[
  {
    "task_id": "J3_compatible_numbers_000642",
    "task_type": "J3_pairwise_efficiency",
    "category": "compatible_numbers",
    "problem": "Estimate 5082 × 1800.",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 9147600",
    "solution_b": "NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9147600",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 5082 × 1800.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 9147600\n\nSolution B: NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9147600"
  },
  {
    "task_id": "J3_cancellation_identity_000568",
    "task_type": "J3_pairwise_efficiency",
    "category": "cancellation_identity",
    "problem": "Evaluate: 9227 + 8064 - 8063",
    "solution_a": "NS approach (2 steps): Near-cancellation: 8064 - 8063 = 1, so answer ≈ 9227 + 1. → 9228",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 9228",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 9227 + 8064 - 8063\n\nSolution A: NS approach (2 steps): Near-cancellation: 8064 - 8063 = 1, so answer ≈ 9227 + 1. → 9228\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 9228"
  },
  {
    "task_id": "J3_equation_reasoning_000709",
    "task_type": "J3_pairwise_efficiency",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  3459 × 5559 × 2959 = ___ × 2959 × 3459",
    "solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 5559",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 5559",
    "correct_answer": "A",
    "ns_steps": 1,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank?  3459 × 5559 × 2959 = ___ × 2959 × 3459\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 5559\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 5559"
  },
  {
    "task_id": "J3_option_elimination_000798",
    "task_type": "J3_pairwise_efficiency",
    "category": "option_elimination",
    "problem": "What is 1760 × 7480?",
    "solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 13164800",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 13164800",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 1760 × 7480?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 13164800\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 13164800"
  },
  {
    "task_id": "J3_magnitude_estimation_000415",
    "task_type": "J3_pairwise_efficiency",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 9900 * 9900?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 98010000",
    "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 98010000",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9900 * 9900?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 98010000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 98010000"
  },
  {
    "task_id": "J3_relative_distance_000547",
    "task_type": "J3_pairwise_efficiency",
    "category": "relative_distance",
    "problem": "Which is larger: 1518/3038 or 3432/6744?",
    "solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3432/6744",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 3432/6744",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1518/3038 or 3432/6744?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3432/6744\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 3432/6744"
  },
  {
    "task_id": "J3_cancellation_identity_000579",
    "task_type": "J3_pairwise_efficiency",
    "category": "cancellation_identity",
    "problem": "Evaluate: 1817 + 5124 - 5125",
    "solution_a": "NS approach (2 steps): Near-cancellation: 5124 - 5125 = -1, so answer ≈ 1817 + -1. → 1816",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 1816",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 1817 + 5124 - 5125\n\nSolution A: NS approach (2 steps): Near-cancellation: 5124 - 5125 = -1, so answer ≈ 1817 + -1. → 1816\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 1816"
  },
  {
    "task_id": "J3_compatible_numbers_000648",
    "task_type": "J3_pairwise_efficiency",
    "category": "compatible_numbers",
    "problem": "Estimate 2520 × 3623.",
    "solution_a": "NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9129960",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 9129960",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 2520 × 3623.\n\nSolution A: NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9129960\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 9129960"
  },
  {
    "task_id": "J3_option_elimination_000788",
    "task_type": "J3_pairwise_efficiency",
    "category": "option_elimination",
    "problem": "What is 2243 × 8255?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 18515965",
    "solution_b": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 18515965",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 2243 × 8255?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 18515965\n\nSolution B: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 18515965"
  },
  {
    "task_id": "J3_cancellation_identity_000559",
    "task_type": "J3_pairwise_efficiency",
    "category": "cancellation_identity",
    "problem": "Evaluate: 5670 + 1297 - 1299",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 5668",
    "solution_b": "NS approach (2 steps): Near-cancellation: 1297 - 1299 = -2, so answer ≈ 5670 + -2. → 5668",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 5670 + 1297 - 1299\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 5668\n\nSolution B: NS approach (2 steps): Near-cancellation: 1297 - 1299 = -2, so answer ≈ 5670 + -2. → 5668"
  },
  {
    "task_id": "J3_landmark_comparison_000664",
    "task_type": "J3_pairwise_efficiency",
    "category": "landmark_comparison",
    "problem": "Is 24% of 44600 greater than 13866?",
    "solution_a": "NS approach (2 steps): Use 25% as landmark: 25% of 44600 = 11150. → No",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → No",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 24% of 44600 greater than 13866?\n\nSolution A: NS approach (2 steps): Use 25% as landmark: 25% of 44600 = 11150. → No\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → No"
  },
  {
    "task_id": "J3_structural_shortcuts_000484",
    "task_type": "J3_pairwise_efficiency",
    "category": "structural_shortcuts",
    "problem": "What is 10001 * 4007?",
    "solution_a": "NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 40074007",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 40074007",
    "correct_answer": "A",
    "ns_steps": 3,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 10001 * 4007?\n\nSolution A: NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 40074007\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 40074007"
  },
  {
    "task_id": "J3_compatible_numbers_000606",
    "task_type": "J3_pairwise_efficiency",
    "category": "compatible_numbers",
    "problem": "Estimate 5081 × 2047.",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 10400807",
    "solution_b": "NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 10400807",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 5081 × 2047.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 10400807\n\nSolution B: NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 10400807"
  },
  {
    "task_id": "J3_structural_shortcuts_000454",
    "task_type": "J3_pairwise_efficiency",
    "category": "structural_shortcuts",
    "problem": "What is 9998 * 5588?",
    "solution_a": "NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 55868824",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 55868824",
    "correct_answer": "A",
    "ns_steps": 3,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9998 * 5588?\n\nSolution A: NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 55868824\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 55868824"
  },
  {
    "task_id": "J3_equation_reasoning_000729",
    "task_type": "J3_pairwise_efficiency",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  9604 + 3781 = ___ + 3591",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 9794",
    "solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 9794",
    "correct_answer": "B",
    "ns_steps": 1,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank?  9604 + 3781 = ___ + 3591\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 9794\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 9794"
  },
  {
    "task_id": "J3_cancellation_identity_000576",
    "task_type": "J3_pairwise_efficiency",
    "category": "cancellation_identity",
    "problem": "Evaluate: 5487 + 9932 - 9930",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 5489",
    "solution_b": "NS approach (2 steps): Near-cancellation: 9932 - 9930 = 2, so answer ≈ 5487 + 2. → 5489",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 5487 + 9932 - 9930\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 5489\n\nSolution B: NS approach (2 steps): Near-cancellation: 9932 - 9930 = 2, so answer ≈ 5487 + 2. → 5489"
  },
  {
    "task_id": "J3_structural_shortcuts_000471",
    "task_type": "J3_pairwise_efficiency",
    "category": "structural_shortcuts",
    "problem": "What is 9998 * 7041?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 70395918",
    "solution_b": "NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 70395918",
    "correct_answer": "B",
    "ns_steps": 3,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9998 * 7041?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 70395918\n\nSolution B: NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 70395918"
  },
  {
    "task_id": "J3_equation_reasoning_000713",
    "task_type": "J3_pairwise_efficiency",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  5328 × (9719 + 5079) = 5328 × ___ + 5328 × 5079",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 9719",
    "solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 9719",
    "correct_answer": "B",
    "ns_steps": 1,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank?  5328 × (9719 + 5079) = 5328 × ___ + 5328 × 5079\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 9719\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 9719"
  },
  {
    "task_id": "J3_landmark_comparison_000654",
    "task_type": "J3_pairwise_efficiency",
    "category": "landmark_comparison",
    "problem": "Is 10% of 95860 greater than 25675?",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → No",
    "solution_b": "NS approach (2 steps): Use 10% as landmark: 10% of 95860 = 9586. → No",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 10% of 95860 greater than 25675?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → No\n\nSolution B: NS approach (2 steps): Use 10% as landmark: 10% of 95860 = 9586. → No"
  },
  {
    "task_id": "J3_structural_shortcuts_000491",
    "task_type": "J3_pairwise_efficiency",
    "category": "structural_shortcuts",
    "problem": "What is 9999 * 8827?",
    "solution_a": "NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 88261173",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 88261173",
    "correct_answer": "A",
    "ns_steps": 3,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9999 * 8827?\n\nSolution A: NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 88261173\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 88261173"
  },
  {
    "task_id": "J3_magnitude_estimation_000440",
    "task_type": "J3_pairwise_efficiency",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 9900 * 9900?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 98010000",
    "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 98010000",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9900 * 9900?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 98010000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 98010000"
  },
  {
    "task_id": "J3_compatible_numbers_000628",
    "task_type": "J3_pairwise_efficiency",
    "category": "compatible_numbers",
    "problem": "Estimate 1248 × 7302.",
    "solution_a": "NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 9112896",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 9112896",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 1248 × 7302.\n\nSolution A: NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 9112896\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 9112896"
  },
  {
    "task_id": "J3_structural_shortcuts_000485",
    "task_type": "J3_pairwise_efficiency",
    "category": "structural_shortcuts",
    "problem": "What is 9999 * 9992?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 99910008",
    "solution_b": "NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 99910008",
    "correct_answer": "B",
    "ns_steps": 3,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9999 * 9992?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99910008\n\nSolution B: NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 99910008"
  },
  {
    "task_id": "J3_structural_shortcuts_000477",
    "task_type": "J3_pairwise_efficiency",
    "category": "structural_shortcuts",
    "problem": "What is 9999 * 3736?",
    "solution_a": "NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 37356264",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 37356264",
    "correct_answer": "A",
    "ns_steps": 3,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9999 * 3736?\n\nSolution A: NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 37356264\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 37356264"
  },
  {
    "task_id": "J3_option_elimination_000778",
    "task_type": "J3_pairwise_efficiency",
    "category": "option_elimination",
    "problem": "What is 1220 × 5134?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 6263480",
    "solution_b": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 6263480",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 1220 × 5134?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 6263480\n\nSolution B: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 6263480"
  },
  {
    "task_id": "J3_compatible_numbers_000638",
    "task_type": "J3_pairwise_efficiency",
    "category": "compatible_numbers",
    "problem": "Estimate 2548 × 3929.",
    "solution_a": "NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 10011092",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 10011092",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 2548 × 3929.\n\nSolution A: NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 10011092\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 10011092"
  },
  {
    "task_id": "J3_relative_distance_000515",
    "task_type": "J3_pairwise_efficiency",
    "category": "relative_distance",
    "problem": "Which is larger: 4405/8858 or 4666/9156?",
    "solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4666/9156",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 4666/9156",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 4405/8858 or 4666/9156?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4666/9156\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 4666/9156"
  },
  {
    "task_id": "J3_landmark_comparison_000680",
    "task_type": "J3_pairwise_efficiency",
    "category": "landmark_comparison",
    "problem": "Is 23% of 72010 greater than 15760?",
    "solution_a": "NS approach (2 steps): Use 25% as landmark: 25% of 72010 = 18002. → Yes",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → Yes",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 23% of 72010 greater than 15760?\n\nSolution A: NS approach (2 steps): Use 25% as landmark: 25% of 72010 = 18002. → Yes\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → Yes"
  },
  {
    "task_id": "J3_landmark_comparison_000688",
    "task_type": "J3_pairwise_efficiency",
    "category": "landmark_comparison",
    "problem": "Is 27% of 63860 greater than 30514?",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → No",
    "solution_b": "NS approach (2 steps): Use 25% as landmark: 25% of 63860 = 15965. → No",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 27% of 63860 greater than 30514?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → No\n\nSolution B: NS approach (2 steps): Use 25% as landmark: 25% of 63860 = 15965. → No"
  },
  {
    "task_id": "J3_equation_reasoning_000748",
    "task_type": "J3_pairwise_efficiency",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  3807 + 1362 + ___ = 1362 + 8347 + 3807",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 8347",
    "solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 8347",
    "correct_answer": "B",
    "ns_steps": 1,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank?  3807 + 1362 + ___ = 1362 + 8347 + 3807\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 8347\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 8347"
  },
  {
    "task_id": "J3_cancellation_identity_000556",
    "task_type": "J3_pairwise_efficiency",
    "category": "cancellation_identity",
    "problem": "Evaluate: 6861 + 5024 - 5026",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 6859",
    "solution_b": "NS approach (2 steps): Near-cancellation: 5024 - 5026 = -2, so answer ≈ 6861 + -2. → 6859",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 6861 + 5024 - 5026\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 6859\n\nSolution B: NS approach (2 steps): Near-cancellation: 5024 - 5026 = -2, so answer ≈ 6861 + -2. → 6859"
  },
  {
    "task_id": "J3_relative_distance_000504",
    "task_type": "J3_pairwise_efficiency",
    "category": "relative_distance",
    "problem": "Which is larger: 570/1150 or 4951/9819?",
    "solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4951/9819",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 4951/9819",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 570/1150 or 4951/9819?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4951/9819\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 4951/9819"
  },
  {
    "task_id": "J3_compatible_numbers_000609",
    "task_type": "J3_pairwise_efficiency",
    "category": "compatible_numbers",
    "problem": "Estimate 5009 × 1968.",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 9857712",
    "solution_b": "NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9857712",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 5009 × 1968.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 9857712\n\nSolution B: NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9857712"
  },
  {
    "task_id": "J3_compatible_numbers_000646",
    "task_type": "J3_pairwise_efficiency",
    "category": "compatible_numbers",
    "problem": "Estimate 2473 × 4227.",
    "solution_a": "NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 10453371",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 10453371",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 2473 × 4227.\n\nSolution A: NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 10453371\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 10453371"
  },
  {
    "task_id": "J3_relative_distance_000524",
    "task_type": "J3_pairwise_efficiency",
    "category": "relative_distance",
    "problem": "Which is larger: 1837/3735 or 2765/5491?",
    "solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 2765/5491",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 2765/5491",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1837/3735 or 2765/5491?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 2765/5491\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 2765/5491"
  },
  {
    "task_id": "J3_cancellation_identity_000595",
    "task_type": "J3_pairwise_efficiency",
    "category": "cancellation_identity",
    "problem": "Evaluate: 2576 + 4339 - 4341",
    "solution_a": "NS approach (2 steps): Near-cancellation: 4339 - 4341 = -2, so answer ≈ 2576 + -2. → 2574",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 2574",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 2576 + 4339 - 4341\n\nSolution A: NS approach (2 steps): Near-cancellation: 4339 - 4341 = -2, so answer ≈ 2576 + -2. → 2574\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 2574"
  },
  {
    "task_id": "J3_structural_shortcuts_000492",
    "task_type": "J3_pairwise_efficiency",
    "category": "structural_shortcuts",
    "problem": "What is 9998 * 2912?",
    "solution_a": "NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 29114176",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 29114176",
    "correct_answer": "A",
    "ns_steps": 3,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9998 * 2912?\n\nSolution A: NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 29114176\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 29114176"
  },
  {
    "task_id": "J3_option_elimination_000753",
    "task_type": "J3_pairwise_efficiency",
    "category": "option_elimination",
    "problem": "What is 6918 × 8652?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 59854536",
    "solution_b": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 59854536",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 6918 × 8652?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 59854536\n\nSolution B: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 59854536"
  },
  {
    "task_id": "J3_magnitude_estimation_000441",
    "task_type": "J3_pairwise_efficiency",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 9800 * 10200?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 99960000",
    "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 99960000",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9800 * 10200?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99960000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 99960000"
  },
  {
    "task_id": "J3_magnitude_estimation_000422",
    "task_type": "J3_pairwise_efficiency",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 9800 * 10200?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 99960000",
    "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 99960000",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9800 * 10200?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99960000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 99960000"
  },
  {
    "task_id": "J3_cancellation_identity_000573",
    "task_type": "J3_pairwise_efficiency",
    "category": "cancellation_identity",
    "problem": "Evaluate: 9000 + 5060 - 5058",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 9002",
    "solution_b": "NS approach (2 steps): Near-cancellation: 5060 - 5058 = 2, so answer ≈ 9000 + 2. → 9002",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 9000 + 5060 - 5058\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 9002\n\nSolution B: NS approach (2 steps): Near-cancellation: 5060 - 5058 = 2, so answer ≈ 9000 + 2. → 9002"
  },
  {
    "task_id": "J3_structural_shortcuts_000457",
    "task_type": "J3_pairwise_efficiency",
    "category": "structural_shortcuts",
    "problem": "What is 9999 * 2376?",
    "solution_a": "NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 23757624",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 23757624",
    "correct_answer": "A",
    "ns_steps": 3,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9999 * 2376?\n\nSolution A: NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 23757624\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 23757624"
  },
  {
    "task_id": "J3_magnitude_estimation_000423",
    "task_type": "J3_pairwise_efficiency",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 10100 * 9800?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 98980000",
    "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 98980000",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10100 * 9800?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 98980000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 98980000"
  },
  {
    "task_id": "J3_structural_shortcuts_000451",
    "task_type": "J3_pairwise_efficiency",
    "category": "structural_shortcuts",
    "problem": "What is 10001 * 5029?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 50295029",
    "solution_b": "NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 50295029",
    "correct_answer": "B",
    "ns_steps": 3,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 10001 * 5029?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 50295029\n\nSolution B: NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 50295029"
  },
  {
    "task_id": "J3_option_elimination_000780",
    "task_type": "J3_pairwise_efficiency",
    "category": "option_elimination",
    "problem": "What is 8020 × 2628?",
    "solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 21076560",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 21076560",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 8020 × 2628?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 21076560\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 21076560"
  },
  {
    "task_id": "J3_magnitude_estimation_000430",
    "task_type": "J3_pairwise_efficiency",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 10100 * 9900?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 99990000",
    "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 99990000",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10100 * 9900?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99990000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 99990000"
  },
  {
    "task_id": "J3_equation_reasoning_000721",
    "task_type": "J3_pairwise_efficiency",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  6468 × (2099 + 2237) = 6468 × ___ + 6468 × 2237",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 2099",
    "solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 2099",
    "correct_answer": "B",
    "ns_steps": 1,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank?  6468 × (2099 + 2237) = 6468 × ___ + 6468 × 2237\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 2099\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 2099"
  },
  {
    "task_id": "J3_cancellation_identity_000578",
    "task_type": "J3_pairwise_efficiency",
    "category": "cancellation_identity",
    "problem": "Evaluate: 5722 + 2063 - 2062",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 5723",
    "solution_b": "NS approach (2 steps): Near-cancellation: 2063 - 2062 = 1, so answer ≈ 5722 + 1. → 5723",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 5722 + 2063 - 2062\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 5723\n\nSolution B: NS approach (2 steps): Near-cancellation: 2063 - 2062 = 1, so answer ≈ 5722 + 1. → 5723"
  },
  {
    "task_id": "J3_compatible_numbers_000616",
    "task_type": "J3_pairwise_efficiency",
    "category": "compatible_numbers",
    "problem": "Estimate 1233 × 7868.",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 9701244",
    "solution_b": "NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 9701244",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 1233 × 7868.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 9701244\n\nSolution B: NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 9701244"
  },
  {
    "task_id": "J3_relative_distance_000512",
    "task_type": "J3_pairwise_efficiency",
    "category": "relative_distance",
    "problem": "Which is larger: 1039/2080 or 3210/6396?",
    "solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3210/6396",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 3210/6396",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1039/2080 or 3210/6396?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3210/6396\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 3210/6396"
  },
  {
    "task_id": "J3_landmark_comparison_000652",
    "task_type": "J3_pairwise_efficiency",
    "category": "landmark_comparison",
    "problem": "Is 9% of 48380 greater than 22179?",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → No",
    "solution_b": "NS approach (2 steps): Use 10% as landmark: 10% of 48380 = 4838. → No",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 9% of 48380 greater than 22179?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → No\n\nSolution B: NS approach (2 steps): Use 10% as landmark: 10% of 48380 = 4838. → No"
  },
  {
    "task_id": "J3_cancellation_identity_000588",
    "task_type": "J3_pairwise_efficiency",
    "category": "cancellation_identity",
    "problem": "Evaluate: 9092 + 3990 - 3991",
    "solution_a": "NS approach (2 steps): Near-cancellation: 3990 - 3991 = -1, so answer ≈ 9092 + -1. → 9091",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 9091",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 9092 + 3990 - 3991\n\nSolution A: NS approach (2 steps): Near-cancellation: 3990 - 3991 = -1, so answer ≈ 9092 + -1. → 9091\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 9091"
  },
  {
    "task_id": "J3_equation_reasoning_000727",
    "task_type": "J3_pairwise_efficiency",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  3305 + 5079 + ___ = 5079 + 3905 + 3305",
    "solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 3905",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 3905",
    "correct_answer": "A",
    "ns_steps": 1,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank?  3305 + 5079 + ___ = 5079 + 3905 + 3305\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 3905\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 3905"
  },
  {
    "task_id": "J3_equation_reasoning_000704",
    "task_type": "J3_pairwise_efficiency",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  9515 + 8703 = ___ + 7313",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 10905",
    "solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 10905",
    "correct_answer": "B",
    "ns_steps": 1,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank?  9515 + 8703 = ___ + 7313\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 10905\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 10905"
  },
  {
    "task_id": "J3_option_elimination_000800",
    "task_type": "J3_pairwise_efficiency",
    "category": "option_elimination",
    "problem": "What is 6809 × 9143?",
    "solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 62254687",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 62254687",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 6809 × 9143?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 62254687\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 62254687"
  },
  {
    "task_id": "J3_magnitude_estimation_000420",
    "task_type": "J3_pairwise_efficiency",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 10200 * 9800?",
    "solution_a": "NS approach (2 steps): Round both to 10000 and multiply. → 99960000",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 99960000",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10200 * 9800?\n\nSolution A: NS approach (2 steps): Round both to 10000 and multiply. → 99960000\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 99960000"
  },
  {
    "task_id": "J3_relative_distance_000509",
    "task_type": "J3_pairwise_efficiency",
    "category": "relative_distance",
    "problem": "Which is larger: 2166/4399 or 1489/2922?",
    "solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1489/2922",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 1489/2922",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 2166/4399 or 1489/2922?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1489/2922\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 1489/2922"
  },
  {
    "task_id": "J3_magnitude_estimation_000407",
    "task_type": "J3_pairwise_efficiency",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 9900 * 10100?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 99990000",
    "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 99990000",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9900 * 10100?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99990000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 99990000"
  },
  {
    "task_id": "J3_compatible_numbers_000605",
    "task_type": "J3_pairwise_efficiency",
    "category": "compatible_numbers",
    "problem": "Estimate 1274 × 8785.",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 11192090",
    "solution_b": "NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 11192090",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 1274 × 8785.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 11192090\n\nSolution B: NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 11192090"
  },
  {
    "task_id": "J3_relative_distance_000543",
    "task_type": "J3_pairwise_efficiency",
    "category": "relative_distance",
    "problem": "Which is larger: 1162/2369 or 1679/3322?",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 1679/3322",
    "solution_b": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1679/3322",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1162/2369 or 1679/3322?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 1679/3322\n\nSolution B: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1679/3322"
  },
  {
    "task_id": "J3_relative_distance_000527",
    "task_type": "J3_pairwise_efficiency",
    "category": "relative_distance",
    "problem": "Which is larger: 1753/3550 or 4210/8308?",
    "solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4210/8308",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 4210/8308",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1753/3550 or 4210/8308?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4210/8308\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 4210/8308"
  },
  {
    "task_id": "J3_equation_reasoning_000726",
    "task_type": "J3_pairwise_efficiency",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  1264 + 1118 = ___ + 7226",
    "solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → -4844",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → -4844",
    "correct_answer": "A",
    "ns_steps": 1,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank?  1264 + 1118 = ___ + 7226\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → -4844\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → -4844"
  },
  {
    "task_id": "J3_magnitude_estimation_000443",
    "task_type": "J3_pairwise_efficiency",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 9800 * 9800?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 96040000",
    "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 96040000",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9800 * 9800?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 96040000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 96040000"
  },
  {
    "task_id": "J3_landmark_comparison_000653",
    "task_type": "J3_pairwise_efficiency",
    "category": "landmark_comparison",
    "problem": "Is 48% of 75650 greater than 34563?",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → Yes",
    "solution_b": "NS approach (2 steps): Use 50% as landmark: 50% of 75650 = 37825. → Yes",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 48% of 75650 greater than 34563?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → Yes\n\nSolution B: NS approach (2 steps): Use 50% as landmark: 50% of 75650 = 37825. → Yes"
  },
  {
    "task_id": "J3_relative_distance_000534",
    "task_type": "J3_pairwise_efficiency",
    "category": "relative_distance",
    "problem": "Which is larger: 4320/8812 or 1806/3591?",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 1806/3591",
    "solution_b": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1806/3591",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 4320/8812 or 1806/3591?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 1806/3591\n\nSolution B: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1806/3591"
  },
  {
    "task_id": "J3_option_elimination_000782",
    "task_type": "J3_pairwise_efficiency",
    "category": "option_elimination",
    "problem": "What is 1133 × 1067?",
    "solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 1208911",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 1208911",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 1133 × 1067?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 1208911\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 1208911"
  },
  {
    "task_id": "J3_compatible_numbers_000608",
    "task_type": "J3_pairwise_efficiency",
    "category": "compatible_numbers",
    "problem": "Estimate 5009 × 1968.",
    "solution_a": "NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9857712",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 9857712",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 5009 × 1968.\n\nSolution A: NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9857712\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 9857712"
  },
  {
    "task_id": "J3_landmark_comparison_000699",
    "task_type": "J3_pairwise_efficiency",
    "category": "landmark_comparison",
    "problem": "Is 11% of 57250 greater than 11559?",
    "solution_a": "NS approach (2 steps): Use 10% as landmark: 10% of 57250 = 5725. → No",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → No",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 11% of 57250 greater than 11559?\n\nSolution A: NS approach (2 steps): Use 10% as landmark: 10% of 57250 = 5725. → No\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → No"
  },
  {
    "task_id": "J3_cancellation_identity_000599",
    "task_type": "J3_pairwise_efficiency",
    "category": "cancellation_identity",
    "problem": "Evaluate: 2021 + 4865 - 4863",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 2023",
    "solution_b": "NS approach (2 steps): Near-cancellation: 4865 - 4863 = 2, so answer ≈ 2021 + 2. → 2023",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 2021 + 4865 - 4863\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 2023\n\nSolution B: NS approach (2 steps): Near-cancellation: 4865 - 4863 = 2, so answer ≈ 2021 + 2. → 2023"
  },
  {
    "task_id": "J3_structural_shortcuts_000460",
    "task_type": "J3_pairwise_efficiency",
    "category": "structural_shortcuts",
    "problem": "What is 10001 * 4123?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 41234123",
    "solution_b": "NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 41234123",
    "correct_answer": "B",
    "ns_steps": 3,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 10001 * 4123?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 41234123\n\nSolution B: NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 41234123"
  },
  {
    "task_id": "J3_structural_shortcuts_000478",
    "task_type": "J3_pairwise_efficiency",
    "category": "structural_shortcuts",
    "problem": "What is 9999 * 2734?",
    "solution_a": "NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 27337266",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 27337266",
    "correct_answer": "A",
    "ns_steps": 3,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9999 * 2734?\n\nSolution A: NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 27337266\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 27337266"
  },
  {
    "task_id": "J3_option_elimination_000758",
    "task_type": "J3_pairwise_efficiency",
    "category": "option_elimination",
    "problem": "What is 7525 × 5474?",
    "solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 41191850",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 41191850",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 7525 × 5474?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 41191850\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 41191850"
  },
  {
    "task_id": "J3_relative_distance_000541",
    "task_type": "J3_pairwise_efficiency",
    "category": "relative_distance",
    "problem": "Which is larger: 1748/3532 or 1376/2725?",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 1376/2725",
    "solution_b": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1376/2725",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1748/3532 or 1376/2725?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 1376/2725\n\nSolution B: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1376/2725"
  },
  {
    "task_id": "J3_landmark_comparison_000695",
    "task_type": "J3_pairwise_efficiency",
    "category": "landmark_comparison",
    "problem": "Is 50% of 45760 greater than 12614?",
    "solution_a": "NS approach (2 steps): Use 50% as landmark: 50% of 45760 = 22880. → Yes",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → Yes",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 50% of 45760 greater than 12614?\n\nSolution A: NS approach (2 steps): Use 50% as landmark: 50% of 45760 = 22880. → Yes\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → Yes"
  },
  {
    "task_id": "J3_option_elimination_000776",
    "task_type": "J3_pairwise_efficiency",
    "category": "option_elimination",
    "problem": "What is 6135 × 7717?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 47343795",
    "solution_b": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 47343795",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 6135 × 7717?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 47343795\n\nSolution B: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 47343795"
  },
  {
    "task_id": "J3_magnitude_estimation_000402",
    "task_type": "J3_pairwise_efficiency",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 10100 * 9900?",
    "solution_a": "NS approach (2 steps): Round both to 10000 and multiply. → 99990000",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 99990000",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10100 * 9900?\n\nSolution A: NS approach (2 steps): Round both to 10000 and multiply. → 99990000\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 99990000"
  },
  {
    "task_id": "J3_structural_shortcuts_000496",
    "task_type": "J3_pairwise_efficiency",
    "category": "structural_shortcuts",
    "problem": "What is 9998 * 3721?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 37202558",
    "solution_b": "NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 37202558",
    "correct_answer": "B",
    "ns_steps": 3,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9998 * 3721?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 37202558\n\nSolution B: NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 37202558"
  },
  {
    "task_id": "J3_equation_reasoning_000734",
    "task_type": "J3_pairwise_efficiency",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  5844 + 3069 + ___ = 3069 + 6695 + 5844",
    "solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 6695",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 6695",
    "correct_answer": "A",
    "ns_steps": 1,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank?  5844 + 3069 + ___ = 3069 + 6695 + 5844\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 6695\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 6695"
  },
  {
    "task_id": "J3_magnitude_estimation_000414",
    "task_type": "J3_pairwise_efficiency",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 10200 * 9800?",
    "solution_a": "NS approach (2 steps): Round both to 10000 and multiply. → 99960000",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 99960000",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10200 * 9800?\n\nSolution A: NS approach (2 steps): Round both to 10000 and multiply. → 99960000\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 99960000"
  },
  {
    "task_id": "J3_cancellation_identity_000555",
    "task_type": "J3_pairwise_efficiency",
    "category": "cancellation_identity",
    "problem": "Evaluate: 7126 + 2057 - 2055",
    "solution_a": "NS approach (2 steps): Near-cancellation: 2057 - 2055 = 2, so answer ≈ 7126 + 2. → 7128",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 7128",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 7126 + 2057 - 2055\n\nSolution A: NS approach (2 steps): Near-cancellation: 2057 - 2055 = 2, so answer ≈ 7126 + 2. → 7128\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 7128"
  },
  {
    "task_id": "J3_equation_reasoning_000703",
    "task_type": "J3_pairwise_efficiency",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  4391 + 8555 + ___ = 8555 + 8523 + 4391",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 8523",
    "solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 8523",
    "correct_answer": "B",
    "ns_steps": 1,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank?  4391 + 8555 + ___ = 8555 + 8523 + 4391\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 8523\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 8523"
  },
  {
    "task_id": "J3_compatible_numbers_000603",
    "task_type": "J3_pairwise_efficiency",
    "category": "compatible_numbers",
    "problem": "Estimate 2520 × 3783.",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 9533160",
    "solution_b": "NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9533160",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 2520 × 3783.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 9533160\n\nSolution B: NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9533160"
  },
  {
    "task_id": "J3_landmark_comparison_000681",
    "task_type": "J3_pairwise_efficiency",
    "category": "landmark_comparison",
    "problem": "Is 9% of 52080 greater than 22238?",
    "solution_a": "NS approach (2 steps): Use 10% as landmark: 10% of 52080 = 5208. → No",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → No",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 9% of 52080 greater than 22238?\n\nSolution A: NS approach (2 steps): Use 10% as landmark: 10% of 52080 = 5208. → No\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → No"
  },
  {
    "task_id": "J3_magnitude_estimation_000434",
    "task_type": "J3_pairwise_efficiency",
    "category": "magnitude_estimation",
    "problem": "Which of the following is the best estimate for 10200 * 9800?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 99960000",
    "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 99960000",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10200 * 9800?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99960000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 99960000"
  },
  {
    "task_id": "J3_equation_reasoning_000718",
    "task_type": "J3_pairwise_efficiency",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  2661 + 1919 + ___ = 1919 + 6614 + 2661",
    "solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 6614",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 6614",
    "correct_answer": "A",
    "ns_steps": 1,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank?  2661 + 1919 + ___ = 1919 + 6614 + 2661\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 6614\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 6614"
  },
  {
    "task_id": "J3_relative_distance_000530",
    "task_type": "J3_pairwise_efficiency",
    "category": "relative_distance",
    "problem": "Which is larger: 3937/7998 or 3703/7314?",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 3703/7314",
    "solution_b": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3703/7314",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 3937/7998 or 3703/7314?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 3703/7314\n\nSolution B: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3703/7314"
  },
  {
    "task_id": "J3_relative_distance_000528",
    "task_type": "J3_pairwise_efficiency",
    "category": "relative_distance",
    "problem": "Which is larger: 2499/5018 or 4280/8455?",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 4280/8455",
    "solution_b": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4280/8455",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 2499/5018 or 4280/8455?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 4280/8455\n\nSolution B: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4280/8455"
  },
  {
    "task_id": "J3_option_elimination_000771",
    "task_type": "J3_pairwise_efficiency",
    "category": "option_elimination",
    "problem": "What is 5562 × 7803?",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 43400286",
    "solution_b": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 43400286",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 5562 × 7803?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 43400286\n\nSolution B: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 43400286"
  },
  {
    "task_id": "J3_landmark_comparison_000668",
    "task_type": "J3_pairwise_efficiency",
    "category": "landmark_comparison",
    "problem": "Is 10% of 93060 greater than 31194?",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → No",
    "solution_b": "NS approach (2 steps): Use 10% as landmark: 10% of 93060 = 9306. → No",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 10% of 93060 greater than 31194?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → No\n\nSolution B: NS approach (2 steps): Use 10% as landmark: 10% of 93060 = 9306. → No"
  },
  {
    "task_id": "J3_landmark_comparison_000677",
    "task_type": "J3_pairwise_efficiency",
    "category": "landmark_comparison",
    "problem": "Is 48% of 23770 greater than 9136?",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → Yes",
    "solution_b": "NS approach (2 steps): Use 50% as landmark: 50% of 23770 = 11885. → Yes",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 48% of 23770 greater than 9136?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → Yes\n\nSolution B: NS approach (2 steps): Use 50% as landmark: 50% of 23770 = 11885. → Yes"
  },
  {
    "task_id": "J3_landmark_comparison_000694",
    "task_type": "J3_pairwise_efficiency",
    "category": "landmark_comparison",
    "problem": "Is 24% of 90400 greater than 25771?",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → No",
    "solution_b": "NS approach (2 steps): Use 25% as landmark: 25% of 90400 = 22600. → No",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 24% of 90400 greater than 25771?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → No\n\nSolution B: NS approach (2 steps): Use 25% as landmark: 25% of 90400 = 22600. → No"
  },
  {
    "task_id": "J3_option_elimination_000792",
    "task_type": "J3_pairwise_efficiency",
    "category": "option_elimination",
    "problem": "What is 4893 × 1523?",
    "solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 7452039",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 7452039",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 4893 × 1523?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 7452039\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 7452039"
  },
  {
    "task_id": "J3_compatible_numbers_000613",
    "task_type": "J3_pairwise_efficiency",
    "category": "compatible_numbers",
    "problem": "Estimate 2540 × 3676.",
    "solution_a": "Algorithmic approach (4 steps): Compute step by step → 9337040",
    "solution_b": "NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9337040",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 2540 × 3676.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 9337040\n\nSolution B: NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9337040"
  },
  {
    "task_id": "J3_cancellation_identity_000585",
    "task_type": "J3_pairwise_efficiency",
    "category": "cancellation_identity",
    "problem": "Evaluate: 4359 + 9463 - 9464",
    "solution_a": "Algorithmic approach (3 steps): Compute step by step → 4358",
    "solution_b": "NS approach (2 steps): Near-cancellation: 9463 - 9464 = -1, so answer ≈ 4359 + -1. → 4358",
    "correct_answer": "B",
    "ns_steps": 2,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 4359 + 9463 - 9464\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 4358\n\nSolution B: NS approach (2 steps): Near-cancellation: 9463 - 9464 = -1, so answer ≈ 4359 + -1. → 4358"
  },
  {
    "task_id": "J3_equation_reasoning_000743",
    "task_type": "J3_pairwise_efficiency",
    "category": "equation_reasoning",
    "problem": "What value fills the blank?  6010 × (2659 + 2481) = 6010 × ___ + 6010 × 2481",
    "solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 2659",
    "solution_b": "Algorithmic approach (3 steps): Compute step by step → 2659",
    "correct_answer": "A",
    "ns_steps": 1,
    "algo_steps": 3,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank?  6010 × (2659 + 2481) = 6010 × ___ + 6010 × 2481\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 2659\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 2659"
  },
  {
    "task_id": "J3_option_elimination_000765",
    "task_type": "J3_pairwise_efficiency",
    "category": "option_elimination",
    "problem": "What is 1104 × 5487?",
    "solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 6057648",
    "solution_b": "Algorithmic approach (4 steps): Compute step by step → 6057648",
    "correct_answer": "A",
    "ns_steps": 2,
    "algo_steps": 4,
    "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 1104 × 5487?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 6057648\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 6057648"
  }
]