{"id": "hmmt25-000", "category": "hmmt25", "answer": "103", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "103", "preds": ["103"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-001", "category": "hmmt25", "answer": "3375", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "3375", "preds": ["3375"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-002", "category": "hmmt25", "answer": "\\frac{1}{576}", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "\\frac{1}{576}", "preds": ["\\frac{1}{576}"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-003", "category": "hmmt25", "answer": "-984", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "-984", "preds": ["-984"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-004", "category": "hmmt25", "answer": "890", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "890", "preds": ["890"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-005", "category": "hmmt25", "answer": "\\frac{1311}{2017}", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "\\frac{1311}{2017}", "preds": ["\\frac{1311}{2017}"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-006", "category": "hmmt25", "answer": "\\frac{9 \\sqrt{23}}{23}", "pass1": 0.0, "passk": 0, "cons": 0, "n": 1, "trunc": 0, "err": 0, "pred": "", "preds": [""], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-007", "category": "hmmt25", "answer": "1-\\frac{2}{\\pi}", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "1-\\frac{2}{\\pi}", "preds": ["1-\\frac{2}{\\pi}"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-008", "category": "hmmt25", "answer": "1037", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "1037", "preds": ["1037"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-009", "category": "hmmt25", "answer": "\\frac{-1+\\sqrt{17}}{2}, \\frac{-1-\\sqrt{17}}{2}", "pass1": 0.0, "passk": 0, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "\\boxed{\\frac{-1+\\sqrt{17}}{2},\\frac{-1-\\sqrt{17}}{2}}.", "preds": ["\\boxed{\\frac{-1+\\sqrt{17}}{2},\\frac{-1-\\sqrt{17}}{2}}."], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-010", "category": "hmmt25", "answer": "56", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "56", "preds": ["56"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-011", "category": "hmmt25", "answer": "29", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "29", "preds": ["29"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-012", "category": "hmmt25", "answer": "105", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "105", "preds": ["105"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-013", "category": "hmmt25", "answer": "2304", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "2304", "preds": ["2304"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-014", "category": "hmmt25", "answer": "200", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "200", "preds": ["200"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-015", "category": "hmmt25", "answer": "6300", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "6300", "preds": ["6300"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-016", "category": "hmmt25", "answer": "2^{25} \\cdot 26!", "pass1": 0.0, "passk": 0, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "26!\\,2^{25}", "preds": ["26!\\,2^{25}"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-017", "category": "hmmt25", "answer": "\\frac{2025}{101}", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "\\frac{2025}{101}", "preds": ["\\frac{2025}{101}"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-018", "category": "hmmt25", "answer": "\\frac{4}{9}", "pass1": 0.0, "passk": 0, "cons": 0, "n": 1, "trunc": 0, "err": 0, "pred": "\\frac{2}{3}", "preds": ["\\frac{2}{3}"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-019", "category": "hmmt25", "answer": "\\frac{448}{3}", "pass1": 0.0, "passk": 0, "cons": 0, "n": 1, "trunc": 1, "err": 0, "pred": "Thus after a step, we can go from (k=4) to (k=3) or (k=2). If X=2, merges happen on two nonadjacent gaps, merging two pairs of snakes simultaneously: that would combine the 4 snakes", "preds": ["Thus after a step, we can go from (k=4) to (k=3) or (k=2). If X=2, merges happen on two nonadjacent gaps, merging two pairs of snakes simultaneously: that would combine the 4 snakes"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-020", "category": "hmmt25", "answer": "26", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "26", "preds": ["26"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-021", "category": "hmmt25", "answer": "63", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "63", "preds": ["63"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-022", "category": "hmmt25", "answer": "8\\sqrt{10}", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "8\\sqrt{10}", "preds": ["8\\sqrt{10}"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-023", "category": "hmmt25", "answer": "20", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "20", "preds": ["20"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-024", "category": "hmmt25", "answer": "\\sqrt{23}-2 \\sqrt{3}", "pass1": 0.0, "passk": 0, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "\\sqrt{23}-2\\sqrt3", "preds": ["\\sqrt{23}-2\\sqrt3"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-025", "category": "hmmt25", "answer": "9\\sqrt{15}", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "9\\sqrt{15}", "preds": ["9\\sqrt{15}"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-026", "category": "hmmt25", "answer": "\\frac{7}{18}", "pass1": 1.0, "passk": 1, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "\\frac{7}{18}", "preds": ["\\frac{7}{18}"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-027", "category": "hmmt25", "answer": "\\sqrt{6}", "pass1": 0.0, "passk": 0, "cons": 1, "n": 1, "trunc": 0, "err": 0, "pred": "\\sqrt6", "preds": ["\\sqrt6"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-028", "category": "hmmt25", "answer": "14+4\\sqrt{37}", "pass1": 0.0, "passk": 0, "cons": 0, "n": 1, "trunc": 1, "err": 0, "pred": "Check triangle AXD sides: AD=24, AX = sqrt(a^2 + s^2) = sqrt(16.04^2 +18.91^2) = sqrt(257.3 + 357.6) = sqrt(614.9) ≈24.79. DX = sqrt(a^2 + (s-24)^2) = sqrt(257.3 + ( -5.09)^2 ≈257.3 +25.91=283.21) => sqrt≈16.83. So sides: AD=24, AX≈24.79, DX≈16.83. Largest side is AX≈24.79 (actually slightly > AD=24). Check angle at D opposite AX? Actually largest side is AX ≈24.79. Check if 24.79^2 >24^2 +16.83^2? 24.79^2≈614.9; 24^2 +16.83^2 =576+283.2≈859.2. So 614.9<859.2, so angle opposite AX is acute. Check also if 24^2 > 24.79^2 +16.83^2? No; 576 <859, so angle at X opposite AD? AD is not the largest side now, but check angle at X opposite side AD=24. So check AD^2 =576 vs other sides sum: 24.79^2 +16.83^2 ≈614.9+283.2=898.1 >576, so angle at X is acute. Check angle at A opposite side DX: DX^2=283.2 vs sum of squares of other two sides: 2", "preds": ["Check triangle AXD sides: AD=24, AX = sqrt(a^2 + s^2) = sqrt(16.04^2 +18.91^2) = sqrt(257.3 + 357.6) = sqrt(614.9) ≈24.79. DX = sqrt(a^2 + (s-24)^2) = sqrt(257.3 + ( -5.09)^2 ≈257.3 +25.91=283.21) => sqrt≈16.83. So sides: AD=24, AX≈24.79, DX≈16.83. Largest side is AX≈24.79 (actually slightly > AD=24). Check angle at D opposite AX? Actually largest side is AX ≈24.79. Check if 24.79^2 >24^2 +16.83^2? 24.79^2≈614.9; 24^2 +16.83^2 =576+283.2≈859.2. So 614.9<859.2, so angle opposite AX is acute. Check also if 24^2 > 24.79^2 +16.83^2? No; 576 <859, so angle at X opposite AD? AD is not the largest side now, but check angle at X opposite side AD=24. So check AD^2 =576 vs other sides sum: 24.79^2 +16.83^2 ≈614.9+283.2=898.1 >576, so angle at X is acute. Check angle at A opposite side DX: DX^2=283.2 vs sum of squares of other two sides: 2"], "served_model": ["vibethinker-3b"]}
{"id": "hmmt25-029", "category": "hmmt25", "answer": "\\sqrt{\\frac{95}{24}}", "pass1": 0.0, "passk": 0, "cons": 0, "n": 1, "trunc": 1, "err": 0, "pred": "Thus compute α = (S - W)/2, β = (W+Y)/2, γ = (S - Y)/2. These", "preds": ["Thus compute α = (S - W)/2, β = (W+Y)/2, γ = (S - Y)/2. These"], "served_model": ["vibethinker-3b"]}