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Answer the following problem. Explain your reasoning step by step. When you are finished, give your answer in this format: <answer>(your answer)</answer>. # Problem Using the numbers in the list [60, 76, 85], create an equation that equals 221. You can use basic arithmetic operations (+, -, *, /) and each number can only be used once. Your solution should include a series of steps "Step X:" where each step is a mathematical operation and the final step ultimately leads to the target number or it should be a single equation that results in the target. Give your answer in the following format: <answer> (your answer) </answer> Where "(your answer)" is the list of steps to reach the target number or it should be a single equation that results in the target. For example: If the list of numbers was [1, 2, 3] and the target was 1, you could write: <answer> Step 1: 1 + 2 = 3 Step 2: 3 / 3 = 1 </answer> or <answer> (1 + 2) / 3 </answer> Let's think step by step.
76 + 85 + 60
countdown_3arg
countdown
[ { "content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer.", "role": "system" }, { "content": "Answer the following problem. E...
[ "To solve the problem, we need to use the numbers [60, 76, 85] and the arithmetic operations (+, -, *, /) to reach the target number 221. \n\nStep 1: Let's start by trying to use the number 85 as the first operation. We can subtract 85 from 221 to get 136. \n\nStep 2: Now we have the number 136. We can use the numb...
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{"source_dataset": "countdown", "source_index": 1641, "numbers": [60, 76, 85], "target": 221, "expression": "76 + 85 + 60"}
[ "Step 1: 221 = 85 - 60 + 76", "Step 1: 76 * 85 = 6460\nStep 2: 6460 - 60 = 6400\nStep 3: 6400 + 85 = 6485", "Step 1: 60 + 76 = 136\nStep 2: 136 + 85 = 221", "Step 1: 60 + 76 = 136\nStep 2: 136 - 85 = 51\nStep 3: 51 * 4 = 204\nStep 4: 204 - 19 = 185\nStep 5: 185 - 36 = 149\nStep 6: 149 + 72 = 221", "Step 1: ...
[ "Could not evaluate line: Step 1: 221 = 85 - 60 + 76", "Line uses unavailable numbers: Step 3: 6400 + 85 = 6485", null, "Line uses unavailable numbers: Step 3: 51 * 4 = 204", null, null, "Line uses unavailable numbers: Step 2: 6460 - 5239 = 1221", "Line uses unavailable numbers: Step 3: 11560 - 11339 ...
[ "Step 1: 60 * 4 = 240 \nStep 2: 240 - 19 = 221 \nStep 3: 76 - 85 = -9 \nStep 4: 240 - 19 + (-9) = 221 \n\n<answer>\nStep 1: 60 * 4 = 240 \nStep 2: 240 - 19 = 221 \nStep 3: 76 - 85 = -9 \nStep 4: 240 - 19 + (-9) = 221\n</answer>", "Step 1: 60 + 76 = 136 \nStep 2: 136 + 85 = 221 \nStep 3: 221 = 221 \n\n<a...
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[ "Step 1: 60 * 4 = 240 \nStep 2: 240 - 19 = 221 \nStep 3: 76 - 85 = -9 \nStep 4: 240 - 19 + (-9) = 221", "Step 1: 60 + 76 = 136 \nStep 2: 136 + 85 = 221 \nStep 3: 221 = 221", "Step 1: 85 * 2 = 170 \nStep 2: 170 + 60 = 230 \nStep 3: 230 - 76 = 154 \nStep 4: 154 + (85 - 76) = 221", "60 * 4 = 240\n240 - (...
[{"extraction_type": "final", "total_spans_found": 1, "non_overlapping_spans": 1, "span_start": 112, "span_end": 214, "original_span": "Step 1: 60 * 4 = 240 \nStep 2: 240 - 19 = 221 \nStep 3: 76 - 85 = -9 \nStep 4: 240 - 19 + (-9) = 221"}, {"extraction_type": "final", "total_spans_found": 1, "non_overlapping_spans": 1, "span_start": 78, "span_end": 146, "original_span": "Step 1: 60 + 76 = 136 \nStep 2: 136 + 85 = 221 \nStep 3: 221 = 221"}, {"extraction_type": "final", "total_spans_found": 1, "non_overlapping_spans": 1, "span_start": 130, "span_end": 236, "original_span": "Step 1: 85 * 2 = 170 \nStep 2: 170 + 60 = 230 \nStep 3: 230 - 76 = 154 \nStep 4: 154 + (85 - 76) = 221"}, {"extraction_type": "final", "total_spans_found": 1, "non_overlapping_spans": 1, "span_start": 104, "span_end": 140, "original_span": "60 * 4 = 240\n240 - (76 - 85) = 221"}, {"extraction_type": "final", "total_spans_found": 1, "non_overlapping_spans": 1, "span_start": 112, "span_end": 214, "original_span": "Step 1: 60 * 4 = 240 \nStep 2: 240 - 19 = 221 \nStep 3: 76 - 85 = -9 \nStep 4: 240 - 19 + (-9) = 221"}, {"extraction_type": "final", "total_spans_found": 1, "non_overlapping_spans": 1, "span_start": 130, "span_end": 271, "original_span": "Step 1: 85 * 2 = 170 \nStep 2: 170 + 60 = 230 \nStep 3: 230 - 76 = 154 \nStep 4: 154 + (85 - 76) = 154 + 9 = 163 \nStep 5: 163 + 58 = 221"}, {"extraction_type": "final", "total_spans_found": 1, "non_overlapping_spans": 1, "span_start": 324, "span_end": 714, "original_span": "Step 1: 60 * 3 = 180 \nStep 2: 180 + 41 = 221 \nStep 3: 41 = 76 - 35 \nStep 4: 35 = 85 - 50 \nStep 5: 50 = 85 - 60 \nStep 6: Substitute 50 into Step 4 \u2192 35 = 85 - (85 - 60) \nStep 7: Simplify Step 6 \u2192 35 = 60 \nStep 8: Substitute 35 into Step 3 \u2192 41 = 76 - 60 \nStep 9: Substitute 41 into Step 2 \u2192 221 = 180 + (76 - 60) \nStep 10: Substitute 180 from Step 1 \u2192 221 = (60 * 3) + (76 - 60)"}, {"extraction_type": "final", "total_spans_found": 1, "non_overlapping_spans": 1, "span_start": 235, "span_end": 257, "original_span": "(60 * 4) - (76 - 57)"}, {"extraction_type": "final", "total_spans_found": 1, "non_overlapping_spans": 1, "span_start": 112, "span_end": 214, "original_span": "Step 1: 60 * 4 = 240 \nStep 2: 240 - 19 = 221 \nStep 3: 76 - 85 = -9 \nStep 4: 240 - 19 + (-9) = 221"}, {"extraction_type": "final", "total_spans_found": 1, "non_overlapping_spans": 1, "span_start": 78, "span_end": 146, "original_span": "Step 1: 60 + 76 = 136 \nStep 2: 136 + 85 = 221 \nStep 3: 221 = 221"}, {"extraction_type": "final", "total_spans_found": 1, "non_overlapping_spans": 1, "span_start": 130, "span_end": 236, "original_span": "Step 1: 85 * 2 = 170 \nStep 2: 170 + 60 = 230 \nStep 3: 230 - 76 = 154 \nStep 4: 154 + (85 - 76) = 221"}, {"extraction_type": "final", "total_spans_found": 1, "non_overlapping_spans": 1, "span_start": 105, "span_end": 128, "original_span": "(85*2)+60-76+67 = 221"}, {"extraction_type": "final"}, {"extraction_type": "final", "total_spans_found": 1, "non_overlapping_spans": 1, "span_start": 171, "span_end": 204, "original_span": "(85 * 2) + 60 - (85 - 76) = 221"}, {"extraction_type": "final", "total_spans_found": 1, "non_overlapping_spans": 1, "span_start": 77, "span_end": 147, "original_span": "Step 1: 60 + 76 = 136 \nStep 2: 136 + 85 = 221 \nStep 3: 221 = 221"}, {"extraction_type": "final", "total_spans_found": 1, "non_overlapping_spans": 1, "span_start": 8, "span_end": 54, "original_span": "Step 1: 60 + 76 = 136\nStep 2: 136 + 85 = 221"}]
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[ [ "Step 1: 60 * 4 = 240 \nStep 2: 240 - 19 = 221 \nStep 3: 76 - 85 = -9 \nStep 4: 240 - 19 + (-9) = 221" ], [ "Step 1: 60 + 76 = 136 \nStep 2: 136 + 85 = 221 \nStep 3: 221 = 221" ], [ "Step 1: 85 * 2 = 170 \nStep 2: 170 + 60 = 230 \nStep 3: 230 - 76 = 154 \nStep 4: 154 + (85 - 76) = 221"...
[[{"pattern_used": "answer tag", "confidence": 1.0, "position": 112, "span_text": "Step 1: 60 * 4 = 240 \nStep 2: 240 - 19 = 221 \nStep 3: 76 - 85 = -9 \nStep 4: 240 - 19 + (-9) = 221", "extraction_type": "internal", "span_start": 112, "span_end": 214, "original_span": "Step 1: 60 * 4 = 240 \nStep 2: 240 - 19 = 221 \nStep 3: 76 - 85 = -9 \nStep 4: 240 - 19 + (-9) = 221"}], [{"pattern_used": "answer tag", "confidence": 1.0, "position": 78, "span_text": "Step 1: 60 + 76 = 136 \nStep 2: 136 + 85 = 221 \nStep 3: 221 = 221", "extraction_type": "internal", "span_start": 78, "span_end": 146, "original_span": "Step 1: 60 + 76 = 136 \nStep 2: 136 + 85 = 221 \nStep 3: 221 = 221"}], [{"pattern_used": "answer tag", "confidence": 1.0, "position": 130, "span_text": "Step 1: 85 * 2 = 170 \nStep 2: 170 + 60 = 230 \nStep 3: 230 - 76 = 154 \nStep 4: 154 + (85 - 76) = 221", "extraction_type": "internal", "span_start": 130, "span_end": 236, "original_span": "Step 1: 85 * 2 = 170 \nStep 2: 170 + 60 = 230 \nStep 3: 230 - 76 = 154 \nStep 4: 154 + (85 - 76) = 221"}], [{"pattern_used": "answer tag", "confidence": 1.0, "position": 104, "span_text": "60 * 4 = 240\n240 - (76 - 85) = 221", "extraction_type": "internal", "span_start": 104, "span_end": 140, "original_span": "60 * 4 = 240\n240 - (76 - 85) = 221"}], [{"pattern_used": "answer tag", "confidence": 1.0, "position": 112, "span_text": "Step 1: 60 * 4 = 240 \nStep 2: 240 - 19 = 221 \nStep 3: 76 - 85 = -9 \nStep 4: 240 - 19 + (-9) = 221", "extraction_type": "internal", "span_start": 112, "span_end": 214, "original_span": "Step 1: 60 * 4 = 240 \nStep 2: 240 - 19 = 221 \nStep 3: 76 - 85 = -9 \nStep 4: 240 - 19 + (-9) = 221"}], [{"pattern_used": "answer tag", "confidence": 1.0, "position": 130, "span_text": "Step 1: 85 * 2 = 170 \nStep 2: 170 + 60 = 230 \nStep 3: 230 - 76 = 154 \nStep 4: 154 + (85 - 76) = 154 + 9 = 163 \nStep 5: 163 + 58 = 221", "extraction_type": "internal", "span_start": 130, "span_end": 271, "original_span": "Step 1: 85 * 2 = 170 \nStep 2: 170 + 60 = 230 \nStep 3: 230 - 76 = 154 \nStep 4: 154 + (85 - 76) = 154 + 9 = 163 \nStep 5: 163 + 58 = 221"}], [{"pattern_used": "answer tag", "confidence": 1.0, "position": 324, "span_text": "Step 1: 60 * 3 = 180 \nStep 2: 180 + 41 = 221 \nStep 3: 41 = 76 - 35 \nStep 4: 35 = 85 - 50 \nStep 5: 50 = 85 - 60 \nStep 6: Substitute 50 into Step 4 \u2192 35 = 85 - (85 - 60) \nStep 7: Simplify Step 6 \u2192 35 = 60 \nStep 8: Substitute 35 into Step 3 \u2192 41 = 76 - 60 \nStep 9: Substitute 41 into Step 2 \u2192 221 = 180 + (76 - 60) \nStep 10: Substitute 180 from Step 1 \u2192 221 = (60 * 3) + (76 - 60)", "extraction_type": "internal", "span_start": 324, "span_end": 714, "original_span": "Step 1: 60 * 3 = 180 \nStep 2: 180 + 41 = 221 \nStep 3: 41 = 76 - 35 \nStep 4: 35 = 85 - 50 \nStep 5: 50 = 85 - 60 \nStep 6: Substitute 50 into Step 4 \u2192 35 = 85 - (85 - 60) \nStep 7: Simplify Step 6 \u2192 35 = 60 \nStep 8: Substitute 35 into Step 3 \u2192 41 = 76 - 60 \nStep 9: Substitute 41 into Step 2 \u2192 221 = 180 + (76 - 60) \nStep 10: Substitute 180 from Step 1 \u2192 221 = (60 * 3) + (76 - 60)"}], [{"pattern_used": "answer tag", "confidence": 1.0, "position": 235, "span_text": "(60 * 4) - (76 - 57)", "extraction_type": "internal", "span_start": 235, "span_end": 257, "original_span": "(60 * 4) - (76 - 57)"}], [{"pattern_used": "answer tag", "confidence": 1.0, "position": 112, "span_text": "Step 1: 60 * 4 = 240 \nStep 2: 240 - 19 = 221 \nStep 3: 76 - 85 = -9 \nStep 4: 240 - 19 + (-9) = 221", "extraction_type": "internal", "span_start": 112, "span_end": 214, "original_span": "Step 1: 60 * 4 = 240 \nStep 2: 240 - 19 = 221 \nStep 3: 76 - 85 = -9 \nStep 4: 240 - 19 + (-9) = 221"}], [{"pattern_used": "answer tag", "confidence": 1.0, "position": 78, "span_text": "Step 1: 60 + 76 = 136 \nStep 2: 136 + 85 = 221 \nStep 3: 221 = 221", "extraction_type": "internal", "span_start": 78, "span_end": 146, "original_span": "Step 1: 60 + 76 = 136 \nStep 2: 136 + 85 = 221 \nStep 3: 221 = 221"}], [{"pattern_used": "answer tag", "confidence": 1.0, "position": 130, "span_text": "Step 1: 85 * 2 = 170 \nStep 2: 170 + 60 = 230 \nStep 3: 230 - 76 = 154 \nStep 4: 154 + (85 - 76) = 221", "extraction_type": "internal", "span_start": 130, "span_end": 236, "original_span": "Step 1: 85 * 2 = 170 \nStep 2: 170 + 60 = 230 \nStep 3: 230 - 76 = 154 \nStep 4: 154 + (85 - 76) = 221"}], [{"pattern_used": "answer tag", "confidence": 1.0, "position": 105, "span_text": "(85*2)+60-76+67 = 221", "extraction_type": "internal", "span_start": 105, "span_end": 128, "original_span": "(85*2)+60-76+67 = 221"}], [], [{"pattern_used": "answer tag", "confidence": 1.0, "position": 171, "span_text": "(85 * 2) + 60 - (85 - 76) = 221", "extraction_type": "internal", "span_start": 171, "span_end": 204, "original_span": "(85 * 2) + 60 - (85 - 76) = 221"}], [{"pattern_used": "answer tag", "confidence": 1.0, "position": 77, "span_text": "Step 1: 60 + 76 = 136 \nStep 2: 136 + 85 = 221 \nStep 3: 221 = 221", "extraction_type": "internal", "span_start": 77, "span_end": 147, "original_span": "Step 1: 60 + 76 = 136 \nStep 2: 136 + 85 = 221 \nStep 3: 221 = 221"}], [{"pattern_used": "answer tag", "confidence": 1.0, "position": 8, "span_text": "Step 1: 60 + 76 = 136\nStep 2: 136 + 85 = 221", "extraction_type": "internal", "span_start": 8, "span_end": 54, "original_span": "Step 1: 60 + 76 = 136\nStep 2: 136 + 85 = 221"}]]
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2*67 - 34
countdown_3arg
countdown
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["Step 1: 67 * 2 = 134\nStep 2: 134 - 34 = 100","Step 1: 2 + 34 = 36\nStep 2: 36 * 67 = 2412\nStep 3(...TRUNCATED)
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["Step 1: 67 * (2 - 34/34) = 100 \nStep 2: (2 - 34/34) = 1 \nStep 3: 67 * 1 = 67 \nStep 4: 67 + 3(...TRUNCATED)
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92*(17 - 9)
countdown_3arg
countdown
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["Step 1: 92 * 8 = 736 \nStep 2: 8 = 17 - 9 \nStep 3: 736 = 92 * (17 - 9) \n<answer>\n92 * (17 - (...TRUNCATED)
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71 + 25 + 56
countdown_3arg
countdown
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[true,false,false,false,false,false,false,false,false,false,false,false,true,true,false,false,false,(...TRUNCATED)
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[null,"Incorrect arithmetic in line: Step 3: 3951 / 56 = 70.26785714285714","Line uses unavailable n(...TRUNCATED)
["Step 1: 56 + 71 = 127 \nStep 2: 127 + 25 = 152 \n<answer>\nStep 1: 56 + 71 = 127 \nStep 2: 127 (...TRUNCATED)
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["Step 1: 56 + 71 = 127 \nStep 2: 127 + 25 = 152","(56 + 71) + 25 = 152","Step 1: 56 + 71 = 127 \n(...TRUNCATED)
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{"flips_by":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"flips_total":0,"num_correct":15,"pass_at_n":1,"percen(...TRUNCATED)
"Answer the following problem. Explain your reasoning step by step. When you are finished, give your(...TRUNCATED)
59*7 - 88
countdown_3arg
countdown
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[false,false,false,false,false,false,false,false,true,false,false,true,false,false,false,false,false(...TRUNCATED)
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"{\"source_dataset\": \"countdown\", \"source_index\": 1646, \"numbers\": [59, 7, 88], \"target\": 3(...TRUNCATED)
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["Step 1: Multiply 59 and 7: 59 * 7 = 413 \nStep 2: Subtract 88 from the result: 413 - 88 = 325 \n(...TRUNCATED)
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"[{\"is_correct\": false, \"error\": \"Could not evaluate expression\", \"answer_block\": \"59 * 7 =(...TRUNCATED)
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[["59 * 7 = 413 \n413 - 88 = 325"],["Step 1: 59 * 7 = 413 \nStep 2: 413 - 88 = 325"],[],["59 * 7 -(...TRUNCATED)
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"Answer the following problem. Explain your reasoning step by step. When you are finished, give your(...TRUNCATED)
97 - 52 + 87
countdown_3arg
countdown
[{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED)
["To solve the problem, we need to use the numbers [52, 87, 97] and the operations (+, -, *, /) to r(...TRUNCATED)
[true,true,false,false,false,false,true,true,false,false,true,true,false,false,false,true,false,true(...TRUNCATED)
original
"{\"source_dataset\": \"countdown\", \"source_index\": 1647, \"numbers\": [52, 87, 97], \"target\": (...TRUNCATED)
["Step 1: 97 - 52 = 45\nStep 2: 87 + 45 = 132","Step 1: 97 - 52 = 45\nStep 2: 45 + 87 = 132","Step 1(...TRUNCATED)
[null,null,"Line uses unavailable numbers: Step 1: 52 * 2 = 104","Incorrect arithmetic in line: Step(...TRUNCATED)
["Step 1: 52 + 87 = 139 \nStep 2: 139 - 97 = 42 \nStep 3: 42 * 3 = 126 \nStep 4: 126 + 6 = 132 \(...TRUNCATED)
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{"api_url":"http://10.32.36.216:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED)
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"Answer the following problem. Explain your reasoning step by step. When you are finished, give your(...TRUNCATED)
37 + 70 + 11
countdown_3arg
countdown
[{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED)
["To solve the problem of creating an equation using the numbers [70, 37, 11] that equals 118, we ca(...TRUNCATED)
[true,false,false,false,false,false,false,true,false,true,false,true,true,false,false,false,true,fal(...TRUNCATED)
original
"{\"source_dataset\": \"countdown\", \"source_index\": 1649, \"numbers\": [70, 37, 11], \"target\": (...TRUNCATED)
["Step 1: 70 + 37 = 107\nStep 2: 107 + 11 = 118","Step 1: 70 * 11 = 770\nStep 2: 770 + 37 = 807\nSte(...TRUNCATED)
[null,"Line uses unavailable numbers: Step 3: 807 - 691 = 116","Incorrect arithmetic in line: Step 2(...TRUNCATED)
["Step 1: 70 + 37 = 107 \nStep 2: 107 + 11 = 118 \n<answer>\nStep 1: 70 + 37 = 107 \nStep 2: 107 (...TRUNCATED)
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"Answer the following problem. Explain your reasoning step by step. When you are finished, give your(...TRUNCATED)
3*51 - 40
countdown_3arg
countdown
[{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED)
["To solve the problem using the numbers [51, 3, 40], we need to create an equation that equals 113.(...TRUNCATED)
[false,false,true,false,false,false,false,true,false,false,true,false,false,false,false,false,false,(...TRUNCATED)
original
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["Step 1: 51 - 3 = 48\nStep 2: 48 + 40 = 88\nStep 3: 88 + 3 = 91\nStep 4: 91 + 2 = 93\nStep 5: 93 + (...TRUNCATED)
["Line uses unavailable numbers: Step 3: 88 + 3 = 91","Incorrect arithmetic in line: Step 3: 2160 - (...TRUNCATED)
["Step 1: 51 + 40 = 91 \nStep 2: 91 + 3 = 94 \nStep 3: 94 - 3 = 91 \nStep 4: 91 + 3 = 94 \nStep (...TRUNCATED)
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{"api_url":"http://10.32.36.216:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED)
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[[],[],["(51 × 3) - 40"],[],[],["Step 1: 51 + 3 = 54 \nStep 2: 54 + 40 = 94 \nStep 3: 94 * 2 = 18(...TRUNCATED)
"[[], [], [{\"pattern_used\": \"answer tag\", \"confidence\": 1.0, \"position\": 493, \"span_text\":(...TRUNCATED)
"[[], [], [{\"is_correct\": false, \"error\": \"Could not evaluate expression\", \"answer_block\": \(...TRUNCATED)
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"Answer the following problem. Explain your reasoning step by step. When you are finished, give your(...TRUNCATED)
99 + 97 + 1
countdown_3arg
countdown
[{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED)
["To solve the problem of creating an equation using the numbers [97, 99, 1] that equals 197, we can(...TRUNCATED)
[false,false,false,true,true,true,false,false,false,false,false,false,false,false,false,false,true,f(...TRUNCATED)
original
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60 + 71 + 45
countdown_3arg
countdown
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