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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 ({'extracted_answers', 'traces', 'GT_answer', 'input_text'})
This happened while the json dataset builder was generating data using
hf://datasets/DanielSc4/neurohike-traces/AIME2025/Qwen3-4B_teacher_traces.json (at revision 7bdb30ba9cacb93797f13d29867a5ab5a72c314f), [/tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/DeepSeek-R1-Distill-Qwen-7B_teacher_traces.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/DeepSeek-R1-Distill-Qwen-7B_teacher_traces.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/Qwen3-4B_teacher_traces.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/Qwen3-4B_teacher_traces.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/gemma-3-4b-it_teacher_traces.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/gemma-3-4b-it_teacher_traces.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/gpt-oss-20b_generation_cache.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/gpt-oss-20b_generation_cache.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/gpt-oss-20b_teacher_traces.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/gpt-oss-20b_teacher_traces.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025a/Qwen3-4B_teacher_traces.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025a/Qwen3-4B_teacher_traces.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025a/batches/batch_000000_000015.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025a/batches/batch_000000_000015.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME_2024/batches/batch_000000_000030.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME_2024/batches/batch_000000_000030.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME_2024/gpt-oss-20b_teacher_traces.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME_2024/gpt-oss-20b_teacher_traces.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME_2024/gpt-oss-20b_teacher_traces_readable.jsonl (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME_2024/gpt-oss-20b_teacher_traces_readable.jsonl), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/ZebraLogic/batches/batch_000000_000050.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/ZebraLogic/batches/batch_000000_000050.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/ZebraLogic/gpt-oss-20b_teacher_traces.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/ZebraLogic/gpt-oss-20b_teacher_traces.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/ZebraLogic/gpt-oss-20b_teacher_traces_readable.jsonl (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/ZebraLogic/gpt-oss-20b_teacher_traces_readable.jsonl), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/Qwen3-4B_teacher_traces.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/Qwen3-4B_teacher_traces.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_000000_000500.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_000000_000500.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_000500_001000.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_000500_001000.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_001000_001500.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_001000_001500.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_001500_002000.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_001500_002000.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_002000_002500.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_002000_002500.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_002500_002980.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_002500_002980.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_002500_003000.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_002500_003000.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_003000_003500.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_003000_003500.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_003500_004000.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_003500_004000.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_004000_004500.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/gsm8k/batches/batch_004000_004500.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/non-math-mmlu-pro/batches/batch_000000_000065.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/non-math-mmlu-pro/batches/batch_000000_000065.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/non-math-mmlu-pro/gpt-oss-20b_teacher_traces.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/non-math-mmlu-pro/gpt-oss-20b_teacher_traces.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/non-math-mmlu-pro/gpt-oss-20b_teacher_traces_readable.jsonl (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/non-math-mmlu-pro/gpt-oss-20b_teacher_traces_readable.jsonl)]
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
input_text: string
traces: list<item: string>
child 0, item: string
extracted_answers: list<item: string>
child 0, item: string
GT_answer: int64
-- schema metadata --
pandas: '{"index_columns": [], "column_indexes": [], "columns": [{"name":' + 586
to
{}
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 ({'extracted_answers', 'traces', 'GT_answer', 'input_text'})
This happened while the json dataset builder was generating data using
hf://datasets/DanielSc4/neurohike-traces/AIME2025/Qwen3-4B_teacher_traces.json (at revision 7bdb30ba9cacb93797f13d29867a5ab5a72c314f), [/tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/DeepSeek-R1-Distill-Qwen-7B_teacher_traces.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/DeepSeek-R1-Distill-Qwen-7B_teacher_traces.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/Qwen3-4B_teacher_traces.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/Qwen3-4B_teacher_traces.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/gemma-3-4b-it_teacher_traces.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/gemma-3-4b-it_teacher_traces.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/gpt-oss-20b_generation_cache.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/gpt-oss-20b_generation_cache.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/gpt-oss-20b_teacher_traces.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025/gpt-oss-20b_teacher_traces.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025a/Qwen3-4B_teacher_traces.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025a/Qwen3-4B_teacher_traces.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025a/batches/batch_000000_000015.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME2025a/batches/batch_000000_000015.json), /tmp/hf-datasets-cache/medium/datasets/94255392728120-config-parquet-and-info-DanielSc4-neurohike-trace-fa0e40fb/hub/datasets--DanielSc4--neurohike-traces/snapshots/7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME_2024/batches/batch_000000_000030.json (origin=hf://datasets/DanielSc4/neurohike-traces@7bdb30ba9cacb93797f13d29867a5ab5a72c314f/AIME_2024/batches/batch_000000_000030.json), 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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)Need help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
input_text string | traces list | extracted_answers list | GT_answer int64 |
|---|---|---|---|
Find the sum of all integer bases $b>9$ for which $17_{b}$ is a divisor of $97_{b}$. | [
"<think>\nOkay, so I need to find the sum of all integer bases $ b > 9 $ for which $ 17_b $ is a divisor of $ 97_b $. Hmm, let me start by recalling how numbers are represented in different bases. \n\nFirst, $ 17_b $ means $ 1 \\times b + 7 $ in decimal, right? Similarly, $ 97_b $ would be $ 9 \\times b + 7 $. So, ... | [
"70",
"70",
"70",
"70",
"70",
"70",
"70",
"70",
"70",
"70",
"70",
"70",
"70",
"70",
"70"
] | 70 |
"On $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=(...TRUNCATED) | ["<think>\nOkay, let's try to tackle this geometry problem. It seems a bit complex with multiple poi(...TRUNCATED) | [
"588",
"588",
"588",
"",
"588",
"588",
"588",
"588",
"588",
"588",
"588",
"588",
"588",
"588",
"588"
] | 588 |
"The 9 members of a baseball team went to an ice cream parlor after their game. Each player had a si(...TRUNCATED) | ["<think>\nOkay, so I need to find the number of different assignments of flavors to players where t(...TRUNCATED) | [
"16",
"16",
"16",
"16",
"16",
"16",
"16",
"16",
"16",
"16",
"16",
"16",
"16",
"16",
"16"
] | 16 |
"Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $1(...TRUNCATED) | ["<think>\nOkay, so I need to find the number of ordered pairs (x, y) where both x and y are integer(...TRUNCATED) | [
"117",
"117",
"117",
"117",
"117",
"117",
"117",
"117",
"117",
"117",
"117",
"117",
"117",
"117",
"117"
] | 117 |
"There are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ ex(...TRUNCATED) | ["<think>\nOkay, so I need to find the number of eight-digit numbers using each digit from 1 to 8 ex(...TRUNCATED) | [
"279",
"279",
"",
"",
"279",
"279",
"",
"",
"135",
"279",
"279",
"279",
"279",
"279",
"279"
] | 279 |
"An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the(...TRUNCATED) | ["<think>\nOkay, so I need to find r² + s² for an isosceles trapezoid that has an inscribed circle(...TRUNCATED) | [
"504",
"504",
"504",
"504",
"504",
"504",
"504",
"504",
"504",
"504",
"504",
"504",
"504",
"504",
"504"
] | 504 |
"The twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters.(...TRUNCATED) | ["<think>\nOkay, so I need to find the probability that the last word listed contains the letter G. (...TRUNCATED) | [
"",
"271",
"",
"",
"",
"",
"239",
"",
"271",
"",
"",
"",
"41",
"271",
"271"
] | 821 |
"Let $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one (...TRUNCATED) | ["<think>\nOkay, let's tackle this problem step by step. The problem is about finding real numbers $(...TRUNCATED) | [
"77",
"77",
"77",
"77",
"77",
"77",
"46",
"77",
"77",
"77",
"77",
"",
"77",
"",
"77"
] | 77 |
"The parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin.(...TRUNCATED) | ["<think>\nOkay, so I need to figure out the coordinates of the intersection point between the origi(...TRUNCATED) | [
"",
"62",
"",
"",
"62",
"",
"",
"",
"",
"",
"62",
"",
"",
"",
""
] | 62 |
"The 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row con(...TRUNCATED) | ["<think>\nOkay, so I need to figure out the number of different ways to fill a 3x9 grid with number(...TRUNCATED) | [
"",
"",
"",
"80",
"",
"",
"",
"",
"",
"",
"",
"",
"",
"",
""
] | 81 |
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