{
  "good": [
    27713,
    27714,
    27715,
    27717,
    27718,
    27719,
    27720,
    27721,
    27722,
    27723,
    27724,
    27725,
    27726,
    27727,
    27728,
    27729,
    27730,
    27731,
    27732,
    27733,
    27734,
    27735,
    27736,
    27737,
    27738,
    27739,
    27740,
    27741,
    27742,
    27743,
    27744,
    27745,
    27746,
    27747,
    27748,
    27749,
    27751,
    27752,
    27753,
    27754,
    27755,
    27756,
    27757,
    27758,
    27759,
    27760,
    27761,
    27762,
    27763,
    27764,
    27765,
    27766,
    27767,
    27768,
    27769,
    27770,
    27771,
    27772,
    27773,
    27774,
    27775,
    27776,
    27777,
    27778,
    27779,
    27780,
    27781,
    27782,
    27783,
    27784,
    27785,
    27786,
    27787,
    27788,
    27789,
    27790,
    27791,
    27792,
    27794,
    27795,
    27796,
    27797,
    27798,
    27799,
    27800,
    27801,
    27802,
    27803,
    27804,
    27805,
    27806,
    27807,
    27808,
    27809,
    27810,
    27811,
    27812,
    27813,
    27814,
    27815,
    27816,
    27817,
    27818,
    27819,
    27820,
    27821,
    27822,
    27823,
    27824,
    27825,
    27826,
    27827,
    27828,
    27829,
    27830,
    27832,
    27833,
    27834,
    27835,
    27836,
    27837,
    27838,
    27839,
    27840,
    27841,
    27842,
    27843,
    27844,
    27845,
    27846,
    27847,
    27848,
    27849,
    27850,
    27851,
    27852,
    27853,
    27854,
    27855,
    27856,
    27857,
    27858,
    27859,
    27860,
    27861,
    27862,
    27863,
    27864,
    27865,
    27866,
    27867,
    27868,
    27869,
    27870,
    27871,
    27872,
    27873,
    27874,
    27875,
    27876,
    27877,
    27878,
    27879,
    27880,
    27881,
    27882,
    27883,
    27884,
    27885,
    27886,
    27887,
    27888,
    27889,
    27890,
    27891,
    27892,
    27893,
    27894,
    27895,
    27896,
    27897,
    27898,
    27899,
    27900,
    27901,
    27902,
    27903,
    27904,
    27905,
    27906,
    27907,
    27908,
    27909,
    27910,
    27911,
    27912,
    27913
  ],
  "needs_revision": {
    "27716": "KEY CONFLICT — solution correctly computes Ken had $28 (option 1), but the recorded correct_index=1 points to $56 (option 2). The answer key is wrong.",
    "27750": "KEY CONFLICT — answer key says 768 cookies but the correct answer is 96 (equal numbers at $540 total: $25n/8 + $2.50n = 540, n=96). Solution is internally confused.",
    "27793": "Inconsistent reasoning — states triangle GFE area = ½×13×12 (=78) then switches to ½×12×5 (=30) without explaining the change of base/height.",
    "27831": "Incomplete/unclear reasoning — ellipsis mid-computation; the arithmetic 6+2−1=7 intervals is not motivated from the 20-cone perimeter setup."
  }
}