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The dataset generation failed because of a cast error
Error code:   DatasetGenerationCastError
Exception:    DatasetGenerationCastError
Message:      An error occurred while generating the dataset

All the data files must have the same columns, but at some point there are 4 new columns ({'run_id', 'input_file', 'created_at', 'artifacts'}) and 5 missing columns ({'problem', 'key_steps', 'rewritten', 'generated', 'stats'}).

This happened while the json dataset builder was generating data using

hf://datasets/yllkryeziu/rewritebench-qwen3-results/run_20260216_235653_Qwen_Qwen3-4B/run_manifest.json (at revision 8af77ab4f2e86c6c2d27ef481990d47256a2d3e8), [/tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260216_235653_Qwen_Qwen3-4B/results.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260216_235653_Qwen_Qwen3-4B/results.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260216_235653_Qwen_Qwen3-4B/run_manifest.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260216_235653_Qwen_Qwen3-4B/run_manifest.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260216_235653_Qwen_Qwen3-4B/summary_generate.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260216_235653_Qwen_Qwen3-4B/summary_generate.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260216_235653_Qwen_Qwen3-4B/summary_rewrite.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260216_235653_Qwen_Qwen3-4B/summary_rewrite.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_110309_Qwen_Qwen3-8B/results.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_110309_Qwen_Qwen3-8B/results.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_110309_Qwen_Qwen3-8B/run_manifest.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_110309_Qwen_Qwen3-8B/run_manifest.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_110309_Qwen_Qwen3-8B/summary_generate.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_110309_Qwen_Qwen3-8B/summary_generate.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_110309_Qwen_Qwen3-8B/summary_rewrite.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_110309_Qwen_Qwen3-8B/summary_rewrite.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_133250_Qwen_Qwen3-14B/results.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_133250_Qwen_Qwen3-14B/results.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_133250_Qwen_Qwen3-14B/run_manifest.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_133250_Qwen_Qwen3-14B/run_manifest.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_133250_Qwen_Qwen3-14B/summary_generate.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_133250_Qwen_Qwen3-14B/summary_generate.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_133250_Qwen_Qwen3-14B/summary_rewrite.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_133250_Qwen_Qwen3-14B/summary_rewrite.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_134527_Qwen_Qwen3-32B/results.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_134527_Qwen_Qwen3-32B/results.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_134527_Qwen_Qwen3-32B/run_manifest.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_134527_Qwen_Qwen3-32B/run_manifest.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_134527_Qwen_Qwen3-32B/summary_generate.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_134527_Qwen_Qwen3-32B/summary_generate.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_134527_Qwen_Qwen3-32B/summary_rewrite.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_134527_Qwen_Qwen3-32B/summary_rewrite.json)]

Please either edit the data files to have matching columns, or separate them into different configurations (see docs at https://hf.co/docs/hub/datasets-manual-configuration#multiple-configurations)
Traceback:    Traceback (most recent call last):
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1887, in _prepare_split_single
                  writer.write_table(table)
                File "/usr/local/lib/python3.12/site-packages/datasets/arrow_writer.py", line 675, in write_table
                  pa_table = table_cast(pa_table, self._schema)
                             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2272, in table_cast
                  return cast_table_to_schema(table, schema)
                         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2218, in cast_table_to_schema
                  raise CastError(
              datasets.table.CastError: Couldn't cast
              run_id: string
              created_at: string
              input_file: string
              artifacts: struct<results: string, summary_generate: string, summary_extract: string, summary_rewrite: string,  (... 24 chars omitted)
                child 0, results: string
                child 1, summary_generate: string
                child 2, summary_extract: string
                child 3, summary_rewrite: string
                child 4, failed_generate: string
              to
              {'problem': {'deepseek_reasoning': Value('string'), 'domain': Value('string'), 'ground_truth_solution': Value('string'), 'id': Value('string'), 'problem': Value('string'), 'source': Value('string')}, 'generated': {'input_conversation': List({'content': Value('string'), 'role': Value('string')}), 'responses': List({'content': Value('string'), 'correctness': Value('bool'), 'reason': Value('string')}), 'token_usages': List({'completion_tokens': Value('int64'), 'prompt_tokens': Value('int64'), 'total_tokens': Value('int64')})}, 'rewritten': {'input_conversation': List({'content': Value('string'), 'role': Value('string')}), 'responses': List({'content': Value('string'), 'correctness': Value('bool'), 'reason': Value('string')}), 'rewritten_extracted_answer': Value('string'), 'rewritten_score': Value('bool'), 'token_usages': List({'completion_tokens': Value('int64'), 'prompt_tokens': Value('int64'), 'total_tokens': Value('int64')})}, 'key_steps': List(Value('null')), 'stats': {'completion_token_reduction': Value('int64'), 'completion_token_reduction_pct': Value('float64'), 'generated_completion_tokens': Value('int64'), 'generated_correct': Value('bool'), 'generated_thinking_tokens': Value('int64'), 'key_steps_count': Value('int64'), 'rewritten_completion_tokens': Value('int64'), 'rewritten_correct': Value('bool'), 'rewritten_thinking_tokens': Value('int64')}}
              because column names don't match
              
              During handling of the above exception, another exception occurred:
              
              Traceback (most recent call last):
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1347, in compute_config_parquet_and_info_response
                  parquet_operations = convert_to_parquet(builder)
                                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 980, in convert_to_parquet
                  builder.download_and_prepare(
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 884, in download_and_prepare
                  self._download_and_prepare(
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 947, in _download_and_prepare
                  self._prepare_split(split_generator, **prepare_split_kwargs)
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1736, in _prepare_split
                  for job_id, done, content in self._prepare_split_single(
                                               ^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1889, in _prepare_split_single
                  raise DatasetGenerationCastError.from_cast_error(
              datasets.exceptions.DatasetGenerationCastError: An error occurred while generating the dataset
              
              All the data files must have the same columns, but at some point there are 4 new columns ({'run_id', 'input_file', 'created_at', 'artifacts'}) and 5 missing columns ({'problem', 'key_steps', 'rewritten', 'generated', 'stats'}).
              
              This happened while the json dataset builder was generating data using
              
              hf://datasets/yllkryeziu/rewritebench-qwen3-results/run_20260216_235653_Qwen_Qwen3-4B/run_manifest.json (at revision 8af77ab4f2e86c6c2d27ef481990d47256a2d3e8), [/tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260216_235653_Qwen_Qwen3-4B/results.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260216_235653_Qwen_Qwen3-4B/results.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260216_235653_Qwen_Qwen3-4B/run_manifest.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260216_235653_Qwen_Qwen3-4B/run_manifest.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260216_235653_Qwen_Qwen3-4B/summary_generate.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260216_235653_Qwen_Qwen3-4B/summary_generate.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260216_235653_Qwen_Qwen3-4B/summary_rewrite.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260216_235653_Qwen_Qwen3-4B/summary_rewrite.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_110309_Qwen_Qwen3-8B/results.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_110309_Qwen_Qwen3-8B/results.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_110309_Qwen_Qwen3-8B/run_manifest.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_110309_Qwen_Qwen3-8B/run_manifest.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_110309_Qwen_Qwen3-8B/summary_generate.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_110309_Qwen_Qwen3-8B/summary_generate.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_110309_Qwen_Qwen3-8B/summary_rewrite.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_110309_Qwen_Qwen3-8B/summary_rewrite.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_133250_Qwen_Qwen3-14B/results.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_133250_Qwen_Qwen3-14B/results.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_133250_Qwen_Qwen3-14B/run_manifest.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_133250_Qwen_Qwen3-14B/run_manifest.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_133250_Qwen_Qwen3-14B/summary_generate.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_133250_Qwen_Qwen3-14B/summary_generate.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_133250_Qwen_Qwen3-14B/summary_rewrite.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_133250_Qwen_Qwen3-14B/summary_rewrite.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_134527_Qwen_Qwen3-32B/results.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_134527_Qwen_Qwen3-32B/results.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_134527_Qwen_Qwen3-32B/run_manifest.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_134527_Qwen_Qwen3-32B/run_manifest.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_134527_Qwen_Qwen3-32B/summary_generate.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_134527_Qwen_Qwen3-32B/summary_generate.json), /tmp/hf-datasets-cache/medium/datasets/21514823048749-config-parquet-and-info-yllkryeziu-rewritebench-q-99518b08/hub/datasets--yllkryeziu--rewritebench-qwen3-results/snapshots/8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_134527_Qwen_Qwen3-32B/summary_rewrite.json (origin=hf://datasets/yllkryeziu/rewritebench-qwen3-results@8af77ab4f2e86c6c2d27ef481990d47256a2d3e8/run_20260217_134527_Qwen_Qwen3-32B/summary_rewrite.json)]
              
              Please either edit the data files to have matching columns, or separate them into different configurations (see docs at https://hf.co/docs/hub/datasets-manual-configuration#multiple-configurations)

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problem
dict
generated
dict
rewritten
dict
key_steps
list
stats
dict
{ "deepseek_reasoning": "Okay, so I need to prove that you need at least seven identical circles to cover a bigger circle that has twice the radius. Let me start by understanding the problem better. \n\nFirst, let's visualize this. The main circle, let's call it K, has radius R. Then each of the smaller circles, K₁, ...
{ "input_conversation": [ { "content": "Please solve the following math problem step by step, and put your final answer within \\boxed{}.\n\nProblem: Prove that the minimum number of identical circles $K_{1}, K_{2}, K_{3}, \\ldots$ needed to cover a circle $K$ with twice the radius is 7.\n", "role": "...
{ "input_conversation": [ { "content": "### TASK\nYou will receive an input containing two parts: a **problem statement** and a **reasoning trace** (an authentic, detailed internal monologue of someone working through the problem).\n\nAsk yourself: was this problem fundamentally easy, moderate, or hard for ...
[]
{ "completion_token_reduction": 10298, "completion_token_reduction_pct": 95.5464835776582, "generated_completion_tokens": 11459, "generated_correct": true, "generated_thinking_tokens": 10778, "key_steps_count": 0, "rewritten_completion_tokens": 1078, "rewritten_correct": true, "rewritten_thinking_toke...
{ "deepseek_reasoning": "Okay, so I need to solve this problem where there's a positive integer n such that (n+1)! + (n+2)! equals n! multiplied by 440. The answer choices are given, and I need to find the sum of the digits of n. Let me start by understanding the equation step by step.\n\nFirst, factorials can get re...
{ "input_conversation": [ { "content": "Please solve the following math problem step by step, and put your final answer within \\boxed{}.\n\nProblem: There is a positive integer $n$ such that $(n+1)! + (n+2)! = n! \\cdot 440$. What is the sum of the digits of $n$?\n$\\textbf{(A) }3\\qquad\\textbf{(B) }8\\qq...
{ "input_conversation": [ { "content": "### TASK\nYou will receive an input containing two parts: a **problem statement** and a **reasoning trace** (an authentic, detailed internal monologue of someone working through the problem).\n\nAsk yourself: was this problem fundamentally easy, moderate, or hard for ...
[]
{ "completion_token_reduction": 1218, "completion_token_reduction_pct": 55.36363636363636, "generated_completion_tokens": 2876, "generated_correct": false, "generated_thinking_tokens": 2200, "key_steps_count": 0, "rewritten_completion_tokens": 1608, "rewritten_correct": false, "rewritten_thinking_toke...
{"deepseek_reasoning":"Okay, so I have this equation to solve: the cube root of (x plus another cube(...TRUNCATED)
{"input_conversation":[{"content":"Please solve the following math problem step by step, and put you(...TRUNCATED)
{"input_conversation":[{"content":"### TASK\nYou will receive an input containing two parts: a **pro(...TRUNCATED)
[]
{"completion_token_reduction":2511,"completion_token_reduction_pct":71.03253182461103,"generated_com(...TRUNCATED)
{"deepseek_reasoning":"Okay, so I need to find the real parameter \\( a \\) such that 2 is the small(...TRUNCATED)
{"input_conversation":[{"content":"Please solve the following math problem step by step, and put you(...TRUNCATED)
{"input_conversation":[{"content":"### TASK\nYou will receive an input containing two parts: a **pro(...TRUNCATED)
[]
{"completion_token_reduction":11828,"completion_token_reduction_pct":90.76816821425831,"generated_co(...TRUNCATED)
{"deepseek_reasoning":"Okay, so I need to prove that in a triangle ABC with medians intersecting at (...TRUNCATED)
{"input_conversation":[{"content":"Please solve the following math problem step by step, and put you(...TRUNCATED)
{"input_conversation":[{"content":"### TASK\nYou will receive an input containing two parts: a **pro(...TRUNCATED)
[]
{"completion_token_reduction":4162,"completion_token_reduction_pct":74.08330366678534,"generated_com(...TRUNCATED)
{"deepseek_reasoning":"Okay, let's see. I need to prove that 3 < A < 4 where A is given by 6 log p +(...TRUNCATED)
{"input_conversation":[{"content":"Please solve the following math problem step by step, and put you(...TRUNCATED)
{"input_conversation":[{"content":"### TASK\nYou will receive an input containing two parts: a **pro(...TRUNCATED)
[]
{"completion_token_reduction":8472,"completion_token_reduction_pct":91.83739837398373,"generated_com(...TRUNCATED)
{"deepseek_reasoning":"Okay, so I need to find the value of x, which is the ratio of two sums: the n(...TRUNCATED)
{"input_conversation":[{"content":"Please solve the following math problem step by step, and put you(...TRUNCATED)
{"input_conversation":[{"content":"### TASK\nYou will receive an input containing two parts: a **pro(...TRUNCATED)
[]
{"completion_token_reduction":3300,"completion_token_reduction_pct":59.055118110236215,"generated_co(...TRUNCATED)
{"deepseek_reasoning":"Okay, so I need to find the minimum value of the function \\( y = \\sqrt{x^2 (...TRUNCATED)
{"input_conversation":[{"content":"Please solve the following math problem step by step, and put you(...TRUNCATED)
{"input_conversation":[{"content":"### TASK\nYou will receive an input containing two parts: a **pro(...TRUNCATED)
[]
{"completion_token_reduction":2738,"completion_token_reduction_pct":85.53577007185254,"generated_com(...TRUNCATED)
{"deepseek_reasoning":"Okay, so I need to prove that 3a + 4b ≤ 5c where a and b are the legs of a (...TRUNCATED)
{"input_conversation":[{"content":"Please solve the following math problem step by step, and put you(...TRUNCATED)
{"input_conversation":[{"content":"### TASK\nYou will receive an input containing two parts: a **pro(...TRUNCATED)
[]
{"completion_token_reduction":3860,"completion_token_reduction_pct":85.20971302428256,"generated_com(...TRUNCATED)
{"deepseek_reasoning":"Okay, so I have this geometry problem here. Let me try to visualize it first.(...TRUNCATED)
{"input_conversation":[{"content":"Please solve the following math problem step by step, and put you(...TRUNCATED)
{"input_conversation":[{"content":"### TASK\nYou will receive an input containing two parts: a **pro(...TRUNCATED)
[]
{"completion_token_reduction":6644,"completion_token_reduction_pct":73.20405464962538,"generated_com(...TRUNCATED)
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