasoning",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "79 × 54 × 80 = ___ × 80 × 79",
      "ns_shortcut": "Recognize commutativity/distributive law — matching terms cancel.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What value fills the blank?  79 × 54 × 80 = ___ × 80 × 79",
        "options": [
          "44",
          "54",
          "64",
          "74"
        ],
        "answer": "54",
        "correct_value": 54,
        "explanation": "A and C appear on both sides; blank = B = 54."
      },
      "distractor_types": [
        "nearby_same_digit",
        "correct",
        "nearby_same_digit",
        "nearby_same_digit"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "46 + 83 + ___ = 83 + 41 + 31",
      "ns_shortcut": "Partial cancellation: B cancels but remaining terms must be computed.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What value fills the blank?  46 + 83 + ___ = 83 + 41 + 31",
        "options": [
          "16",
          "46",
          "36",
          "26"
        ],
        "answer": "26",
        "correct_value": 26,
        "explanation": "B cancels; blank = C + D − A = 41 + 31 − 46 = 26."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "79 + 66 + ___ = 16 + 26",
      "ns_shortcut": "No algebraic shortcut; compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What value fills the blank?  79 + 66 + ___ = 16 + 26",
        "options": [
          "-87",
          "-117",
          "-97",
          "-103"
        ],
        "answer": "-103",
        "correct_value": -103,
        "explanation": "No matching terms; blank = 16 + 26 − 79 − 66 = -103."
      },
      "distractor_types": [
        "nearby_same_digit",
        "nearby_same_digit",
        "nearby_same_digit",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000351",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "70 × 16",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 70 × 16?",
        "options": [
          "1123",
          "1119",
          "1121",
          "1120"
        ],
        "answer": "1120",
        "correct_value": 1120,
        "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": "20 × 98",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 20 × 98?",
        "options": [
          "1959",
          "1961",
          "1980",
          "1960"
        ],
        "answer": "1960",
        "correct_value": 1960,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "33 × 87",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 33 × 87?",
        "options": [
          "3031",
          "2973",
          "3187",
          "2871"
        ],
        "answer": "2871",
        "correct_value": 2871,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000352",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "54 × 30",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 54 × 30?",
        "options": [
          "1619",
          "1622",
          "1620",
          "1621"
        ],
        "answer": "1620",
        "correct_value": 1620,
        "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": "85 × 24",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 85 × 24?",
        "options": [
          "2041",
          "2040",
          "2020",
          "2039"
        ],
        "answer": "2040",
        "correct_value": 2040,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "57 × 61",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 57 × 61?",
        "options": [
          "3117",
          "3881",
          "3477",
          "3711"
        ],
        "answer": "3477",
        "correct_value": 3477,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000353",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "55 × 87",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 55 × 87?",
        "options": [
          "4788",
          "4785",
          "4784",
          "4786"
        ],
        "answer": "4785",
        "correct_value": 4785,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "95 × 30",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 95 × 30?",
        "options": [
          "2851",
          "2870",
          "2850",
          "2849"
        ],
        "answer": "2850",
        "correct_value": 2850,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "61 × 23",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 61 × 23?",
        "options": [
          "1547",
          "1325",
          "1403",
          "1507"
        ],
        "answer": "1403",
        "correct_value": 1403,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000354",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "98 × 85",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 98 × 85?",
        "options": [
          "14994",
          "8330",
          "15827",
          "16660"
        ],
        "answer": "8330",
        "correct_value": 8330,
        "explanation": "Product has 4 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "40 × 36",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 40 × 36?",
        "options": [
          "1440",
          "1420",
          "1439",
          "1441"
        ],
        "answer": "1440",
        "correct_value": 1440,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "21 × 37",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 21 × 37?",
        "options": [
          "777",
          "719",
          "701",
          "757"
        ],
        "answer": "777",
        "correct_value": 777,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000355",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "75 × 96",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 75 × 96?",
        "options": [
          "7201",
          "7202",
          "7200",
          "7199"
        ],
        "answer": "7200",
        "correct_value": 7200,
        "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": "25 × 46",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 25 × 46?",
        "options": [
          "1150",
          "1151",
          "1149",
          "1140"
        ],
        "answer": "1150",
        "correct_value": 1150,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "89 × 75",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 89 × 75?",
        "options": [
          "6739",
          "6807",
          "7239",
          "6675"
        ],
        "answer": "6675",
        "correct_value": 6675,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000356",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "59 × 61",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 59 × 61?",
        "options": [
          "3598",
          "3599",
          "3600",
          "3602"
        ],
        "answer": "3599",
        "correct_value": 3599,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "30 × 26",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 30 × 26?",
        "options": [
          "770",
          "779",
          "781",
          "780"
        ],
        "answer": "780",
        "correct_value": 780,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "95 × 33",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 95 × 33?",
        "options": [
          "2849",
          "3207",
          "3135",
          "3321"
        ],
        "answer": "3135",
        "correct_value": 3135,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000357",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "72 × 94",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 72 × 94?",
        "options": [
          "676875",
          "6768",
          "675",
          "14204"
        ],
        "answer": "6768",
        "correct_value": 6768,
        "explanation": "Product has 4 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "30 × 88",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 30 × 88?",
        "options": [
          "2639",
          "2640",
          "2620",
          "2641"
        ],
        "answer": "2640",
        "correct_value": 2640,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "95 × 47",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 95 × 47?",
        "options": [
          "3947",
          "4551",
          "4171",
          "4465"
        ],
        "answer": "4465",
        "correct_value": 4465,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000358",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "35 × 84",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 35 × 84?",
        "options": [
          "2940",
          "2943",
          "2939",
          "2941"
        ],
        "answer": "2940",
        "correct_value": 2940,
        "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": "30 × 86",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 30 × 86?",
        "options": [
          "2580",
          "2581",
          "2590",
          "2579"
        ],
        "answer": "2580",
        "correct_value": 2580,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "57 × 33",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 57 × 33?",
        "options": [
          "1755",
          "1675",
          "2083",
          "1881"
        ],
        "answer": "1881",
        "correct_value": 1881,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000359",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "94 × 66",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 94 × 66?",
        "options": [
          "615",
          "6204",
          "11784",
          "13024"
        ],
        "answer": "6204",
        "correct_value": 6204,
        "explanation": "Product has 4 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "15 × 12",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 15 × 12?",
        "options": [
          "170",
          "179",
          "181",
          "180"
        ],
        "answer": "180",
        "correct_value": 180,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "97 × 11",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 97 × 11?",
        "options": [
          "1125",
          "1067",
          "1063",
          "1093"
        ],
        "answer": "1067",
        "correct_value": 1067,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000360",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "25 × 20",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 25 × 20?",
        "options": [
          "499",
          "500",
          "503",
          "501"
        ],
        "answer": "500",
        "correct_value": 500,
        "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": "60 × 42",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 60 × 42?",
        "options": [
          "2521",
          "2519",
          "2530",
          "2520"
        ],
        "answer": "2520",
        "correct_value": 2520,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "25 × 33",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 25 × 33?",
        "options": [
          "825",
          "911",
          "863",
          "743"
        ],
        "answer": "825",
        "correct_value": 825,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000361",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "45 × 39",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 45 × 39?",
        "options": [
          "1757",
          "1754",
          "1756",
          "1755"
        ],
        "answer": "1755",
        "correct_value": 1755,
        "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": "80 × 42",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 80 × 42?",
        "options": [
          "3350",
          "3361",
          "3359",
          "3360"
        ],
        "answer": "3360",
        "correct_value": 3360,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "33 × 67",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 33 × 67?",
        "options": [
          "1959",
          "2009",
          "2211",
          "2137"
        ],
        "answer": "2211",
        "correct_value": 2211,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000362",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "67 × 13",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 67 × 13?",
        "options": [
          "872",
          "870",
          "871",
          "874"
        ],
        "answer": "871",
        "correct_value": 871,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "85 × 64",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 85 × 64?",
        "options": [
          "5460",
          "5439",
          "5441",
          "5440"
        ],
        "answer": "5440",
        "correct_value": 5440,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "15 × 95",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 15 × 95?",
        "options": [
          "1573",
          "1495",
          "1339",
          "1425"
        ],
        "answer": "1425",
        "correct_value": 1425,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000363",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "70 × 98",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 70 × 98?",
        "options": [
          "6859",
          "6861",
          "6860",
          "6863"
        ],
        "answer": "6860",
        "correct_value": 6860,
        "explanation": "Product ends in 0 (5 × even); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "55 × 92",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 55 × 92?",
        "options": [
          "5059",
          "5060",
          "5061",
          "5070"
        ],
        "answer": "5060",
        "correct_value": 5060,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "53 × 97",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 53 × 97?",
        "options": [
          "5689",
          "5553",
          "5141",
          "5047"
        ],
        "answer": "5141",
        "correct_value": 5141,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000364",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "72 × 27",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 72 × 27?",
        "options": [
          "1944",
          "1945",
          "1946",
          "1943"
        ],
        "answer": "1944",
        "correct_value": 1944,
        "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": "45 × 72",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 45 × 72?",
        "options": [
          "3239",
          "3260",
          "3241",
          "3240"
        ],
        "answer": "3240",
        "correct_value": 3240,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "23 × 91",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 23 × 91?",
        "options": [
          "2343",
          "1867",
          "2021",
          "2093"
        ],
        "answer": "2093",
        "correct_value": 2093,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000365",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "60 × 99",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 60 × 99?",
        "options": [
          "5941",
          "5939",
          "5940",
          "5942"
        ],
        "answer": "5940",
        "correct_value": 5940,
        "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": "20 × 14",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 20 × 14?",
        "options": [
          "290",
          "280",
          "281",
          "279"
        ],
        "answer": "280",
        "correct_value": 280,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "53 × 17",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 53 × 17?",
        "options": [
          "989",
          "901",
          "873",
          "849"
        ],
        "answer": "901",
        "correct_value": 901,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000366",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "96 × 96",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 96 × 96?",
        "options": [
          "9217",
          "9215",
          "9218",
          "9216"
        ],
        "answer": "9216",
        "correct_value": 9216,
        "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": "85 × 86",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 85 × 86?",
        "options": [
          "7311",
          "7320",
          "7309",
          "7310"
        ],
        "answer": "7310",
        "correct_value": 7310,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "11 × 33",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 11 × 33?",
        "options": [
          "343",
          "333",
          "325",
          "363"
        ],
        "answer": "363",
        "correct_value": 363,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000367",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "97 × 61",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 97 × 61?",
        "options": [
          "5918",
          "5920",
          "5917",
          "5916"
        ],
        "answer": "5917",
        "correct_value": 5917,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "35 × 98",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 35 × 98?",
        "options": [
          "3431",
          "3430",
          "3429",
          "3410"
        ],
        "answer": "3430",
        "correct_value": 3430,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "51 × 37",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 51 × 37?",
        "options": [
          "1855",
          "1735",
          "1887",
          "1801"
        ],
        "answer": "1887",
        "correct_value": 1887,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000368",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "30 × 22",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 30 × 22?",
        "options": [
          "661",
          "659",
          "660",
          "663"
        ],
        "answer": "660",
        "correct_value": 660,
        "explanation": "Product ends in 0 (5 × even); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "40 × 28",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 40 × 28?",
        "options": [
          "1121",
          "1120",
          "1100",
          "1119"
        ],
        "answer": "1120",
        "correct_value": 1120,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "73 × 21",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 73 × 21?",
        "options": [
          "1531",
          "1533",
          "1509",
          "1641"
        ],
        "answer": "1533",
        "correct_value": 1533,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000369",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "88 × 98",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 88 × 98?",
        "options": [
          "17244",
          "16382",
          "8624",
          "18968"
        ],
        "answer": "8624",
        "correct_value": 8624,
        "explanation": "Product has 4 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "75 × 42",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 75 × 42?",
        "options": [
          "3130",
          "3151",
          "3150",
          "3149"
        ],
        "answer": "3150",
        "correct_value": 3150,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "25 × 29",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 25 × 29?",
        "options": [
          "717",
          "725",
          "789",
          "703"
        ],
        "answer": "725",
        "correct_value": 725,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000370",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "95 × 32",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 95 × 32?",
        "options": [
          "3039",
          "3043",
          "3040",
          "3041"
        ],
        "answer": "3040",
        "correct_value": 3040,
        "explanation": "Product ends in 0 (5 × even); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "60 × 38",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 60 × 38?",
        "options": [
          "2270",
          "2279",
          "2280",
          "2281"
        ],
        "answer": "2280",
        "correct_value": 2280,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "75 × 25",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 75 × 25?",
        "options": [
          "2027",
          "1875",
          "1645",
          "1689"
        ],
        "answer": "1875",
        "correct_value": 1875,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000371",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "62 × 35",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 62 × 35?",
        "options": [
          "21755",
          "217062",
          "2170",
          "21758"
        ],
        "answer": "2170",
        "correct_value": 2170,
        "explanation": "Product has 4 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "55 × 30",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 55 × 30?",
        "options": [
          "1649",
          "1651",
          "1670",
          "1650"
        ],
        "answer": "1650",
        "correct_value": 1650,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "81 × 11",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 81 × 11?",
        "options": [
          "845",
          "919",
          "923",
          "891"
        ],
        "answer": "891",
        "correct_value": 891,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000372",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "61 × 33",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 61 × 33?",
        "options": [
          "201323",
          "20152",
          "2013",
          "201310"
        ],
        "answer": "2013",
        "correct_value": 2013,
        "explanation": "Product has 4 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "10 × 46",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 10 × 46?",
        "options": [
          "470",
          "461",
          "459",
          "460"
        ],
        "answer": "460",
        "correct_value": 460,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "73 × 29",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 73 × 29?",
        "options": [
          "2117",
          "1873",
          "2105",
          "2331"
        ],
        "answer": "2117",
        "correct_value": 2117,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000373",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "63 × 85",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 63 × 85?",
        "options": [
          "5355",
          "5356",
          "5358",
          "5354"
        ],
        "answer": "5355",
        "correct_value": 5355,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "85 × 56",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 85 × 56?",
        "options": [
          "4761",
          "4740",
          "4759",
          "4760"
        ],
        "answer": "4760",
        "correct_value": 4760,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "73 × 85",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 73 × 85?",
        "options": [
          "6787",
          "6205",
          "5891",
          "6675"
        ],
        "answer": "6205",
        "correct_value": 6205,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000374",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "69 × 31",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 69 × 31?",
        "options": [
          "2139",
          "2142",
          "2138",
          "2140"
        ],
        "answer": "2139",
        "correct_value": 2139,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "65 × 32",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 65 × 32?",
        "options": [
          "2079",
          "2090",
          "2081",
          "2080"
        ],
        "answer": "2080",
        "correct_value": 2080,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "33 × 33",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 33 × 33?",
        "options": [
          "1089",
          "1059",
          "1007",
          "1047"
        ],
        "answer": "1089",
        "correct_value": 1089,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000375",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "29 × 57",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 29 × 57?",
        "options": [
          "1654",
          "1653",
          "1652",
          "1656"
        ],
        "answer": "1653",
        "correct_value": 1653,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "30 × 10",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 30 × 10?",
        "options": [
          "300",
          "299",
          "280",
          "301"
        ],
        "answer": "300",
        "correct_value": 300,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "79 × 49",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 79 × 49?",
        "options": [
          "3871",
          "3663",
          "4265",
          "3399"
        ],
        "answer": "3871",
        "correct_value": 3871,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000376",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "82 × 66",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 82 × 66?",
        "options": [
          "11363",
          "5412",
          "10822",
          "10281"
        ],
        "answer": "5412",
        "correct_value": 5412,
        "explanation": "Product has 4 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "75 × 32",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 75 × 32?",
        "options": [
          "2399",
          "2401",
          "2400",
          "2420"
        ],
        "answer": "2400",
        "correct_value": 2400,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "29 × 37",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 29 × 37?",
        "options": [
          "1097",
          "1091",
          "1195",
          "1073"
        ],
        "answer": "1073",
        "correct_value": 1073,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000377",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "36 × 60",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 36 × 60?",
        "options": [
          "2159",
          "2161",
          "2160",
          "2162"
        ],
        "answer": "2160",
        "correct_value": 2160,
        "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": "25 × 92",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 25 × 92?",
        "options": [
          "2301",
          "2280",
          "2300",
          "2299"
        ],
        "answer": "2300",
        "correct_value": 2300,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "85 × 49",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 85 × 49?",
        "options": [
          "4165",
          "4007",
          "4641",
          "4137"
        ],
        "answer": "4165",
        "correct_value": 4165,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000378",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "13 × 25",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 13 × 25?",
        "options": [
          "325",
          "3265",
          "28",
          "3253"
        ],
        "answer": "325",
        "correct_value": 325,
        "explanation": "Product has 3 digits; only one option matches."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "30 × 98",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 30 × 98?",
        "options": [
          "2950",
          "2939",
          "2940",
          "2941"
        ],
        "answer": "2940",
        "correct_value": 2940,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "57 × 27",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 57 × 27?",
        "options": [
          "1693",
          "1585",
          "1547",
          "1539"
        ],
        "answer": "1539",
        "correct_value": 1539,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000379",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "20 × 64",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 20 × 64?",
        "options": [
          "256",
          "128",
          "1280",
          "128016"
        ],
        "answer": "1280",
        "correct_value": 1280,
        "explanation": "Product has 4 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "55 × 96",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 55 × 96?",
        "options": [
          "5280",
          "5279",
          "5281",
          "5300"
        ],
        "answer": "5280",
        "correct_value": 5280,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "73 × 57",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 73 × 57?",
        "options": [
          "4161",
          "3825",
          "4203",
          "4281"
        ],
        "answer": "4161",
        "correct_value": 4161,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000380",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "65 × 35",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 65 × 35?",
        "options": [
          "2278",
          "2274",
          "2276",
          "2275"
        ],
        "answer": "2275",
        "correct_value": 2275,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "70 × 60",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 70 × 60?",
        "options": [
          "4201",
          "4199",
          "4200",
          "4190"
        ],
        "answer": "4200",
        "correct_value": 4200,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "33 × 11",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 33 × 11?",
        "options": [
          "407",
          "337",
          "397",
          "363"
        ],
        "answer": "363",
        "correct_value": 363,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000381",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "53 × 35",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 53 × 35?",
        "options": [
          "185556",
          "1855",
          "367",
          "18590"
        ],
        "answer": "1855",
        "correct_value": 1855,
        "explanation": "Product has 4 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "85 × 84",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 85 × 84?",
        "options": [
          "7140",
          "7139",
          "7160",
          "7141"
        ],
        "answer": "7140",
        "correct_value": 7140,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "83 × 97",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 83 × 97?",
        "options": [
          "7531",
          "8539",
          "8727",
          "8051"
        ],
        "answer": "8051",
        "correct_value": 8051,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000382",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "10 × 84",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 10 × 84?",
        "options": [
          "839",
          "841",
          "843",
          "840"
        ],
        "answer": "840",
        "correct_value": 840,
        "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": "15 × 94",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 15 × 94?",
        "options": [
          "1411",
          "1409",
          "1410",
          "1420"
        ],
        "answer": "1410",
        "correct_value": 1410,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "55 × 85",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 55 × 85?",
        "options": [
          "4675",
          "5029",
          "4325",
          "4775"
        ],
        "answer": "4675",
        "correct_value": 4675,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000383",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "20 × 48",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 20 × 48?",
        "options": [
          "959",
          "963",
          "961",
          "960"
        ],
        "answer": "960",
        "correct_value": 960,
        "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": "85 × 84",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 85 × 84?",
        "options": [
          "7140",
          "7139",
          "7130",
          "7141"
        ],
        "answer": "7140",
        "correct_value": 7140,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "13 × 79",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 13 × 79?",
        "options": [
          "1113",
          "1027",
          "1033",
          "1101"
        ],
        "answer": "1027",
        "correct_value": 1027,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000384",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "83 × 23",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 83 × 23?",
        "options": [
          "1910",
          "1908",
          "1909",
          "1912"
        ],
        "answer": "1909",
        "correct_value": 1909,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "95 × 36",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 95 × 36?",
        "options": [
          "3419",
          "3400",
          "3420",
          "3421"
        ],
        "answer": "3420",
        "correct_value": 3420,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "53 × 73",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 53 × 73?",
        "options": [
          "3955",
          "3869",
          "4057",
          "3973"
        ],
        "answer": "3869",
        "correct_value": 3869,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000385",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "84 × 30",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 84 × 30?",
        "options": [
          "2521",
          "2522",
          "2519",
          "2520"
        ],
        "answer": "2520",
        "correct_value": 2520,
        "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": "90 × 48",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 90 × 48?",
        "options": [
          "4319",
          "4340",
          "4320",
          "4321"
        ],
        "answer": "4320",
        "correct_value": 4320,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "85 × 53",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 85 × 53?",
        "options": [
          "4149",
          "4575",
          "4943",
          "4505"
        ],
        "answer": "4505",
        "correct_value": 4505,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000386",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "33 × 66",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 33 × 66?",
        "options": [
          "2179",
          "2178",
          "2177",
          "2180"
        ],
        "answer": "2178",
        "correct_value": 2178,
        "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": "90 × 34",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 90 × 34?",
        "options": [
          "3040",
          "3061",
          "3060",
          "3059"
        ],
        "answer": "3060",
        "correct_value": 3060,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "13 × 91",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 13 × 91?",
        "options": [
          "1055",
          "1183",
          "1063",
          "1321"
        ],
        "answer": "1183",
        "correct_value": 1183,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000387",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "97 × 48",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 97 × 48?",
        "options": [
          "928",
          "462",
          "10236",
          "4656"
        ],
        "answer": "4656",
        "correct_value": 4656,
        "explanation": "Product has 4 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "75 × 36",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 75 × 36?",
        "options": [
          "2710",
          "2701",
          "2699",
          "2700"
        ],
        "answer": "2700",
        "correct_value": 2700,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "73 × 21",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 73 × 21?",
        "options": [
          "1379",
          "1533",
          "1451",
          "1683"
        ],
        "answer": "1533",
        "correct_value": 1533,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000388",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "67 × 63",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 67 × 63?",
        "options": [
          "4222",
          "4221",
          "4224",
          "4220"
        ],
        "answer": "4221",
        "correct_value": 4221,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "65 × 70",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 65 × 70?",
        "options": [
          "4530",
          "4549",
          "4550",
          "4551"
        ],
        "answer": "4550",
        "correct_value": 4550,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "73 × 79",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 73 × 79?",
        "options": [
          "5441",
          "5767",
          "6255",
          "6485"
        ],
        "answer": "5767",
        "correct_value": 5767,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000389",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "45 × 42",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 45 × 42?",
        "options": [
          "1890",
          "1889",
          "1891",
          "1893"
        ],
        "answer": "1890",
        "correct_value": 1890,
        "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": "55 × 36",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 55 × 36?",
        "options": [
          "1980",
          "1990",
          "1981",
          "1979"
        ],
        "answer": "1980",
        "correct_value": 1980,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "97 × 25",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 97 × 25?",
        "options": [
          "2197",
          "2557",
          "2425",
          "2431"
        ],
        "answer": "2425",
        "correct_value": 2425,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000390",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "84 × 12",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 84 × 12?",
        "options": [
          "1010",
          "1009",
          "1008",
          "1007"
        ],
        "answer": "1008",
        "correct_value": 1008,
        "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": "95 × 50",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 95 × 50?",
        "options": [
          "4770",
          "4751",
          "4749",
          "4750"
        ],
        "answer": "4750",
        "correct_value": 4750,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "71 × 63",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 71 × 63?",
        "options": [
          "4993",
          "4307",
          "4907",
          "4473"
        ],
        "answer": "4473",
        "correct_value": 4473,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000391",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "84 × 69",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 84 × 69?",
        "options": [
          "5795",
          "5798",
          "5796",
          "5797"
        ],
        "answer": "5796",
        "correct_value": 5796,
        "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": "60 × 66",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 60 × 66?",
        "options": [
          "3961",
          "3960",
          "3959",
          "3980"
        ],
        "answer": "3960",
        "correct_value": 3960,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "35 × 91",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 35 × 91?",
        "options": [
          "3185",
          "3057",
          "3127",
          "3347"
        ],
        "answer": "3185",
        "correct_value": 3185,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000392",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "47 × 35",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 47 × 35?",
        "options": [
          "1648",
          "1644",
          "1646",
          "1645"
        ],
        "answer": "1645",
        "correct_value": 1645,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "40 × 42",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 40 × 42?",
        "options": [
          "1679",
          "1681",
          "1690",
          "1680"
        ],
        "answer": "1680",
        "correct_value": 1680,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "33 × 61",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 33 × 61?",
        "options": [
          "2007",
          "1775",
          "2013",
          "2255"
        ],
        "answer": "2013",
        "correct_value": 2013,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000393",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "29 × 21",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 29 × 21?",
        "options": [
          "610",
          "612",
          "609",
          "608"
        ],
        "answer": "609",
        "correct_value": 609,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "40 × 44",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 40 × 44?",
        "options": [
          "1761",
          "1760",
          "1740",
          "1759"
        ],
        "answer": "1760",
        "correct_value": 1760,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "11 × 77",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 11 × 77?",
        "options": [
          "863",
          "847",
          "935",
          "947"
        ],
        "answer": "847",
        "correct_value": 847,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000394",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "90 × 27",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 90 × 27?",
        "options": [
          "2429",
          "2430",
          "2432",
          "2431"
        ],
        "answer": "2430",
        "correct_value": 2430,
        "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": "80 × 20",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 80 × 20?",
        "options": [
          "1601",
          "1590",
          "1600",
          "1599"
        ],
        "answer": "1600",
        "correct_value": 1600,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "63 × 33",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 63 × 33?",
        "options": [
          "1929",
          "2155",
          "2079",
          "2201"
        ],
        "answer": "2079",
        "correct_value": 2079,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000395",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "72 × 27",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 72 × 27?",
        "options": [
          "1944",
          "1945",
          "1943",
          "1946"
        ],
        "answer": "1944",
        "correct_value": 1944,
        "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": "10 × 42",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 10 × 42?",
        "options": [
          "420",
          "419",
          "440",
          "421"
        ],
        "answer": "420",
        "correct_value": 420,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "87 × 43",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 87 × 43?",
        "options": [
          "3713",
          "3741",
          "3691",
          "3863"
        ],
        "answer": "3741",
        "correct_value": 3741,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000396",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "81 × 15",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 81 × 15?",
        "options": [
          "121573",
          "1215",
          "239",
          "117"
        ],
        "answer": "1215",
        "correct_value": 1215,
        "explanation": "Product has 4 digits; only one option matches."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "55 × 96",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 55 × 96?",
        "options": [
          "5281",
          "5280",
          "5270",
          "5279"
        ],
        "answer": "5280",
        "correct_value": 5280,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "77 × 83",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 77 × 83?",
        "options": [
          "6137",
          "7085",
          "5963",
          "6391"
        ],
        "answer": "6391",
        "correct_value": 6391,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    }
  },
  {
    "family_id": "option_elimination_000397",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "29 × 13",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 29 × 13?",
        "options": [
          "380",
          "376",
          "378",
          "377"
        ],
        "answer": "377",
        "correct_value": 377,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "40 × 16",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 40 × 16?",
        "options": [
          "620",
          "639",
          "640",
          "641"
        ],
        "answer": "640",
        "correct_value": 640,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "69 × 91",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 69 × 91?",
        "options": [
          "5941",
          "6279",
          "6889",
          "5607"
        ],
        "answer": "6279",
        "correct_value": 6279,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000398",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "15 × 45",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 15 × 45?",
        "options": [
          "676",
          "677",
          "675",
          "674"
        ],
        "answer": "675",
        "correct_value": 675,
        "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": "85 × 64",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 85 × 64?",
        "options": [
          "5441",
          "5440",
          "5439",
          "5420"
        ],
        "answer": "5440",
        "correct_value": 5440,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "61 × 21",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 61 × 21?",
        "options": [
          "1181",
          "1355",
          "1281",
          "1227"
        ],
        "answer": "1281",
        "correct_value": 1281,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000399",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "75 × 35",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 75 × 35?",
        "options": [
          "2625",
          "2624",
          "2626",
          "2628"
        ],
        "answer": "2625",
        "correct_value": 2625,
        "explanation": "Product odd (odd × odd); only one option matches."
      },
      "distractor_types": [
        "correct",
        "distractor",
        "distractor",
        "distractor"
      ]
    },
    "weak_shortcut": {
      "task_type": "weak_shortcut",
      "math_expression": "90 × 52",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 90 × 52?",
        "options": [
          "4679",
          "4680",
          "4681",
          "4700"
        ],
        "answer": "4680",
        "correct_value": 4680,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "71 × 45",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 71 × 45?",
        "options": [
          "3243",
          "3385",
          "3195",
          "2971"
        ],
        "answer": "3195",
        "correct_value": 3195,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "correct",
        "distractor"
      ]
    }
  },
  {
    "family_id": "option_elimination_000400",
    "category": "option_elimination",
    "strong_shortcut": {
      "task_type": "strong_shortcut",
      "math_expression": "57 × 69",
      "ns_shortcut": "Check trailing digit / parity / magnitude — only one option matches.",
      "shortcut_strength": 1.0,
      "pure_math": {
        "question": "What is 57 × 69?",
        "options": [
          "3935",
          "3932",
          "3934",
          "3933"
        ],
        "answer": "3933",
        "correct_value": 3933,
        "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": "95 × 18",
      "ns_shortcut": "Trailing digit narrows options but does not uniquely identify the answer.",
      "shortcut_strength": 0.5,
      "pure_math": {
        "question": "What is 95 × 18?",
        "options": [
          "1709",
          "1700",
          "1711",
          "1710"
        ],
        "answer": "1710",
        "correct_value": 1710,
        "explanation": "Feature narrows to 2 options; eliminates some but not all distractors."
      },
      "distractor_types": [
        "distractor",
        "distractor",
        "distractor",
        "correct"
      ]
    },
    "control": {
      "task_type": "control",
      "math_expression": "65 × 21",
      "ns_shortcut": "All options have same structural features; must compute precisely.",
      "shortcut_strength": 0.0,
      "pure_math": {
        "question": "What is 65 × 21?",
        "options": [
          "1331",
          "1365",
          "1443",
          "1429"
        ],
        "answer": "1365",
        "correct_value": 1365,
        "explanation": "All options have same structural features; must compute precisely."
      },
      "distractor_types": [
        "distractor",
        "correct",
        "distractor",
        "distractor"
      ]
    }
  }
]