Dataset Preview
The full dataset viewer is not available (click to read why). Only showing a preview of the rows.
The dataset generation failed
Error code: DatasetGenerationError
Exception: TypeError
Message: Couldn't cast array of type
struct<dataset: string, revision: string, repo: string, task: string, turn: int64, trajectory_id: string, dataset_license: string, repository_license: string, prefix_sha256: string, export_scope: string, domain: string, uuid: string, license: string>
to
{'dataset': Value('string'), 'revision': Value('string'), 'domain': Value('string'), 'uuid': Value('string'), 'license': Value('string'), 'prefix_sha256': Value('string')}
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1827, in _prepare_split_single
for key, table in generator:
^^^^^^^^^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 613, in wrapped
for item in generator(*args, **kwargs):
~~~~~~~~~^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 343, in _generate_tables
self._cast_table(pa_table, json_field_paths=json_field_paths),
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 132, in _cast_table
pa_table = table_cast(pa_table, self.info.features.arrow_schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2378, in table_cast
return cast_table_to_schema(table, schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2312, in cast_table_to_schema
cast_array_to_feature(
~~~~~~~~~~~~~~~~~~~~~^
table[name] if name in table_column_names else pa.array([None] * len(table), type=schema.field(name).type),
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
feature,
^^^^^^^^
)
^
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 1861, in wrapper
return pa.chunked_array([func(chunk, *args, **kwargs) for chunk in array.chunks])
~~~~^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2158, in cast_array_to_feature
raise TypeError(f"Couldn't cast array of type\n{_short_str(array.type)}\nto\n{_short_str(feature)}")
TypeError: Couldn't cast array of type
struct<dataset: string, revision: string, repo: string, task: string, turn: int64, trajectory_id: string, dataset_license: string, repository_license: string, prefix_sha256: string, export_scope: string, domain: string, uuid: string, license: string>
to
{'dataset': Value('string'), 'revision': Value('string'), 'domain': Value('string'), 'uuid': Value('string'), 'license': Value('string'), 'prefix_sha256': Value('string')}
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1369, in compute_config_parquet_and_info_response
parquet_operations, partial, estimated_dataset_info = stream_convert_to_parquet(
~~~~~~~~~~~~~~~~~~~~~~~~~^
builder, max_dataset_size_bytes=max_dataset_size_bytes
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
)
^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 948, in stream_convert_to_parquet
builder._prepare_split(split_generator=splits_generators[split], file_format="parquet")
~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1694, in _prepare_split
for job_id, done, content in self._prepare_split_single(
~~~~~~~~~~~~~~~~~~~~~~~~~~^
gen_kwargs=gen_kwargs, job_id=job_id, **_prepare_split_args
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
):
^
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1879, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
id string | messages list | target null | split string | provenance dict | prefix_tokens int64 | prefix_input_ids list | prefix_tokenizer_sha256 string |
|---|---|---|---|---|---|---|---|
nemotron-71ea4633b0ec4bc632bbc9dfe451edc176761bb606b4f205496832c5516d29fd | [
{
"role": "user",
"content": "In a regular quadrangular pyramid the lateral edge of length $m$ is inclined to the plane of the base at an angle $\\alpha $. Find the volume of the pyramid."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "fb215f9b-9372-4a08-875e-94184764ad51",
"license": "CC BY 4.0",
"prefix_sha256": "71ea4633b0ec4bc632bbc9dfe451edc176761bb606b4f205496832c5516d29fd"
} | 44 | [
2,
105,
2364,
107,
902,
496,
4841,
16176,
8725,
55428,
506,
21747,
7377,
529,
3861,
609,
236757,
236795,
563,
37105,
531,
506,
8180,
529,
506,
3225,
657,
614,
7275,
874,
2482,
20120,
9100,
506,
5542,
529,
506,
55428,
236761,
106,
107,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-084a24ce152dd0867a77cbe440e11f2beffeac3b56df18be796f43fa996e8067 | [
{
"role": "user",
"content": "Given a $5 \\times 2019$ grid where each square is painted either red or green, what is the largest $N$ such that there will always be two rows which have matching colors in at least $N$ columns?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "2d489ee9-8a25-4320-a3ad-80813e44bc49",
"license": "CC BY 4.0",
"prefix_sha256": "084a24ce152dd0867a77cbe440e11f2beffeac3b56df18be796f43fa996e8067"
} | 59 | [
2,
105,
2364,
107,
26479,
496,
609,
236810,
621,
3841,
236743,
236778,
236771,
236770,
236819,
236795,
8411,
1298,
1546,
6281,
563,
16715,
3477,
2604,
653,
3826,
236764,
1144,
563,
506,
7488,
609,
236797,
236795,
1288,
600,
993,
795,
2462,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-1155c27cf822000ea99c9a8f40d95f49c47f1778bd69b810116236386347a5ca | [
{
"role": "user",
"content": "A cuboid with a square base has a diagonal of length $d$ and a surface area of $b$. Calculate the sum of the lengths of all edges of the cuboid."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "b6f0bf25-3f08-455d-b7e4-d2960dc6e4d0",
"license": "CC BY 4.0",
"prefix_sha256": "1155c27cf822000ea99c9a8f40d95f49c47f1778bd69b810116236386347a5ca"
} | 46 | [
2,
105,
2364,
107,
236776,
11351,
1433,
607,
496,
6281,
3225,
815,
496,
22219,
529,
3861,
609,
236753,
236795,
532,
496,
3761,
2433,
529,
609,
236763,
2104,
22241,
506,
2324,
529,
506,
25565,
529,
784,
14453,
529,
506,
11351,
1433,
2367... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-721f6db64b8970542640f47f98213b9b9cfa5d7c2ffaae11188b13aa410173f3 | [
{
"role": "user",
"content": "Two teams worked together for 15 days. A third team then joined them as a result of which in 5 days the whole job was completed. The daily output of the second team is 20\\% higher than that of the first team. The second and third teams together could have fulfilled the whole j... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "a2471a2d-6dfa-4f20-a499-7c2a0416bd14",
"license": "CC BY 4.0",
"prefix_sha256": "721f6db64b8970542640f47f98213b9b9cfa5d7c2ffaae11188b13aa410173f3"
} | 120 | [
2,
105,
2364,
107,
11634,
7974,
5934,
3075,
573,
236743,
236770,
236810,
2668,
236761,
562,
4168,
2434,
1299,
10438,
1091,
618,
496,
1354,
529,
837,
528,
236743,
236810,
2668,
506,
3697,
3195,
691,
7723,
236761,
669,
6376,
3938,
529,
506,... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-9d81b307df0e072950ec767218b7d818d294f46bd3b965eaaf45cdb3bac7636d | [
{
"role": "user",
"content": "Suppose that $A$ is an $m \\times n$ matrix whose columns span $\\mathbb{R}^{m}$. Construct an $n \\times m$ matrix $D$ such that $AD = I_{m}$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "d8d1d1f2-d35d-4563-a9f3-cd0b63900ac7",
"license": "CC BY 4.0",
"prefix_sha256": "9d81b307df0e072950ec767218b7d818d294f46bd3b965eaaf45cdb3bac7636d"
} | 54 | [
2,
105,
2364,
107,
43916,
600,
609,
236776,
236795,
563,
614,
609,
236757,
621,
3841,
538,
236795,
6113,
5769,
11312,
15184,
874,
3603,
236782,
236794,
1244,
236757,
2532,
41719,
614,
609,
236749,
621,
3841,
520,
236795,
6113,
609,
236796,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-b58309d7c9ec9bc190e0b19f7cd0d893d522346eb1b564c00d579162644640bf | [
{
"role": "user",
"content": "A goods train left Moscow at \\( x \\) hours \\( y \\) minutes and arrived in Saratov at \\( y \\) hours \\( z \\) minutes. The journey took \\( z \\) hours \\( x \\) minutes. Find all possible values of \\( x \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "e6ee03b4-576f-49b3-b6e6-78d7d2cee442",
"license": "CC BY 4.0",
"prefix_sha256": "b58309d7c9ec9bc190e0b19f7cd0d893d522346eb1b564c00d579162644640bf"
} | 59 | [
2,
105,
2364,
107,
236776,
9061,
2519,
2378,
18749,
657,
33556,
1123,
160670,
3885,
33556,
570,
160670,
4310,
532,
12208,
528,
116535,
869,
657,
33556,
570,
160670,
3885,
33556,
904,
160670,
4310,
236761,
669,
9338,
3721,
33556,
904,
160670... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-1184ea5c8d0515035daa389423f14ec61bdeb65f779ab26889cc7e64022af58c | [
{
"role": "user",
"content": "What is the least total number of pens that can be distributed into 49 packages such that each package contains a different number of pens, and no package is left empty?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "bfa90f1b-54c1-4834-8343-d4b9275b1b6d",
"license": "CC BY 4.0",
"prefix_sha256": "1184ea5c8d0515035daa389423f14ec61bdeb65f779ab26889cc7e64022af58c"
} | 44 | [
2,
105,
2364,
107,
3689,
563,
506,
3198,
2558,
1548,
529,
11934,
600,
740,
577,
10861,
1131,
236743,
236812,
236819,
17489,
1288,
600,
1546,
8289,
6097,
496,
1607,
1548,
529,
11934,
236764,
532,
951,
8289,
563,
2378,
7738,
236881,
106,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-119a60df7b2acae4d0f2d8efa94bff40eb9cbef86c4f48a400cb196d054ca027 | [
{
"role": "user",
"content": "If there is a rectangular garden with an area of 250 square meters next to a building and fenced on three sides, with the building acting as the fourth fence, and if the side of the garden parallel to the building has length \\( x \\) meters, express the amount of fencing requi... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "2c9cf8b6-dabc-4dd6-b7db-b6a9f83edc1a",
"license": "CC BY 4.0",
"prefix_sha256": "119a60df7b2acae4d0f2d8efa94bff40eb9cbef86c4f48a400cb196d054ca027"
} | 76 | [
2,
105,
2364,
107,
2859,
993,
563,
496,
30777,
7972,
607,
614,
2433,
529,
236743,
236778,
236810,
236771,
6281,
15930,
2148,
531,
496,
3788,
532,
94210,
580,
1806,
9174,
236764,
607,
506,
3788,
13011,
618,
506,
10080,
22295,
236764,
532,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-215d76d297a10a6937ec7ade01015f2b2d66c525cccdbf80ac57d2ecc3ea4fc9 | [
{
"role": "user",
"content": "Find the set of points of affix \\( z \\) in the complex plane such that \\( |z-3| - |z+3| > 4 \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "604654f5-f91b-4bef-a3ec-37610e5450c4",
"license": "CC BY 4.0",
"prefix_sha256": "215d76d297a10a6937ec7ade01015f2b2d66c525cccdbf80ac57d2ecc3ea4fc9"
} | 42 | [
2,
105,
2364,
107,
11823,
506,
1076,
529,
3298,
529,
216081,
33556,
904,
160670,
528,
506,
3996,
8180,
1288,
600,
33556,
1109,
236802,
236772,
236800,
236909,
753,
1109,
236802,
236862,
236800,
236909,
1890,
236743,
236812,
621,
769,
106,
1... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-171a0d6959f8223181ef7445283da0d9c8648efbf4816ba45ce333083b541850 | [
{
"role": "user",
"content": "Find some positive integers $a$, $b$, and $c$ such that for any $n > 2$,\n$$b-\\frac{c}{(n-2)!} < \\frac{2^3-a}{2!}+\\frac{3^3-a}{3!}+...+\\frac{n^3-a}{n!}<b$$"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "4e12d56d-50f7-4c9b-a55f-1e54fe135c4e",
"license": "CC BY 4.0",
"prefix_sha256": "171a0d6959f8223181ef7445283da0d9c8648efbf4816ba45ce333083b541850"
} | 83 | [
2,
105,
2364,
107,
11823,
1070,
4414,
25630,
609,
236746,
2500,
609,
236763,
2500,
532,
609,
236755,
236795,
1288,
600,
573,
1027,
609,
236749,
1890,
236743,
236778,
2500,
107,
9873,
236763,
2242,
1420,
236782,
236755,
39495,
236749,
236772,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-f2c192e128a5c080ed64b3fcbbf75d867140bfb9c7f5f35e2acd71cca15ae0c9 | [
{
"role": "user",
"content": "Use the sum of the geometric series $1 - u + u^2 - u^3 + \\cdots + (-1)^{n-1} u^{n-1}$ to find an expression for the error in using the Maclaurin polynomial of degree $n$ as an approximation to $\\ln(1+x)$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "e3e16131-7316-41e7-8b20-90b93e809090",
"license": "CC BY 4.0",
"prefix_sha256": "f2c192e128a5c080ed64b3fcbbf75d867140bfb9c7f5f35e2acd71cca15ae0c9"
} | 75 | [
2,
105,
2364,
107,
10896,
506,
2324,
529,
506,
16085,
3605,
609,
236770,
753,
559,
900,
559,
236884,
236778,
753,
559,
236884,
236800,
900,
621,
8690,
900,
15554,
236770,
5625,
236749,
236772,
236770,
236783,
559,
790,
236749,
236772,
23677... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-e499cd9934ad5aec4f7aa54825b62ba1582ed285708b26e7e86c562112f6c13f | [
{
"role": "user",
"content": "How many ways can the 4 sides of a square be colored using two colors, considering the square can rotate?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "e7454223-75b6-4b1f-8c7d-50f03b6c3a43",
"license": "CC BY 4.0",
"prefix_sha256": "e499cd9934ad5aec4f7aa54825b62ba1582ed285708b26e7e86c562112f6c13f"
} | 32 | [
2,
105,
2364,
107,
3910,
1551,
4861,
740,
506,
236743,
236812,
9174,
529,
496,
6281,
577,
16128,
1699,
1156,
7913,
236764,
11337,
506,
6281,
740,
24036,
236881,
106,
107,
105,
4368,
107
] | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-13c6b2daa0279db4335dcd3a2356db5f7ef1ad5e3a46c7bce0db57ba6eb2757c | [
{
"role": "user",
"content": "Find the range of the function \\( f(x) = \\sqrt{\\sin\\left(\\log_{e}\\left(\\dfrac{x^2+e}{x^2+1}\\right)\\right)} + \\sqrt{\\cos\\left(\\log_{e}\\left(\\dfrac{x^2+e}{x^2+1}\\right)\\right)} \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "4e4b4345-0eec-406d-8677-d8d9da767f5a",
"license": "CC BY 4.0",
"prefix_sha256": "13c6b2daa0279db4335dcd3a2356db5f7ef1ad5e3a46c7bce0db57ba6eb2757c"
} | 86 | [
2,
105,
2364,
107,
11823,
506,
2644,
529,
506,
1292,
33556,
517,
236769,
236781,
236768,
578,
621,
4784,
1564,
5322,
236785,
989,
1314,
1587,
681,
236744,
958,
989,
1314,
12304,
236782,
236781,
236884,
236778,
236862,
236744,
1170,
236781,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-0d97dd971d0e6be9319eef6be43c4c772bad56a2bfaba64ddb3b752fc03c11d9 | [
{
"role": "user",
"content": "Find all functions \\( f: \\mathbb{Q} \\to \\mathbb{R} \\) such that for all \\( x, y \\in \\mathbb{Q} \\):\n\\[ f(x+y) - yf(x) - xf(y) = f(x)f(y) - x - y + xy, \\]\n\\[ f(x) = 2f(x+1) + 2 + x, \\]\nand\n\\[ f(1) + 1 > 0. \\]"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "cd420acf-d46d-4016-9058-4d036ef95210",
"license": "CC BY 4.0",
"prefix_sha256": "0d97dd971d0e6be9319eef6be43c4c772bad56a2bfaba64ddb3b752fc03c11d9"
} | 120 | [
2,
105,
2364,
107,
11823,
784,
5151,
33556,
517,
236787,
621,
3603,
236782,
236935,
236783,
621,
1071,
621,
3603,
236782,
236794,
236783,
160670,
1288,
600,
573,
784,
33556,
1123,
236764,
570,
621,
495,
621,
3603,
236782,
236935,
236783,
62... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-072d0dee72a1f55983eed967231d27916f5f0e774588928a02d55a027f5aa39b | [
{
"role": "user",
"content": "A syndicate has 12 members, one of whom is the president. A board of 4 positions needs to be formed from these members, with the condition that the president cannot be one of the board members. How many ways can this board be formed?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "9528edb9-1951-444f-be46-e418928df677",
"license": "CC BY 4.0",
"prefix_sha256": "072d0dee72a1f55983eed967231d27916f5f0e774588928a02d55a027f5aa39b"
} | 61 | [
2,
105,
2364,
107,
236776,
139970,
815,
236743,
236770,
236778,
3295,
236764,
886,
529,
8761,
563,
506,
6207,
236761,
562,
3905,
529,
236743,
236812,
10681,
3548,
531,
577,
8254,
699,
1239,
3295,
236764,
607,
506,
4194,
600,
506,
6207,
39... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-c467095297a0d3fcabecf01a2e0c290eeb07e92455c951d576343b85e4a3bdb1 | [
{
"role": "user",
"content": "Evaluate the integral\n\\[\n\\int_{3}^{6} \\left[ \\frac{\\int_{0}^{5} \\psi \\sum_{l=1}^{\\infty} \\left( \\frac{\\psi}{l^2} \\right)^l \\, d\\psi}{\\sum_{n=1}^{\\infty} \\frac{1}{n^2}} \\right] (\\omega^2 - 3\\omega + 5) \\, d\\omega,\n\\]\nwhere $[\\gamma]$ denotes the great... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "6af8d173-f77b-4b35-a6f8-c83eaeef6924",
"license": "CC BY 4.0",
"prefix_sha256": "c467095297a0d3fcabecf01a2e0c290eeb07e92455c951d576343b85e4a3bdb1"
} | 120 | [
2,
105,
2364,
107,
99009,
506,
11826,
107,
2318,
107,
236785,
720,
681,
236800,
1244,
236825,
236783,
621,
989,
236840,
621,
1420,
1564,
720,
681,
236771,
1244,
236810,
236783,
621,
7614,
621,
2330,
681,
236752,
236784,
236770,
3181,
5087,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-b1d45d5dfbf5d3607b614da6376cbffe2a836c3a65b06fd03aa65b02ce80acd1 | [
{
"role": "user",
"content": "Solve the equation $$1 +\\frac{1}{1 +\\frac{1}{1 +\\frac{1}{ \\begin{array}{ccc} 1+\\\\ & \\ddots\\\\ && 1+\\frac{1}{x} \\end{array}}}}=x$$ where in the expression on the left-hand side the sign of a fraction is repeated $n$ times."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "e5565271-ed92-46f8-b623-b3fa9546c4a3",
"license": "CC BY 4.0",
"prefix_sha256": "b1d45d5dfbf5d3607b614da6376cbffe2a836c3a65b06fd03aa65b02ce80acd1"
} | 86 | [
2,
105,
2364,
107,
76857,
506,
4901,
18666,
236770,
31010,
1420,
236782,
236770,
1170,
236770,
31010,
1420,
236782,
236770,
1170,
236770,
31010,
1420,
236782,
236770,
1170,
621,
1906,
236782,
2513,
1170,
6450,
236783,
236743,
236770,
3908,
2367... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-b9bb9ad0743911c2667f5f368815f5160069b82787de3885d36de1f987850381 | [
{
"role": "user",
"content": "Let $f(x) = x^2-3x$. For what values of $x$ is $f(f(x)) = f(x)$? Enter all the solutions, separated by commas."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "55fe5a30-496e-4216-a14e-cf07f210cd1e",
"license": "CC BY 4.0",
"prefix_sha256": "b9bb9ad0743911c2667f5f368815f5160069b82787de3885d36de1f987850381"
} | 54 | [
2,
105,
2364,
107,
6481,
609,
236760,
236769,
236781,
236768,
578,
1123,
236884,
236778,
236772,
236800,
236781,
2104,
1701,
1144,
2979,
529,
609,
236781,
236795,
563,
609,
236760,
236769,
236760,
236769,
236781,
1223,
578,
517,
236769,
236781,... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-a0369d8b027c45de45414edcde59c8151b03187778c45ce6f19aa7865b24fcb5 | [
{
"role": "user",
"content": "Let \\( x \\) and \\( y \\) be positive integers that are at least 2. Johnny hits 1 out of every 10 free throws, Abigail hits 1 out of every \\( x \\) free throws, and Demar hits 2 out of every \\( y \\) free throws. The mean of Abigail's and Demar's individual free throw perce... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "f46ba639-8f28-4ee7-9115-468eefb8fc7a",
"license": "CC BY 4.0",
"prefix_sha256": "a0369d8b027c45de45414edcde59c8151b03187778c45ce6f19aa7865b24fcb5"
} | 106 | [
2,
105,
2364,
107,
6481,
33556,
1123,
160670,
532,
33556,
570,
160670,
577,
4414,
25630,
600,
659,
657,
3198,
236743,
236778,
236761,
40156,
16737,
236743,
236770,
855,
529,
1418,
236743,
236770,
236771,
2196,
9160,
236764,
138482,
16737,
236... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-a09d1872663eb53a660b55ee87513cb785448fa9d782871ea84db1e0547f6b03 | [
{
"role": "user",
"content": "Find the smallest number which is the sum of 2002 numbers (not necessarily different) with the same sum of digits and also the sum of 2003 numbers with the same sum of digits."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "cffd7efe-8121-43b2-b03d-ed9d61c0774f",
"license": "CC BY 4.0",
"prefix_sha256": "a09d1872663eb53a660b55ee87513cb785448fa9d782871ea84db1e0547f6b03"
} | 53 | [
2,
105,
2364,
107,
11823,
506,
21548,
1548,
837,
563,
506,
2324,
529,
236743,
236778,
236771,
236771,
236778,
4945,
568,
2217,
12832,
1607,
236768,
607,
506,
1638,
2324,
529,
26798,
532,
992,
506,
2324,
529,
236743,
236778,
236771,
236771,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-e62427d112eeac1aec87736144b9bcb3bf26f4ef194fe282615f0b059d58391c | [
{
"role": "user",
"content": "Given the function \\( f(x) = \\sqrt{2x^2 - 2x + 1} - \\sqrt{2x^2 + 2x + 5} \\), find the range of values for \\( f(x) \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "0f5e86da-a364-429a-944b-4c7e7b338ba5",
"license": "CC BY 4.0",
"prefix_sha256": "e62427d112eeac1aec87736144b9bcb3bf26f4ef194fe282615f0b059d58391c"
} | 64 | [
2,
105,
2364,
107,
26479,
506,
1292,
33556,
517,
236769,
236781,
236768,
578,
621,
4784,
236782,
236778,
236781,
236884,
236778,
753,
236743,
236778,
236781,
900,
236743,
236770,
236783,
753,
621,
4784,
236782,
236778,
236781,
236884,
236778,
9... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-4a0c313257d564b4a603e1e8b37a4547b276a25e85f64ff695569f33471f5454 | [
{
"role": "user",
"content": "A fat muffin likes to eat jelly beans. He has an infinite amount of them. Every day he rolls 5 pairs of normal 6-sided dice. Each jelly bean weighs 5 pounds, and the muffin never loses weight. He starts weighing 5 pounds. After 10 days, what is the expected value of his weight ... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "971233ef-48d5-462a-a927-ccb081d469a9",
"license": "CC BY 4.0",
"prefix_sha256": "4a0c313257d564b4a603e1e8b37a4547b276a25e85f64ff695569f33471f5454"
} | 80 | [
2,
105,
2364,
107,
236776,
6477,
108675,
15975,
531,
9039,
51925,
21556,
236761,
1293,
815,
614,
18304,
2886,
529,
1091,
236761,
7685,
1719,
668,
28809,
236743,
236810,
14491,
529,
3867,
236743,
236825,
236772,
42794,
15713,
236761,
7714,
519... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-55e3c782a1aa0d50a4cb94107f153c52a240279a6d0b17dafe93ac31d978c284 | [
{
"role": "user",
"content": "In a metallic disk, a circular sector is removed so that the remaining part can form a conical glass of maximum volume. Calculate, in radians, the angle of the sector that is removed."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "149e139c-54b4-456b-ae3c-f1a51b77786f",
"license": "CC BY 4.0",
"prefix_sha256": "55e3c782a1aa0d50a4cb94107f153c52a240279a6d0b17dafe93ac31d978c284"
} | 47 | [
2,
105,
2364,
107,
902,
496,
26713,
13403,
236764,
496,
16971,
7095,
563,
8476,
834,
600,
506,
9866,
912,
740,
1183,
496,
91617,
4896,
529,
5783,
5542,
236761,
22241,
236764,
528,
78208,
236764,
506,
7275,
529,
506,
7095,
600,
563,
8476... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-5e745ca95dfff4381afa5dfc6b9e956af05dcbd34b44136e5a7f086f89120a70 | [
{
"role": "user",
"content": "Let \\( f \\) be the function defined on the set of positive integers by \\( f(1) = 1 \\), \\( f(2n+1) = f(2n) + 1 \\), and \\( f(2n) = 3f(n) \\). Determine how close to \\( 1991 \\) the value of \\( f(n) \\) can get."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "bee0d84e-633d-43db-b2f4-a45cc53dfe26",
"license": "CC BY 4.0",
"prefix_sha256": "5e745ca95dfff4381afa5dfc6b9e956af05dcbd34b44136e5a7f086f89120a70"
} | 92 | [
2,
105,
2364,
107,
6481,
33556,
517,
160670,
577,
506,
1292,
5221,
580,
506,
1076,
529,
4414,
25630,
684,
33556,
517,
236769,
236770,
236768,
578,
236743,
236770,
621,
779,
33556,
517,
236769,
236778,
236749,
236862,
236770,
236768,
578,
51... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-aac763faece4537f6f7f0eaec1b5325e630c8986bc4e7ad83fc4bb92b97bd660 | [
{
"role": "user",
"content": "For which values of the parameter $a$ are the systems of equations $$\\left\\{\\begin{array}{lll} \\sin (x+y)=0\\medskip \\\\ x^2+y^2=a \\end{array}\\right. \\mbox{and} \\left\\{\\begin{array}{lll} x+y=0\\medskip \\\\ x^2+y^2=a \\end{array}\\right.$$ equivalent?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "9dbcef79-28cc-44b3-905d-69c4ecb2a4c3",
"license": "CC BY 4.0",
"prefix_sha256": "aac763faece4537f6f7f0eaec1b5325e630c8986bc4e7ad83fc4bb92b97bd660"
} | 99 | [
2,
105,
2364,
107,
2542,
837,
2979,
529,
506,
7689,
609,
236746,
236795,
659,
506,
3797,
529,
8520,
49696,
989,
11801,
1906,
236782,
2513,
1170,
40145,
236783,
621,
5322,
568,
236781,
236862,
236762,
3483,
236771,
236785,
125505,
1704,
1123... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-62c88b03b6c9921dc3282178f81d7a500fb843faf1d2d41a29193334572d7fc5 | [
{
"role": "user",
"content": "Solve the given systems of equations: $\\left\\{\\begin{array}{lll} x+y=a\\medskip \\\\ x^4+y^4=a^4. \\end{array}\\right.$"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "319a9783-1db8-466d-a534-f16c2e7441aa",
"license": "CC BY 4.0",
"prefix_sha256": "62c88b03b6c9921dc3282178f81d7a500fb843faf1d2d41a29193334572d7fc5"
} | 52 | [
2,
105,
2364,
107,
76857,
506,
2238,
3797,
529,
8520,
236787,
874,
989,
11801,
1906,
236782,
2513,
1170,
40145,
236783,
1123,
236862,
236762,
236784,
236746,
236785,
125505,
1704,
1123,
236884,
236812,
236862,
236762,
236884,
236812,
236784,
23... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-31bfd20318a043699cd8abc98d8aebe091dd73e6044362fe332f758298e80655 | [
{
"role": "user",
"content": "The sum of three positive numbers $\\alpha ,\\beta ,\\gamma $ is equal to $\\pi /2$. Compute the product $\\cot \\alpha \\cot \\gamma $ if we know that $\\cot \\alpha $, $\\cot \\beta $, $\\cot \\gamma $ form an arithmetic progression."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "57d763b1-1da4-4185-9927-061829fc88a3",
"license": "CC BY 4.0",
"prefix_sha256": "31bfd20318a043699cd8abc98d8aebe091dd73e6044362fe332f758298e80655"
} | 66 | [
2,
105,
2364,
107,
818,
2324,
529,
1806,
4414,
4945,
874,
2482,
118676,
3357,
118676,
4223,
609,
563,
4745,
531,
874,
2160,
965,
236778,
2104,
42187,
506,
1698,
874,
24434,
621,
2482,
621,
24434,
621,
4223,
609,
768,
692,
1281,
600,
8... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-c85c5a9d4b1dd1ed49939299e38a94bd42536e06b02ad629311d08fa8840852c | [
{
"role": "user",
"content": "Let \\( n > 1 \\) be a positive integer. Find the number of binary strings \\((a_1, a_2, \\ldots, a_n)\\) such that the number of indices \\( 1 \\leq i \\leq n-1 \\) for which \\( a_i = a_{i+1} = 0 \\) is equal to the number of indices \\( 1 \\leq i \\leq n-1 \\) for which \\( ... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "a98fd6ed-200f-4a3c-8086-a62056652ba8",
"license": "CC BY 4.0",
"prefix_sha256": "c85c5a9d4b1dd1ed49939299e38a94bd42536e06b02ad629311d08fa8840852c"
} | 117 | [
2,
105,
2364,
107,
6481,
33556,
538,
1890,
236743,
236770,
160670,
577,
496,
4414,
11995,
236761,
9100,
506,
1548,
529,
14820,
16587,
621,
3283,
236746,
236779,
236770,
236764,
496,
236779,
236778,
236764,
621,
2989,
236764,
496,
236779,
2367... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-a3674526dfaabf75fbde92f692faf9e2dc0d959afb227ee6dfa4d04290ccf288 | [
{
"role": "user",
"content": "A circle $\\omega_1$ of radius $6\\sqrt{2}$ is internally tangent to a larger circle $\\omega_2$ of radius $12\\sqrt{2}$ such that the center of $\\omega_2$ lies on $\\omega_1$. A diameter $AB$ of $\\omega_2$ is drawn tangent to $\\omega_1$. A second line $\\ell$ is drawn from ... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "a403c63f-8283-40e8-a039-df814c4d0a4f",
"license": "CC BY 4.0",
"prefix_sha256": "a3674526dfaabf75fbde92f692faf9e2dc0d959afb227ee6dfa4d04290ccf288"
} | 133 | [
2,
105,
2364,
107,
236776,
10059,
874,
4445,
236779,
236770,
236795,
529,
12425,
609,
236825,
236785,
4784,
236782,
236778,
823,
563,
45205,
30954,
531,
496,
6268,
10059,
874,
4445,
236779,
236778,
236795,
529,
12425,
609,
236770,
236778,
236... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-c5e84c59fe3a1eec2a506ede46df06f566fe7f876aadffa33748140e8687a1a5 | [
{
"role": "user",
"content": "Alice, Bob, and Carol each think of an expression that is a fraction with 1 as the numerator and a constant integer times some power of \\( x \\) as the denominator. The simplest common denominator of Alice's and Bob's expressions is \\( 4x^2 \\). The simplest common denominato... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "ea9afbbd-09c4-4e4e-9304-4ed8f290ed6c",
"license": "CC BY 4.0",
"prefix_sha256": "c5e84c59fe3a1eec2a506ede46df06f566fe7f876aadffa33748140e8687a1a5"
} | 124 | [
2,
105,
2364,
107,
85305,
236764,
15943,
236764,
532,
10304,
1546,
1751,
529,
614,
5619,
600,
563,
496,
10742,
607,
236743,
236770,
618,
506,
43354,
532,
496,
4512,
11995,
2782,
1070,
2066,
529,
33556,
1123,
160670,
618,
506,
31637,
23676... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-9a48dfb8a6722656970d71cddc068331545ac8bee4a7b3740d33893139db6304 | [
{
"role": "user",
"content": "In a round-robin golf tournament, Simon beat Garfunkle in the first game. Garfunkle scored 8 total victories with no ties, while Simon scored exactly 8 points, including the point for a victory over Garfunkle. Every other player at the tournament scored exactly $n$ points. Find... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "48b86b69-1549-4e3e-a2ae-b41aa3e60647",
"license": "CC BY 4.0",
"prefix_sha256": "9a48dfb8a6722656970d71cddc068331545ac8bee4a7b3740d33893139db6304"
} | 82 | [
2,
105,
2364,
107,
902,
496,
4886,
236772,
141013,
15576,
18006,
236764,
20420,
12222,
10994,
110546,
519,
528,
506,
1171,
2290,
236761,
10994,
110546,
519,
15568,
236743,
236828,
2558,
58559,
607,
951,
23948,
236764,
1651,
20420,
15568,
7121... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-b33fc8f3114afcb261fc25df049e33958a9e68a2d6c47d35809cceadb2b42c9a | [
{
"role": "user",
"content": "Solve the differential equation $f'''(x) = f(x)$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "e1ad0640-62e7-4e1b-b635-edbba023bd6d",
"license": "CC BY 4.0",
"prefix_sha256": "b33fc8f3114afcb261fc25df049e33958a9e68a2d6c47d35809cceadb2b42c9a"
} | 24 | [
2,
105,
2364,
107,
76857,
506,
13992,
4901,
609,
236760,
26610,
236769,
236781,
236768,
578,
517,
236769,
236781,
4605,
106,
107,
105,
4368,
107
] | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-bab94521200c3ab3998cf96c990efb848a923f9765b34fa40b1d588548347a93 | [
{
"role": "user",
"content": "Compute the area of each of the three types of square-circle tiles: \"bloated squares,\" \"half diamonds,\" and \"arrowhead triangles,\" given that there are four \"bloated squares,\" eight \"half diamonds,\" and twelve \"arrowhead triangles\" in a circle with radius 1, and one... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "2eb6571a-e9d6-46fa-809f-a9a4dcc4d828",
"license": "CC BY 4.0",
"prefix_sha256": "bab94521200c3ab3998cf96c990efb848a923f9765b34fa40b1d588548347a93"
} | 97 | [
2,
105,
2364,
107,
55822,
506,
2433,
529,
1546,
529,
506,
1806,
4458,
529,
6281,
236772,
19045,
25583,
236787,
623,
16927,
774,
23441,
2098,
623,
19836,
41793,
2098,
532,
623,
2681,
2834,
38397,
2098,
2238,
600,
993,
659,
2390,
623,
169... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-c63d16c6019f556d22400f31f51bd01f0af937c2fc47dd15da0cccb6e49b56b3 | [
{
"role": "user",
"content": "Solve the equation \\(4(a+b+c) + 2(ab+bc+ac) + abc = 33033\\) where \\(a\\), \\(b\\), and \\(c\\) are natural integers."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "6e7ddd3e-b3fb-45ef-b740-f69d5e1fda79",
"license": "CC BY 4.0",
"prefix_sha256": "c63d16c6019f556d22400f31f51bd01f0af937c2fc47dd15da0cccb6e49b56b3"
} | 58 | [
2,
105,
2364,
107,
76857,
506,
4901,
33556,
236812,
236769,
236746,
236862,
236763,
236862,
236755,
236768,
900,
236743,
236778,
236769,
596,
236862,
17027,
236862,
552,
236768,
900,
13334,
578,
236743,
236800,
236800,
236771,
236800,
236800,
689... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-286f235187d5c4a0a3e98a8d6b976886fcd09de368205eb03ffeaf6fc738e3af | [
{
"role": "user",
"content": "Solve the system of equations:\n\\[\n\\left\\{\\begin{matrix}\nx^2 + \\sqrt[3]{y^2+1}=\\sqrt{y^2+9}+5\\\\ \ny^2 + \\sqrt[3]{z^2+1}=\\sqrt{z^2+9}+5\\\\\nz^2 + \\sqrt[3]{x^2+1}=\\sqrt{x^2+9}+5\n\\end{matrix}\\right.\n\\]"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "fb36b38e-3f82-4ffa-90f3-85d2f76f85e0",
"license": "CC BY 4.0",
"prefix_sha256": "286f235187d5c4a0a3e98a8d6b976886fcd09de368205eb03ffeaf6fc738e3af"
} | 113 | [
2,
105,
2364,
107,
76857,
506,
1458,
529,
8520,
236787,
107,
2318,
107,
236785,
989,
11801,
1906,
236782,
10098,
236783,
107,
236781,
236884,
236778,
900,
621,
4784,
236840,
236800,
5546,
236762,
236884,
236778,
236862,
236770,
3450,
4784,
23... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-e7d1ce750906e78c237c0dcd87f4ef4ffcf099991949ee43eb8b3f0786f233f9 | [
{
"role": "user",
"content": "Find the value of $\\text{Arg}(i \\ln((a-ib)/(a+ib)))$ where $a$ and $b$ are real numbers."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "0ac9efbf-6365-487b-92e3-e59d8f7d7295",
"license": "CC BY 4.0",
"prefix_sha256": "e7d1ce750906e78c237c0dcd87f4ef4ffcf099991949ee43eb8b3f0786f233f9"
} | 43 | [
2,
105,
2364,
107,
11823,
506,
1550,
529,
874,
1005,
236782,
11694,
2014,
236747,
621,
3269,
3283,
236746,
236772,
748,
38555,
236746,
236862,
748,
1223,
1370,
1298,
609,
236746,
236795,
532,
609,
236763,
236795,
659,
1759,
4945,
236761,
10... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-e207067dffd691943a49688214c8b1ad2aa2ddb25b3384b90b9de00f01688b64 | [
{
"role": "user",
"content": "Simplify the given expressions: $\\left(b^\\frac{\\log _{100}a}{\\log a}\\cdot a^\\frac{\\log _{100}b}{\\sin b}\\right)^{2\\log _{ab}(a+b)}$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "29a4c747-deef-44c3-8841-9e2e5df1d513",
"license": "CC BY 4.0",
"prefix_sha256": "e207067dffd691943a49688214c8b1ad2aa2ddb25b3384b90b9de00f01688b64"
} | 60 | [
2,
105,
2364,
107,
148828,
506,
2238,
19094,
236787,
874,
989,
236769,
236763,
11909,
1420,
1564,
1587,
13436,
236770,
236771,
236771,
236783,
236746,
3378,
1587,
496,
958,
4172,
496,
11909,
1420,
1564,
1587,
13436,
236770,
236771,
236771,
23... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-b2bed37692b6362555a034b8cbd292eaff07627f8792ef1c62ba6d0acd8a8159 | [
{
"role": "user",
"content": "Solve the equation $(ax-b)^2 + (bx-a)^2 = x$ for integers $a$ and $b$, given that one root of the equation is an integer."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "4f07a7ac-4faf-45d9-b9f6-f9684a98c90f",
"license": "CC BY 4.0",
"prefix_sha256": "b2bed37692b6362555a034b8cbd292eaff07627f8792ef1c62ba6d0acd8a8159"
} | 48 | [
2,
105,
2364,
107,
76857,
506,
4901,
3498,
1124,
236772,
236763,
13365,
236778,
900,
568,
45576,
236772,
236746,
13365,
236778,
578,
1123,
236795,
573,
25630,
609,
236746,
236795,
532,
609,
236763,
2500,
2238,
600,
886,
5989,
529,
506,
4901... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-a36dd022609b99e282bc1c2e44e31a473ba4735b5db9389a5aa43cc9b505d2da | [
{
"role": "user",
"content": "Let \\( f(x) = x^n + 2x^{n-1} + 3x^{n-2} + \\ldots + nx + n + 1 \\) where \\( n \\in \\mathbb{N}^* \\) and \\( \\varepsilon = \\cos\\frac{2\\pi}{n+2} + i\\sin\\frac{2\\pi}{n+2} \\). Evaluate \\( \\prod_{k=1}^{n+1} f(\\varepsilon^k) \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "30bf4b51-0450-46ff-9467-0327061eb857",
"license": "CC BY 4.0",
"prefix_sha256": "a36dd022609b99e282bc1c2e44e31a473ba4735b5db9389a5aa43cc9b505d2da"
} | 115 | [
2,
105,
2364,
107,
6481,
33556,
517,
236769,
236781,
236768,
578,
1123,
236884,
236749,
900,
236743,
236778,
236781,
790,
236749,
236772,
236770,
236783,
900,
236743,
236800,
236781,
790,
236749,
236772,
236778,
236783,
900,
621,
2989,
900,
536... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-08255ebf6a8db4db1af8d8a2dc38ea4f33ecfe28705856f30436a9f6add23ba0 | [
{
"role": "user",
"content": "A clock has a $10\\text{cm}$ long minute hand and a $5\\text{cm}$ long hour hand. How fast is the distance between the end of the minute hand and the end of the hour hand changing (in $\\frac{\\text{cm}}{\\text{hr}}$) at $3\\text{ o'clock}$?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "c9c74d08-50a5-4c68-9d07-36c260345e0b",
"license": "CC BY 4.0",
"prefix_sha256": "08255ebf6a8db4db1af8d8a2dc38ea4f33ecfe28705856f30436a9f6add23ba0"
} | 82 | [
2,
105,
2364,
107,
236776,
11072,
815,
496,
609,
236770,
236771,
236785,
1005,
236782,
3696,
823,
1440,
9641,
1526,
532,
496,
609,
236810,
236785,
1005,
236782,
3696,
823,
1440,
6468,
1526,
236761,
2088,
4592,
563,
506,
5149,
1534,
506,
1... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-131ffa866198f83230f3553c277ab2fcddc1e24d2737207410cdf91e685bd219 | [
{
"role": "user",
"content": "What is the sum of all the numbers that can be obtained by rearranging the digits of $2016$?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "2d88b800-d526-46e5-bd87-170a2727cb89",
"license": "CC BY 4.0",
"prefix_sha256": "131ffa866198f83230f3553c277ab2fcddc1e24d2737207410cdf91e685bd219"
} | 32 | [
2,
105,
2364,
107,
3689,
563,
506,
2324,
529,
784,
506,
4945,
600,
740,
577,
4597,
684,
170205,
506,
26798,
529,
609,
236778,
236771,
236770,
236825,
223680,
106,
107,
105,
4368,
107
] | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-e7faf2d686bdffb4fbcfe177136a916b38b06565bfd3feb8fe0174a0d848ad81 | [
{
"role": "user",
"content": "Express $\\displaystyle\\sum_{r=1}^{n}\\ \\frac{r^2+r-1}{(r+2)!}$ in terms of $n$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "0ca4b3b8-1f95-4434-ae8e-b62ee0c1c270",
"license": "CC BY 4.0",
"prefix_sha256": "e7faf2d686bdffb4fbcfe177136a916b38b06565bfd3feb8fe0174a0d848ad81"
} | 43 | [
2,
105,
2364,
107,
28396,
874,
12131,
236785,
2330,
681,
236750,
236784,
236770,
1244,
236749,
958,
621,
1420,
236782,
236750,
236884,
236778,
236862,
236750,
236772,
236770,
39495,
236750,
236862,
236778,
47473,
823,
528,
3755,
529,
609,
23674... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-ae5fd89d040106520b7b799d1f983c77810416806285a13d931856fd4fd1ed33 | [
{
"role": "user",
"content": "Given that \\( af(\\tan x) + bf(\\cot x) = x \\), find \\( \\frac{d}{dx}(f(\\cot x)) \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "0b850ef3-6d9f-4e5b-a33e-227b70c7592b",
"license": "CC BY 4.0",
"prefix_sha256": "ae5fd89d040106520b7b799d1f983c77810416806285a13d931856fd4fd1ed33"
} | 43 | [
2,
105,
2364,
107,
26479,
600,
33556,
4549,
1314,
13257,
1123,
236768,
900,
96504,
1314,
24434,
1123,
236768,
578,
1123,
621,
779,
1586,
33556,
621,
1420,
236782,
236753,
1170,
12275,
2014,
236760,
1314,
24434,
1123,
1223,
621,
769,
106,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-73b44ef64540365ab616878dd626f0285d0d83377c1e24e1cad557916ae9f352 | [
{
"role": "user",
"content": "For what values of \\( n \\in \\mathbb{Z} \\) is \\( K_n = n^2 + 20n + 12 \\) a perfect square?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "f67a7b29-0592-4522-ac39-46e120f2d118",
"license": "CC BY 4.0",
"prefix_sha256": "73b44ef64540365ab616878dd626f0285d0d83377c1e24e1cad557916ae9f352"
} | 46 | [
2,
105,
2364,
107,
2542,
1144,
2979,
529,
33556,
538,
621,
495,
621,
3603,
236782,
236953,
236783,
160670,
563,
33556,
751,
236779,
236749,
578,
538,
236884,
236778,
900,
236743,
236778,
236771,
236749,
900,
236743,
236770,
236778,
160670,
49... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-77ab52e375f552bb4ec4e456ed645a9d4b34e3b9928adb2db6868f6a8565ba40 | [
{
"role": "user",
"content": "Find the coordinates for the vertices of a lattice rectangle (with vertices on lattice points) whose long-side length is triple its short-side length, and none of whose sides is parallel to the horizontal axis."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "2eabb953-d8d0-4b24-9e07-2557e0439b25",
"license": "CC BY 4.0",
"prefix_sha256": "77ab52e375f552bb4ec4e456ed645a9d4b34e3b9928adb2db6868f6a8565ba40"
} | 51 | [
2,
105,
2364,
107,
11823,
506,
15375,
573,
506,
20078,
529,
496,
18928,
32891,
568,
4060,
20078,
580,
18928,
3298,
236768,
5769,
1440,
236772,
2897,
3861,
563,
22178,
1061,
2822,
236772,
2897,
3861,
236764,
532,
7293,
529,
5769,
9174,
563... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-7122a640f275b82bfe44f47ac9822db70a39667641670f4ce9409032ccd9caef | [
{
"role": "user",
"content": "Find \\( \\lim_{x \\rightarrow \\frac{\\pi}{4}} \\frac{\\tan x - 1}{x - \\frac{\\pi}{4}} \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "2dc9e4b3-ce19-41dc-8512-09125f601e15",
"license": "CC BY 4.0",
"prefix_sha256": "7122a640f275b82bfe44f47ac9822db70a39667641670f4ce9409032ccd9caef"
} | 44 | [
2,
105,
2364,
107,
11823,
33556,
621,
3824,
681,
236781,
621,
4063,
621,
1420,
1564,
2160,
1170,
236812,
1807,
621,
1420,
1564,
13257,
1123,
753,
236743,
236770,
1170,
236781,
753,
621,
1420,
1564,
2160,
1170,
236812,
1807,
621,
769,
106,... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-fa7a407f3dc750d3404189499a011a7efa3fb7eb53933e459fe5d81e6e7c3d42 | [
{
"role": "user",
"content": "How many 4-digit numbers have exactly 2 identical and adjacent digits, similar to the number 2009?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "e48883d1-047b-46a1-9fa9-f1ae1926aa5a",
"license": "CC BY 4.0",
"prefix_sha256": "fa7a407f3dc750d3404189499a011a7efa3fb7eb53933e459fe5d81e6e7c3d42"
} | 35 | [
2,
105,
2364,
107,
3910,
1551,
236743,
236812,
236772,
29345,
4945,
735,
7121,
236743,
236778,
15779,
532,
18191,
26798,
236764,
3361,
531,
506,
1548,
236743,
236778,
236771,
236771,
236819,
236881,
106,
107,
105,
4368,
107
] | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-5b250289acaf615ce03a8e1346726ed37413ed2ebb3e9e917e22fce3435e4ad3 | [
{
"role": "user",
"content": "In a triangle \\(ABC\\), let \\(K\\) be a point on \\(AC\\) such that \\(AK = 16\\) and \\(KC = 20\\). Let \\(D\\) be the foot of the angle bisector through \\(A\\), and let \\(E\\) be the point of intersection of \\(AD\\) with \\(BK\\). If \\(BD = BE = 12\\), find the perimete... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "9050cdc3-75c8-4b69-8952-2a7677cc5263",
"license": "CC BY 4.0",
"prefix_sha256": "5b250289acaf615ce03a8e1346726ed37413ed2ebb3e9e917e22fce3435e4ad3"
} | 101 | [
2,
105,
2364,
107,
902,
496,
17852,
33556,
31348,
236785,
779,
1531,
33556,
236855,
68966,
577,
496,
1523,
580,
33556,
2714,
68966,
1288,
600,
33556,
9978,
578,
236743,
236770,
236825,
68966,
532,
33556,
119547,
578,
236743,
236778,
236771,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-73b42ec442065c7a9dcb9feeb1074f733cfc9f84367d2711e3aa2248fa49591c | [
{
"role": "user",
"content": "In a game, a participant chooses a nine-digit positive integer $\\overline{ABCDEFGHI}$ with distinct non-zero digits. The score of the participant is $A^{B^{C^{D^{E^{F^{G^{H^{I}}}}}}}}$. Which nine-digit number should be chosen in order to maximize the score?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "e236254f-592f-4a0f-be83-51da3b1e6ddc",
"license": "CC BY 4.0",
"prefix_sha256": "73b42ec442065c7a9dcb9feeb1074f733cfc9f84367d2711e3aa2248fa49591c"
} | 77 | [
2,
105,
2364,
107,
902,
496,
2290,
236764,
496,
32571,
46251,
496,
10155,
236772,
29345,
4414,
11995,
874,
10665,
236782,
31348,
157324,
823,
607,
9245,
1908,
236772,
13321,
26798,
236761,
669,
6317,
529,
506,
32571,
563,
609,
236776,
790,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-8e218f776ded9472f47ed116d0cf53ee4a2a2ac89428b1466daacf57fa08a91d | [
{
"role": "user",
"content": "Solve the following equations. $7\\cdot 4^{x^2}-9\\cdot 14^{x^2}+2\\cdot 49^{x^2}=0$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "c13e68bd-7065-411f-bc96-0e8c141c7a9e",
"license": "CC BY 4.0",
"prefix_sha256": "8e218f776ded9472f47ed116d0cf53ee4a2a2ac89428b1466daacf57fa08a91d"
} | 49 | [
2,
105,
2364,
107,
76857,
506,
2269,
8520,
236761,
609,
236832,
236785,
4172,
236743,
236812,
790,
236781,
236884,
236778,
3807,
236819,
236785,
4172,
236743,
236770,
236812,
790,
236781,
236884,
236778,
2666,
236778,
236785,
4172,
236743,
236812... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-8199364767f0598655c82b7c6988462362dd5657f1431b6b0c6f46bc1c97eb41 | [
{
"role": "user",
"content": "Given a fixed segment \\( BC \\) and a variable point \\( A \\), consider the diameter of the circumcircle of triangle \\( ABC \\) that is parallel to \\( \\overline{BC} \\). Reflect \\( A \\) over this diameter to get \\( A' \\). Find the locus of points \\( A \\) such that th... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "014a01fc-243c-4e54-9342-d0b0934e8457",
"license": "CC BY 4.0",
"prefix_sha256": "8199364767f0598655c82b7c6988462362dd5657f1431b6b0c6f46bc1c97eb41"
} | 95 | [
2,
105,
2364,
107,
26479,
496,
6530,
9951,
33556,
19339,
160670,
532,
496,
6471,
1523,
33556,
562,
621,
779,
1966,
506,
13634,
529,
506,
8010,
19045,
529,
17852,
33556,
21593,
160670,
600,
563,
10616,
531,
33556,
621,
10665,
236782,
5901,... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-5bde25ba3a2f1c713be210b605275111f6dd922b8e8daa2ccbc5a847cc3fb6cb | [
{
"role": "user",
"content": "Let \\(a, b, c > 0\\) such that \\(abc = 1\\). Find the best constant \\(k\\) so that the following inequality holds for all \\(a, b, c\\):\n\\[\n\\frac{1}{(a^k+1)(b+c)} + \\frac{1}{(b^k+1)(c+a)} + \\frac{1}{(c^k+1)(a+b)} \\le \\frac{3}{4}\n\\]"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "6b9d9b1d-c28c-4d1a-8642-bcc3603d5d81",
"license": "CC BY 4.0",
"prefix_sha256": "5bde25ba3a2f1c713be210b605275111f6dd922b8e8daa2ccbc5a847cc3fb6cb"
} | 113 | [
2,
105,
2364,
107,
6481,
33556,
236746,
236764,
518,
236764,
505,
1890,
236743,
236771,
68966,
1288,
600,
33556,
28180,
578,
236743,
236770,
236785,
769,
9100,
506,
1791,
4512,
33556,
236767,
68966,
834,
600,
506,
2269,
18292,
9258,
573,
78... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-77209e565f55aca337927507da0ba4a6f98be8b990a72b09e44d9caf25f8c225 | [
{
"role": "user",
"content": "A furniture company has warehouses at Albany, Buffalo, Montreal, and Toronto. Deliveries need to be made to Kingston, Rochester, and Syracuse. Each warehouse has one truck which can visit at most one city in a day. The constraints are:\n(i) The Albany warehouse does not serve K... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "59b637c4-80ce-40c2-8361-bf348eece3fa",
"license": "CC BY 4.0",
"prefix_sha256": "77209e565f55aca337927507da0ba4a6f98be8b990a72b09e44d9caf25f8c225"
} | 137 | [
2,
105,
2364,
107,
236776,
15795,
2544,
815,
82070,
657,
61773,
236764,
37686,
236764,
34483,
236764,
532,
20422,
236761,
67023,
695,
1202,
531,
577,
1603,
531,
63242,
236764,
57778,
236764,
532,
74925,
236761,
7714,
31882,
815,
886,
9685,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-6eaa0ae082ab8c6f7a446fa2e49d983756616ea2cd62032eef4ee5f256bd82da | [
{
"role": "user",
"content": "From the numbers 1, 3, 5, 6, 8, 9, how many three-digit odd numbers greater than 200 can be formed using three different numbers?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "9244c758-625f-4527-b988-e90d8dbcfc91",
"license": "CC BY 4.0",
"prefix_sha256": "6eaa0ae082ab8c6f7a446fa2e49d983756616ea2cd62032eef4ee5f256bd82da"
} | 51 | [
2,
105,
2364,
107,
4663,
506,
4945,
236743,
236770,
236764,
236743,
236800,
236764,
236743,
236810,
236764,
236743,
236825,
236764,
236743,
236828,
236764,
236743,
236819,
236764,
1217,
1551,
1806,
236772,
29345,
11049,
4945,
5314,
1082,
236743,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-19dbaa8f49f7936565f9969a03b33246abb999d1fe88e98ecc0e902187a9a838 | [
{
"role": "user",
"content": "Let \\( (a,b,c) \\in \\mathbb{Z}^3 \\) and define \\( f(a,b,c) = (a+b+c, ab+bc+ca, abc) \\). Find all integer triples \\( (a,b,c) \\) such that \\( f(f(a,b,c)) = (a,b,c) \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "6e73ba4c-0ac4-4bad-9f60-d4b18b191523",
"license": "CC BY 4.0",
"prefix_sha256": "19dbaa8f49f7936565f9969a03b33246abb999d1fe88e98ecc0e902187a9a838"
} | 92 | [
2,
105,
2364,
107,
6481,
33556,
568,
236746,
236764,
236763,
236764,
236755,
236768,
621,
495,
621,
3603,
236782,
236953,
9914,
236800,
160670,
532,
8540,
33556,
517,
236769,
236746,
236764,
236763,
236764,
236755,
236768,
578,
568,
236746,
236... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-46fb8df37edc4da53cc50857d09032e71213f1a7a37fc1b6dcd6f95c07b356d2 | [
{
"role": "user",
"content": "Find the smallest integer \\( n \\) such that for any set \\( A \\) with \\( \\text{card}(A) = n \\), there exist elements \\( a_1, a_2, \\ldots, a_{15} \\) in \\( A \\) such that \\( a_1 + a_2 + \\cdots + a_{15} \\) is divisible by 15."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "c8fd75be-f5b7-40fc-936a-a6b9dec0301c",
"license": "CC BY 4.0",
"prefix_sha256": "46fb8df37edc4da53cc50857d09032e71213f1a7a37fc1b6dcd6f95c07b356d2"
} | 89 | [
2,
105,
2364,
107,
11823,
506,
21548,
11995,
33556,
538,
160670,
1288,
600,
573,
1027,
1076,
33556,
562,
160670,
607,
33556,
621,
1005,
236782,
6307,
2014,
236776,
236768,
578,
538,
621,
779,
993,
2849,
4820,
33556,
496,
236779,
236770,
2... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-56acb7dd8b1abeda7490fba923138f629734689dbd5ee14a57828c3a5db6024e | [
{
"role": "user",
"content": "How many pairs of 3-digit numbers \\( p \\) and \\( q \\) satisfy the condition \\(\\frac{p+1}{q+3} \\leq \\frac{1}{2}\\) where \\(\\frac{p}{q}\\) is a proper fraction?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "7da1d27f-dbd4-444a-8c27-5115841f5a79",
"license": "CC BY 4.0",
"prefix_sha256": "56acb7dd8b1abeda7490fba923138f629734689dbd5ee14a57828c3a5db6024e"
} | 65 | [
2,
105,
2364,
107,
3910,
1551,
14491,
529,
236743,
236800,
236772,
29345,
4945,
33556,
510,
160670,
532,
33556,
3752,
160670,
16529,
506,
4194,
621,
1314,
1420,
236782,
236758,
236862,
236770,
1170,
236809,
236862,
236800,
236783,
621,
4131,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-2de8fa5bad76fd576cd69f3d9a1593f89c88d696919b2d03f9c0841789b81f8c | [
{
"role": "user",
"content": "Given \\( n \\in \\mathbb{N}^* \\) and \\( x \\in \\mathbb{N}^* \\), find the maximum value of \\( \\min\\{nx, \\frac{1}{\\sin{\\frac{x}{2}}}\\} \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "51163390-041e-4146-8d7d-7ea689e3a892",
"license": "CC BY 4.0",
"prefix_sha256": "2de8fa5bad76fd576cd69f3d9a1593f89c88d696919b2d03f9c0841789b81f8c"
} | 59 | [
2,
105,
2364,
107,
26479,
33556,
538,
621,
495,
621,
3603,
236782,
236797,
73891,
160670,
532,
33556,
1123,
621,
495,
621,
3603,
236782,
236797,
73891,
621,
779,
1586,
506,
5783,
1550,
529,
33556,
621,
1387,
7228,
35133,
236764,
621,
1420... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-0ee3fc8bffe1bfb31215cd05c284db4b37ef575553c3e6d549899c8d0234c8ec | [
{
"role": "user",
"content": "The polynomial \\( P(x) = x^3 + ax^2 + bx + c \\) has the property that the mean of its zeros, the product of its zeros, and the sum of its coefficients are all equal. If the \\( y \\)-intercept of the graph of \\( y = P(x) \\) is 2, then what is \\( b \\)?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "f75a1658-280b-46a8-8175-61385a301bc1",
"license": "CC BY 4.0",
"prefix_sha256": "0ee3fc8bffe1bfb31215cd05c284db4b37ef575553c3e6d549899c8d0234c8ec"
} | 85 | [
2,
105,
2364,
107,
818,
14337,
33556,
593,
236769,
236781,
236768,
578,
1123,
236884,
236800,
900,
4385,
236884,
236778,
900,
65992,
900,
505,
160670,
815,
506,
3670,
600,
506,
2689,
529,
1061,
36509,
236764,
506,
1698,
529,
1061,
36509,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-261b066f47ce6db6da927db769dce91f0a7cdba57186914c74d4aaa5fb791c0b | [
{
"role": "user",
"content": "Let $A$ denote the set of all integers $n$ such that $1 \\leq n \\leq 10000$, and the sum of the decimal digits of $n$ is 2. Find the sum of the squares of the elements of $A$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "15380bca-2881-486a-b58d-eb317aebf253",
"license": "CC BY 4.0",
"prefix_sha256": "261b066f47ce6db6da927db769dce91f0a7cdba57186914c74d4aaa5fb791c0b"
} | 66 | [
2,
105,
2364,
107,
6481,
609,
236776,
236795,
16451,
506,
1076,
529,
784,
25630,
609,
236749,
236795,
1288,
600,
609,
236770,
621,
4131,
538,
621,
4131,
236743,
236770,
236771,
236771,
236771,
236771,
2500,
532,
506,
2324,
529,
506,
20632,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-b63da8df2410b4ae36e0f75a3752f8d512bc64f8b3e8b857d396222ec231fef2 | [
{
"role": "user",
"content": "Evaluate the integral \\(\\int_{1}^{e} \\frac{\\ln x}{x (\\sqrt{1 - \\ln x} + \\sqrt{\\ln x + 1})} \\, dx\\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "f017dae8-73e0-4e7d-86e6-286962dd5c29",
"license": "CC BY 4.0",
"prefix_sha256": "b63da8df2410b4ae36e0f75a3752f8d512bc64f8b3e8b857d396222ec231fef2"
} | 50 | [
2,
105,
2364,
107,
99009,
506,
11826,
621,
1314,
720,
681,
236770,
1244,
236744,
236783,
621,
1420,
1564,
3269,
1123,
1170,
236781,
8718,
4784,
236782,
236770,
753,
621,
3269,
1123,
236783,
900,
621,
4784,
1564,
3269,
1123,
900,
236743,
2... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-58edbd6f408d0883046cc3417575809110b977599c07ed578aae43a6a9982cde | [
{
"role": "user",
"content": "In a right-angle triangle with sides \\( b \\) and \\( c \\) (\\( b > c \\)), the bisector of the right angle is drawn. Find the distance between the orthocenters of the two triangles formed by this bisector."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "9efc42d8-afb0-4ecf-a463-7ad0e3bff7d9",
"license": "CC BY 4.0",
"prefix_sha256": "58edbd6f408d0883046cc3417575809110b977599c07ed578aae43a6a9982cde"
} | 59 | [
2,
105,
2364,
107,
902,
496,
1447,
236772,
2925,
17852,
607,
9174,
33556,
518,
160670,
532,
33556,
505,
160670,
8718,
236769,
518,
1890,
505,
621,
8914,
506,
8668,
4363,
529,
506,
1447,
7275,
563,
9710,
236761,
9100,
506,
5149,
1534,
50... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-a5c131a023cc34c9e98debd504044c6f22607974384e23ac3cc8bd2b0e57ec1e | [
{
"role": "user",
"content": "Calculate the integral $\\int_{\\frac{1}{2}}^{2}\\frac{\\tan^{-1}x}{x^{2}-x+1}dx$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "172bcb9a-5f42-4bd5-bebe-b43de28d58d9",
"license": "CC BY 4.0",
"prefix_sha256": "a5c131a023cc34c9e98debd504044c6f22607974384e23ac3cc8bd2b0e57ec1e"
} | 41 | [
2,
105,
2364,
107,
50702,
506,
11826,
874,
720,
1738,
1420,
236782,
236770,
1170,
236778,
11176,
236778,
958,
1420,
1564,
13257,
3903,
236770,
236783,
236781,
1170,
236781,
790,
236778,
3807,
236781,
236862,
236770,
236783,
12275,
2104,
106,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-f1ab19d00f62a640c134a90c088ebb6be4401f773961415b5278a6cd7a18390a | [
{
"role": "user",
"content": "Let \\(a, b, c, x, y, z\\) be real numbers such that \\(xyz \\neq 0\\) and \\(a = \\frac{by}{z} + \\frac{cz}{y}\\), \\(b = \\frac{cz}{x} + \\frac{ax}{z}\\), \\(c = \\frac{ax}{y} + \\frac{by}{x}\\). Find the value of \\(a^3 + b^3 + c^3\\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "c7703436-afcc-4484-87bf-ab2242a05bc8",
"license": "CC BY 4.0",
"prefix_sha256": "f1ab19d00f62a640c134a90c088ebb6be4401f773961415b5278a6cd7a18390a"
} | 111 | [
2,
105,
2364,
107,
6481,
33556,
236746,
236764,
518,
236764,
505,
236764,
1123,
236764,
570,
236764,
904,
68966,
577,
1759,
4945,
1288,
600,
33556,
56660,
621,
11547,
236743,
236771,
68966,
532,
33556,
236746,
578,
621,
1420,
236782,
2003,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-cddccbde43b74b1a744c494438b0d76d194a71864120e1e486ba988c5448401e | [
{
"role": "user",
"content": "Find the sum of the interior angles for a complex polygon with Schlafli symbol $\\{ 9/3 \\}$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "20b5e82d-0ef0-4272-aa69-2fa448e89da3",
"license": "CC BY 4.0",
"prefix_sha256": "cddccbde43b74b1a744c494438b0d76d194a71864120e1e486ba988c5448401e"
} | 31 | [
2,
105,
2364,
107,
11823,
506,
2324,
529,
506,
9228,
14608,
573,
496,
3996,
44494,
607,
138334,
1554,
5404,
28713,
236743,
236819,
236786,
236800,
621,
2532,
106,
107,
105,
4368,
107
] | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-4f94d17b8e14d5031bb1f31b0c8d337a71d7144c5521b342ab2ddec07a5c4ee7 | [
{
"role": "user",
"content": "Evaluate \\( A^{100} \\) where \\( A = \\begin{bmatrix} 1 & 0 & 0 \\\\ 1 & 0 & 1 \\\\ 0 & 1 & 0 \\end{bmatrix} \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "af516d82-9723-499e-ae20-d6530b8a8bdc",
"license": "CC BY 4.0",
"prefix_sha256": "4f94d17b8e14d5031bb1f31b0c8d337a71d7144c5521b342ab2ddec07a5c4ee7"
} | 60 | [
2,
105,
2364,
107,
99009,
33556,
562,
790,
236770,
236771,
236771,
236783,
160670,
1298,
33556,
562,
578,
621,
1906,
236782,
68264,
236783,
236743,
236770,
833,
236743,
236771,
833,
236743,
236771,
1704,
236743,
236770,
833,
236743,
236771,
833... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-c77d27c7beab2c010335662d2421b29680a4768871a5391c57cd0b25416e29a6 | [
{
"role": "user",
"content": "Find all integer solutions to the equation \\( y^2 + y = x^4 + x^3 + x^2 + x \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "744cfb10-ffb9-4c9d-a30e-b4956fa12e77",
"license": "CC BY 4.0",
"prefix_sha256": "c77d27c7beab2c010335662d2421b29680a4768871a5391c57cd0b25416e29a6"
} | 38 | [
2,
105,
2364,
107,
11823,
784,
11995,
5434,
531,
506,
4901,
33556,
570,
236884,
236778,
900,
570,
578,
1123,
236884,
236812,
900,
1123,
236884,
236800,
900,
1123,
236884,
236778,
900,
1123,
621,
769,
106,
107,
105,
4368,
107
] | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-3774c3a3e0df88b84b6107de88ef50e35e666dbc882cfa0ec3f415bee5b782e3 | [
{
"role": "user",
"content": "Given a line segment \\( AB \\) of length 3 with endpoints \\( A \\) on the \\( y \\)-axis and \\( B \\) on the \\( x \\)-axis, and a point \\( C \\) such that \\( d(A, C) = 1 \\). Determine the curve on which point \\( C \\) lies as points \\( A \\) and \\( B \\) slide along t... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "18216ddf-f677-49c4-85de-7a78bccb87ca",
"license": "CC BY 4.0",
"prefix_sha256": "3774c3a3e0df88b84b6107de88ef50e35e666dbc882cfa0ec3f415bee5b782e3"
} | 89 | [
2,
105,
2364,
107,
26479,
496,
1757,
9951,
33556,
14802,
160670,
529,
3861,
236743,
236800,
607,
61925,
33556,
562,
160670,
580,
506,
33556,
570,
621,
4787,
11569,
532,
33556,
603,
160670,
580,
506,
33556,
1123,
621,
4787,
11569,
236764,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-c607dfd879d3a11e7e0e1c8d6325f3f1ea039e6caf32daf32ab965573bda0200 | [
{
"role": "user",
"content": "Solve the following equations applying the methods presented above. $\\frac{2\\tan\\frac{x}{2}}{1+\\tan^2 \\frac{x}{2}}=y^2-4y+5$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "b7685f63-24a7-453f-9051-84233967222f",
"license": "CC BY 4.0",
"prefix_sha256": "c607dfd879d3a11e7e0e1c8d6325f3f1ea039e6caf32daf32ab965573bda0200"
} | 53 | [
2,
105,
2364,
107,
76857,
506,
2269,
8520,
14253,
506,
4615,
6212,
2787,
236761,
874,
1420,
236782,
236778,
236785,
13257,
236785,
1420,
236782,
236781,
1170,
236778,
5763,
236770,
3908,
13257,
236884,
236778,
621,
1420,
236782,
236781,
1170,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-0fc0a6cfd47119becb034b8b6e48424feb19c1597d9dcd88e048e2e98a8fd937 | [
{
"role": "user",
"content": "Solve the following equations: $\\frac{(a-x)\\sqrt {a-x}+(x-b)\\sqrt {x-b}}{\\sqrt {a-x}+\\sqrt {x-b}}=a-b$"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "a031897d-33d8-4575-935d-179b1ec28e7d",
"license": "CC BY 4.0",
"prefix_sha256": "0fc0a6cfd47119becb034b8b6e48424feb19c1597d9dcd88e048e2e98a8fd937"
} | 53 | [
2,
105,
2364,
107,
76857,
506,
2269,
8520,
236787,
874,
1420,
18946,
236746,
236772,
236781,
2911,
4784,
642,
236746,
236772,
236781,
49976,
236781,
236772,
236763,
2911,
4784,
642,
236781,
236772,
236763,
10024,
4784,
642,
236746,
236772,
2367... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-133aba77646253b04acaa5e2219ca10d9c8eb3b687e6ebd164d4acb6ba806aba | [
{
"role": "user",
"content": "Compute the limit \\(\\lim_{n\\to+\\infty}\\frac{1}{n^2}\\int_{1}^{e}\\ln(1+x^n)\\ln(1+2x^n)dx\\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "c8583b0b-0e7c-4e24-b44b-1b4c13e553df",
"license": "CC BY 4.0",
"prefix_sha256": "133aba77646253b04acaa5e2219ca10d9c8eb3b687e6ebd164d4acb6ba806aba"
} | 56 | [
2,
105,
2364,
107,
55822,
506,
4576,
621,
1314,
3824,
681,
236749,
236785,
1071,
3908,
5087,
958,
1420,
236782,
236770,
1170,
236749,
236884,
236778,
958,
720,
681,
236770,
1244,
236744,
958,
3269,
236769,
236770,
236862,
236781,
236884,
2367... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-0fb2d01741fa94cf6839d6a1248b6ad4e919381bad8fe6ee073e20ca25670a23 | [
{
"role": "user",
"content": "How many different units digits can a number have if its square has a tens digit of 7?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "3ca29c3c-c79d-4645-9c99-5c4ee8100922",
"license": "CC BY 4.0",
"prefix_sha256": "0fb2d01741fa94cf6839d6a1248b6ad4e919381bad8fe6ee073e20ca25670a23"
} | 29 | [
2,
105,
2364,
107,
3910,
1551,
1607,
6630,
26798,
740,
496,
1548,
735,
768,
1061,
6281,
815,
496,
19162,
15958,
529,
236743,
236832,
236881,
106,
107,
105,
4368,
107
] | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-530293e4dbc069711b87509514d2a94a4bb14df7a86e18ca36c0bb8883044627 | [
{
"role": "user",
"content": "Given trapezoid $PQRS$ inscribed in a circle with center $O$, where $PQ \\parallel RS$, $\\angle ROS = 3\\angle POQ$, and $\\frac{PQ}{RS} = \\frac{3}{8}$. Determine the value of $\\frac{[POQ]}{[QOR]}$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "ee9b1094-c559-4b66-901c-d87a27077216",
"license": "CC BY 4.0",
"prefix_sha256": "530293e4dbc069711b87509514d2a94a4bb14df7a86e18ca36c0bb8883044627"
} | 73 | [
2,
105,
2364,
107,
26479,
100373,
1433,
609,
83793,
12971,
236795,
87689,
528,
496,
10059,
607,
3988,
609,
236806,
2500,
1298,
609,
83793,
621,
52725,
20949,
2500,
874,
2925,
37564,
578,
236743,
236800,
236785,
2925,
13174,
236935,
2500,
53... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-8fc28f21f2d356ac8f86c4c9980b2a308ba1ef5244b0c978aa5524d8bb5cbf2e | [
{
"role": "user",
"content": "Determine the Laurent expansion of \\(\\frac{z^2 + 2z}{z^3 - 1}\\) in the annulus \\(0 < |z-1| < R\\) about \\(z = 1\\). Find the largest \\(R\\) that can be used."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "a01d4e85-245b-4755-ad7c-5d50322d7cd6",
"license": "CC BY 4.0",
"prefix_sha256": "8fc28f21f2d356ac8f86c4c9980b2a308ba1ef5244b0c978aa5524d8bb5cbf2e"
} | 67 | [
2,
105,
2364,
107,
102752,
506,
52610,
10534,
529,
621,
1314,
1420,
236782,
236802,
236884,
236778,
900,
236743,
236778,
236802,
1170,
236802,
236884,
236800,
753,
236743,
236770,
958,
236768,
528,
506,
221736,
33556,
236771,
655,
1109,
236802,... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-1a7345c93818c2d8e908b05024f6407bf1555c9301bdd920b5c7f02a51b369be | [
{
"role": "user",
"content": "Solve the equation:\n$$2{{\\log }_{\\frac{1}{2}}}\\left( x-1 \\right)-{{\\log }_{\\frac{1}{4}}}\\left( 3x-1 \\right)=1$$"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "f0794656-66f3-4b80-9a37-09978925fd2a",
"license": "CC BY 4.0",
"prefix_sha256": "1a7345c93818c2d8e908b05024f6407bf1555c9301bdd920b5c7f02a51b369be"
} | 54 | [
2,
105,
2364,
107,
76857,
506,
4901,
236787,
107,
9873,
236778,
41367,
1587,
66299,
1420,
236782,
236770,
1170,
236778,
42545,
989,
236769,
1123,
236772,
236770,
621,
898,
4787,
41367,
1587,
66299,
1420,
236782,
236770,
1170,
236812,
42545,
9... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-dfd8fc19c9040fb9ac623aa7937508188a030fa76c62390cfaf88981a3a6dea6 | [
{
"role": "user",
"content": "Calculate the total present value of the following payments: $600 made at the end of each of the years 1 to 8 and $900 made at the end of each of the years 9 to 15, given an annual effective interest rate of 7.5% for the first ten years and 9% thereafter."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "6fa28703-8af8-4664-a640-979a242b515c",
"license": "CC BY 4.0",
"prefix_sha256": "dfd8fc19c9040fb9ac623aa7937508188a030fa76c62390cfaf88981a3a6dea6"
} | 81 | [
2,
105,
2364,
107,
50702,
506,
2558,
1861,
1550,
529,
506,
2269,
13192,
236787,
609,
236825,
236771,
236771,
1603,
657,
506,
1345,
529,
1546,
529,
506,
1518,
236743,
236770,
531,
236743,
236828,
532,
609,
236819,
236771,
236771,
1603,
657,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-39a196bb0e433723f2bc3c5192899aea923bf3d36fd2f44b6bc074f6cb886cb0 | [
{
"role": "user",
"content": "For which lattice points \\( Q \\) in the positive \\( x \\)-\\( y \\) plane does there exist a straight line passing through \\( Q \\) that forms a triangle with the coordinate axes, such that the area of this triangle is 2?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "7f84590e-5610-43a6-92b3-d231d2008409",
"license": "CC BY 4.0",
"prefix_sha256": "39a196bb0e433723f2bc3c5192899aea923bf3d36fd2f44b6bc074f6cb886cb0"
} | 58 | [
2,
105,
2364,
107,
2542,
837,
18928,
3298,
33556,
1366,
160670,
528,
506,
4414,
33556,
1123,
621,
16233,
236769,
570,
160670,
8180,
1677,
993,
2849,
496,
6850,
1757,
11332,
1343,
33556,
1366,
160670,
600,
6667,
496,
17852,
607,
506,
16422... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-7b19668f55fde0a7f5a3722aa4d1dca4bbffefa20b5727121b3dc71c3a1f9035 | [
{
"role": "user",
"content": "Given that \\( x_1, x_2, \\ldots, x_{20} \\) are roots of the equation \\( x^{20} - 123x^{10} + 1 = 0 \\), find the value of \\( (|x_1| + |x_2| + \\cdots + |x_{20}|)^2 \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "1b5f793e-dbc5-4769-ae0c-05713516c345",
"license": "CC BY 4.0",
"prefix_sha256": "7b19668f55fde0a7f5a3722aa4d1dca4bbffefa20b5727121b3dc71c3a1f9035"
} | 88 | [
2,
105,
2364,
107,
26479,
600,
33556,
1123,
236779,
236770,
236764,
1123,
236779,
236778,
236764,
621,
2989,
236764,
1123,
681,
236778,
236771,
236783,
160670,
659,
14546,
529,
506,
4901,
33556,
1123,
790,
236778,
236771,
236783,
753,
236743,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-fb5950f2eefcfa759c23dd1c6661f4b6f6ca0751de17e27399802d78dc1856b6 | [
{
"role": "user",
"content": "Let $ABCD$ be a rectangle with side lengths $3$ and $4$. When the rectangle is folded over the diagonal $BD$, the area of the new shape can be expressed as $\\frac{a}{b}$, where $a$ and $b$ are integers with $\\gcd(a, b) = 1$. What is the value of $a + b$? (If there is overlapp... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "d2a5f5ab-4e06-4234-988a-0ababf0f7455",
"license": "CC BY 4.0",
"prefix_sha256": "fb5950f2eefcfa759c23dd1c6661f4b6f6ca0751de17e27399802d78dc1856b6"
} | 100 | [
2,
105,
2364,
107,
6481,
609,
181242,
236795,
577,
496,
32891,
607,
2678,
25565,
609,
236800,
236795,
532,
609,
236812,
2104,
3026,
506,
32891,
563,
42252,
1024,
506,
22219,
609,
11217,
2500,
506,
2433,
529,
506,
861,
6230,
740,
577,
89... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-30504bd4e320888fb621abbaba4d666ba7d615d952cff2c26320357094d16fde | [
{
"role": "user",
"content": "Given that the weights of the 1, 5, and 10 dollar coins are 3, 5, and 2 oz respectively, what is the minimum weight $q_n$ needed to buy an item priced at $n$ dollars?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "35220e93-dbe9-4f53-9035-13aabf875745",
"license": "CC BY 4.0",
"prefix_sha256": "30504bd4e320888fb621abbaba4d666ba7d615d952cff2c26320357094d16fde"
} | 62 | [
2,
105,
2364,
107,
26479,
600,
506,
18710,
529,
506,
236743,
236770,
236764,
236743,
236810,
236764,
532,
236743,
236770,
236771,
15285,
21237,
659,
236743,
236800,
236764,
236743,
236810,
236764,
532,
236743,
236778,
16109,
6619,
236764,
1144,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-f04911a21d593ab61dea74ef57f792f61dfca2ed8176980a2b413fc1e285caf8 | [
{
"role": "user",
"content": "Evaluate the integral $\\int \\frac{x}{\\cos^2 x} \\, dx$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "0b5a3a5f-1ba3-4a1b-ac23-be8c0e9d35ff",
"license": "CC BY 4.0",
"prefix_sha256": "f04911a21d593ab61dea74ef57f792f61dfca2ed8176980a2b413fc1e285caf8"
} | 27 | [
2,
105,
2364,
107,
99009,
506,
11826,
874,
720,
621,
1420,
236782,
236781,
3378,
4425,
236884,
236778,
1123,
236783,
20832,
20753,
2104,
106,
107,
105,
4368,
107
] | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-35c05211f1f4a56d679d9a891e837848efce7976a7bd352f944c99f8084bcc7f | [
{
"role": "user",
"content": "Solve the equation $\\lvert \\sin x \\rvert ^{\\tan x} + \\lvert \\cos x \\rvert ^{\\tan x} = 1$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "850a98cc-70e5-4c87-93b4-6b1e079fa9ea",
"license": "CC BY 4.0",
"prefix_sha256": "35c05211f1f4a56d679d9a891e837848efce7976a7bd352f944c99f8084bcc7f"
} | 43 | [
2,
105,
2364,
107,
76857,
506,
4901,
874,
236752,
2515,
621,
5322,
1123,
621,
236750,
2515,
137281,
13257,
1123,
236783,
900,
621,
236752,
2515,
621,
4425,
1123,
621,
236750,
2515,
137281,
13257,
1123,
236783,
578,
236743,
236770,
2104,
106... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-930faae9aeb80c578716e32d42c9c9ef162fdb02dc5b8968b2cbfc9c213e19c8 | [
{
"role": "user",
"content": "Find two matrices \\( A, B \\in \\mathcal{M}_2(\\mathbb{R}) \\) such that \\( A^2 + B^2 = \\begin{pmatrix} 2 & 3 \\\\ 3 & 2 \\end{pmatrix} \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "5631bda4-1074-4386-b6bf-c09745b36843",
"license": "CC BY 4.0",
"prefix_sha256": "930faae9aeb80c578716e32d42c9c9ef162fdb02dc5b8968b2cbfc9c213e19c8"
} | 64 | [
2,
105,
2364,
107,
11823,
1156,
20934,
33556,
562,
236764,
603,
621,
495,
621,
2374,
236782,
236792,
10996,
236778,
1314,
3603,
236782,
236794,
2454,
160670,
1288,
600,
33556,
562,
236884,
236778,
900,
603,
236884,
236778,
578,
621,
1906,
2... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-246654b1082f8994ef04263128ccf4d2444a6903ab178a1c4a5483ed16928505 | [
{
"role": "user",
"content": "Find \\(\\lim_{n\\rightarrow\\infty} n \\tan\\left(\\frac{\\pi e n!}{5}\\right)\\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "4d0e80bf-f381-4ea0-9150-6849ffb79286",
"license": "CC BY 4.0",
"prefix_sha256": "246654b1082f8994ef04263128ccf4d2444a6903ab178a1c4a5483ed16928505"
} | 37 | [
2,
105,
2364,
107,
11823,
621,
1314,
3824,
681,
236749,
236785,
4063,
236785,
5087,
236783,
538,
621,
13257,
236785,
989,
1314,
1420,
1564,
2160,
545,
538,
175016,
236810,
958,
898,
2911,
769,
106,
107,
105,
4368,
107
] | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-5c11ee17d37ec204f379ff45d5131a0ec11663689c73e239933b306d7e9ec4a8 | [
{
"role": "user",
"content": "Let \\( P(x) \\) be a polynomial of degree \\( n \\). If \\( P(k) = \\frac{k}{k+1} \\) for \\( k = 0, 1, \\ldots, n \\), evaluate \\( P(m) \\) where \\( m > n \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "3de3c890-bcf0-40c5-af00-a5f80dd8e125",
"license": "CC BY 4.0",
"prefix_sha256": "5c11ee17d37ec204f379ff45d5131a0ec11663689c73e239933b306d7e9ec4a8"
} | 72 | [
2,
105,
2364,
107,
6481,
33556,
593,
236769,
236781,
236768,
160670,
577,
496,
14337,
529,
5802,
33556,
538,
621,
769,
1637,
33556,
593,
236769,
236767,
236768,
578,
621,
1420,
236782,
236767,
1170,
236767,
236862,
236770,
236783,
160670,
573... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-4ce7fb54d62a60d345fe71f95fe4c597596eed8b33d433b00670b86acbb521d1 | [
{
"role": "user",
"content": "Given a quadrilateral \\(ABCD\\) inscribed in a circle with radius 2, where \\(AC\\) and \\(BD\\) intersect at \\(E\\) such that \\(AE = EC\\), and \\(AB = \\sqrt{2} \\cdot AE\\), \\(BD = 2\\sqrt{3}\\), find the area of quadrilateral \\(ABCD\\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "3c8dabee-d128-46d8-a0cf-170017f5404d",
"license": "CC BY 4.0",
"prefix_sha256": "4ce7fb54d62a60d345fe71f95fe4c597596eed8b33d433b00670b86acbb521d1"
} | 79 | [
2,
105,
2364,
107,
26479,
496,
142131,
33556,
181242,
68966,
87689,
528,
496,
10059,
607,
12425,
236743,
236778,
236764,
1298,
33556,
2714,
68966,
532,
33556,
11217,
68966,
33647,
657,
33556,
236788,
68966,
1288,
600,
33556,
14196,
578,
19521... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-fea7882289b14d6ce38ad6915d61ed7de4681d0735f13a084d2ee73392c8fe84 | [
{
"role": "user",
"content": "Find all functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) such that \\( f(x+y) = f(x)f(y) - f(xy) + 1 \\) for all \\( x, y \\in \\mathbb{R} \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "7dd97a09-feb4-42c1-9116-b9f43d18b3e0",
"license": "CC BY 4.0",
"prefix_sha256": "fea7882289b14d6ce38ad6915d61ed7de4681d0735f13a084d2ee73392c8fe84"
} | 70 | [
2,
105,
2364,
107,
11823,
784,
5151,
33556,
517,
236787,
621,
3603,
236782,
236794,
236783,
621,
4063,
621,
3603,
236782,
236794,
236783,
160670,
1288,
600,
33556,
517,
236769,
236781,
236862,
236762,
236768,
578,
517,
236769,
236781,
236768,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-507b6d6140ae447af28cc4d0115d9906f8b8e3044f2fd22645adae12e15af0c0 | [
{
"role": "user",
"content": "A bored student walks down a hall that contains a row of closed lockers, numbered $1$ to $1024$. He opens the locker numbered 1, and then alternates between skipping and opening each locker thereafter. When he reaches the end of the hall, the student turns around and starts bac... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "ab761e16-1ab4-487a-a195-cd19d0bb1766",
"license": "CC BY 4.0",
"prefix_sha256": "507b6d6140ae447af28cc4d0115d9906f8b8e3044f2fd22645adae12e15af0c0"
} | 119 | [
2,
105,
2364,
107,
236776,
38670,
5117,
23241,
1679,
496,
11967,
600,
6097,
496,
2050,
529,
6535,
147765,
236764,
49597,
609,
236770,
236795,
531,
609,
236770,
236771,
236778,
236812,
2104,
1293,
19015,
506,
57455,
49597,
236743,
236770,
2367... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-91b5036a54f5dddb7422042476c042c000d9502299cf935eb04230bdb085743c | [
{
"role": "user",
"content": "Let \\( m \\) be a positive integer with \\( m \\leq 2024 \\). Ana and Banana play a game alternately on a \\( 1 \\times 2024 \\) board, with squares initially painted white. Ana starts the game. Each move by Ana consists of choosing any \\( k \\leq m \\) white squares on the b... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "773eb601-dada-43fc-bf9a-7155bcf0a14d",
"license": "CC BY 4.0",
"prefix_sha256": "91b5036a54f5dddb7422042476c042c000d9502299cf935eb04230bdb085743c"
} | 136 | [
2,
105,
2364,
107,
6481,
33556,
520,
160670,
577,
496,
4414,
11995,
607,
33556,
520,
621,
4131,
236743,
236778,
236771,
236778,
236812,
621,
769,
30855,
532,
94704,
1441,
496,
2290,
99786,
580,
496,
33556,
236743,
236770,
621,
3841,
236743,... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-251dce94531b10bfe8701eff3ee0ae51b72b62892777031ccf9df1fce6ae7670 | [
{
"role": "user",
"content": "Evaluate the integral $\\int{\\frac{\\sec x}{1+\\csc x}} \\, dx$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "5676622f-902a-4e3e-aac9-bd976023c3b5",
"license": "CC BY 4.0",
"prefix_sha256": "251dce94531b10bfe8701eff3ee0ae51b72b62892777031ccf9df1fce6ae7670"
} | 28 | [
2,
105,
2364,
107,
99009,
506,
11826,
874,
720,
1564,
1420,
1564,
4706,
1123,
1170,
236770,
3908,
85612,
1123,
1807,
20832,
20753,
2104,
106,
107,
105,
4368,
107
] | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-53f570c08c776398f2313b5caf1aecd63127c2feea1c9c717d7d030bfe0cabc5 | [
{
"role": "user",
"content": "Determine all functions \\( f : \\mathbb{R}^+ \\to \\mathbb{R} \\) such that \n\\[ f((x + z)(y + z)) = (f(x) + f(z))(f(y) + f(z)) \\]\nfor all \\( x, y \\in \\mathbb{R}^+ \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "c41ca14f-64b0-4afd-9b29-9393bdfa9299",
"license": "CC BY 4.0",
"prefix_sha256": "53f570c08c776398f2313b5caf1aecd63127c2feea1c9c717d7d030bfe0cabc5"
} | 82 | [
2,
105,
2364,
107,
102752,
784,
5151,
33556,
517,
1017,
621,
3603,
236782,
236794,
9914,
236862,
621,
1071,
621,
3603,
236782,
236794,
236783,
160670,
1288,
600,
236743,
107,
2318,
517,
3283,
236781,
900,
904,
3460,
236762,
900,
904,
1223,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-57ce7ede5d3c274c85836ef5e1a7dcff9645d1df61a5448df2f763f58478f94a | [
{
"role": "user",
"content": "Solve the following equations and inequalities: $\\sqrt {2x-1}+\\sqrt {3x-2}>\\sqrt {4x-3}+\\sqrt {5x-4}$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "c5b8641e-483c-4799-8be5-5172ec936f8e",
"license": "CC BY 4.0",
"prefix_sha256": "57ce7ede5d3c274c85836ef5e1a7dcff9645d1df61a5448df2f763f58478f94a"
} | 45 | [
2,
105,
2364,
107,
76857,
506,
2269,
8520,
532,
39975,
236787,
874,
4784,
642,
236778,
236781,
236772,
236770,
5269,
4784,
642,
236800,
236781,
236772,
236778,
65192,
4784,
642,
236812,
236781,
236772,
236800,
5269,
4784,
642,
236810,
236781,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-9d5459a12df66c74a5193ce211bc0119a3121423524d6ff129876c7761906412 | [
{
"role": "user",
"content": "Find the flow of the vector field $X = x\\frac{\\partial}{\\partial y} - y\\frac{\\partial}{\\partial x}$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "7a660127-765b-420c-8434-93d09d52f38c",
"license": "CC BY 4.0",
"prefix_sha256": "9d5459a12df66c74a5193ce211bc0119a3121423524d6ff129876c7761906412"
} | 38 | [
2,
105,
2364,
107,
11823,
506,
2727,
529,
506,
3550,
2135,
609,
236917,
578,
1123,
236785,
1420,
1564,
4218,
3378,
4218,
570,
236783,
753,
570,
236785,
1420,
1564,
4218,
3378,
4218,
1123,
2532,
106,
107,
105,
4368,
107
] | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-a4ca22053c84489447aad864fb9d0d64130b840d041ea708db8a1ca6b3ba6767 | [
{
"role": "user",
"content": "Factor \\( (x-1)^3 - 27 \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "dd692ce6-b825-4885-95c8-581249f6ce32",
"license": "CC BY 4.0",
"prefix_sha256": "a4ca22053c84489447aad864fb9d0d64130b840d041ea708db8a1ca6b3ba6767"
} | 23 | [
2,
105,
2364,
107,
35231,
33556,
568,
236781,
236772,
236770,
13365,
236800,
753,
236743,
236778,
236832,
621,
769,
106,
107,
105,
4368,
107
] | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-153d42ca0e6c1a35298add5a3e1a72228e37c44f5c5b6b9846cc2ef1ea88b7d0 | [
{
"role": "user",
"content": "Let the polynomial \\( P(x) \\) have degree \\( m \\) with positive coefficients. Denote \\( A_n \\) and \\( G_n \\) as the arithmetic mean and geometric mean of \\( P(1), P(2), \\ldots, P(n) \\). Find \\( \\lim_{n \\to +\\infty} \\frac{A_n}{G_n} \\)."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "d1dde91f-f30a-4261-bc90-4cff76863962",
"license": "CC BY 4.0",
"prefix_sha256": "153d42ca0e6c1a35298add5a3e1a72228e37c44f5c5b6b9846cc2ef1ea88b7d0"
} | 89 | [
2,
105,
2364,
107,
6481,
506,
14337,
33556,
593,
236769,
236781,
236768,
160670,
735,
5802,
33556,
520,
160670,
607,
4414,
15841,
236761,
108122,
33556,
562,
236779,
236749,
160670,
532,
33556,
667,
236779,
236749,
160670,
618,
506,
40442,
26... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-f37b8130517a5f26b536244a9c3d4b2dd35a8e5eac0c21fce1e07482f1c1adfe | [
{
"role": "user",
"content": "In a right trapezoid, the acute angle is equal to the angle between the diagonals, and one of the diagonals is perpendicular to one of the lateral sides. Find the ratio of the lengths of the bases of the trapezoid."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "45f1158d-a573-4ad6-8942-ad817062543a",
"license": "CC BY 4.0",
"prefix_sha256": "f37b8130517a5f26b536244a9c3d4b2dd35a8e5eac0c21fce1e07482f1c1adfe"
} | 55 | [
2,
105,
2364,
107,
902,
496,
1447,
100373,
1433,
236764,
506,
20719,
7275,
563,
4745,
531,
506,
7275,
1534,
506,
140651,
236764,
532,
886,
529,
506,
140651,
563,
26219,
531,
886,
529,
506,
21747,
9174,
236761,
9100,
506,
7232,
529,
506,... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-740622160ba63c31b60735695078adfe71706104c95ae6dadbd6a829a46d96ba | [
{
"role": "user",
"content": "How many paths are there from $A$ to $B$ that consist of $5$ horizontal segments and $5$ vertical segments of length $1$ each?"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "f4915e21-d3b4-4a68-9a6f-46edb173474e",
"license": "CC BY 4.0",
"prefix_sha256": "740622160ba63c31b60735695078adfe71706104c95ae6dadbd6a829a46d96ba"
} | 43 | [
2,
105,
2364,
107,
3910,
1551,
16412,
659,
993,
699,
609,
236776,
236795,
531,
609,
236799,
236795,
600,
4551,
529,
609,
236810,
236795,
12344,
20875,
532,
609,
236810,
236795,
9351,
20875,
529,
3861,
609,
236770,
236795,
1546,
236881,
106,... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-12c65817701b45354e37d832c45abde3f797d6aaff23c85fb2ded6635ffa5efa | [
{
"role": "user",
"content": "A lift with seven people stops at ten floors. From zero to seven people go out at each floor. How many ways are there for the lift to empty? (The ways only differ by the number of people leaving at each floor.)"
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "6cab00af-8306-443f-808f-85a1c4906544",
"license": "CC BY 4.0",
"prefix_sha256": "12c65817701b45354e37d832c45abde3f797d6aaff23c85fb2ded6635ffa5efa"
} | 56 | [
2,
105,
2364,
107,
236776,
12693,
607,
6819,
1331,
20627,
657,
3595,
26273,
236761,
4934,
5743,
531,
6819,
1331,
817,
855,
657,
1546,
6413,
236761,
2088,
1551,
4861,
659,
993,
573,
506,
12693,
531,
7738,
236881,
568,
818,
4861,
1186,
13... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-b6b8b1b2a41971a22f7def0e97a9856d0b195ce14333fd400c5251e5eeccef03 | [
{
"role": "user",
"content": "The function $(x^2-1)(x^2-4)=k$ has four real solutions which form an arithmetic sequence. Find the value of $k$."
}
] | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "25077ac7-b2a3-48f3-987a-93c7759f11a4",
"license": "CC BY 4.0",
"prefix_sha256": "b6b8b1b2a41971a22f7def0e97a9856d0b195ce14333fd400c5251e5eeccef03"
} | 43 | [
2,
105,
2364,
107,
818,
1292,
3498,
236781,
236884,
236778,
236772,
236770,
3460,
236781,
236884,
236778,
236772,
236812,
3483,
236767,
236795,
815,
2390,
1759,
5434,
837,
1183,
614,
40442,
7501,
236761,
9100,
506,
1550,
529,
609,
236767,
210... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
nemotron-2dcd92fe6ac9398ba349b101ad2ab348b533762b3f10049853a46b998622f656 | [
{
"role": "user",
"content": "The square of an integral positive prime number $N$ is divided (with a remainder) by 3, the resulting incomplete quotient is divided (without a remainder) by 3, the quotient is again divided (with a remainder) by 3, and, finally, the resulting incomplete quotient is again divid... | null | train | {
"dataset": "nvidia/Nemotron-Post-Training-Dataset-v1",
"revision": "74e23eb6f830fef4a9e96a92f6f6262214cbb9a8",
"domain": "math",
"uuid": "09e23d7e-71b8-4112-9c3e-aee187da06be",
"license": "CC BY 4.0",
"prefix_sha256": "2dcd92fe6ac9398ba349b101ad2ab348b533762b3f10049853a46b998622f656"
} | 90 | [
2,
105,
2364,
107,
818,
6281,
529,
614,
11826,
4414,
8355,
1548,
609,
236797,
236795,
563,
11310,
568,
4060,
496,
24232,
236768,
684,
236743,
236800,
236764,
506,
9113,
36289,
37689,
563,
11310,
568,
31048,
496,
24232,
236768,
684,
236743,
... | bca34862f49c6a63155300a313b0d3f901ad1c16d619d19c2677ba963449085d |
End of preview.
OPD prefixes
Prompt-only subsets of NVIDIA Nemotron-Post-Training-Dataset-v1 and NVIDIA SWE-Zero-openhands-trajectories, plus codeparrot/APPS and GSM8K training questions. Nemotron tool-call entries preserve native tools in metadata and tokenize through the model native tool template. These are first-decision contexts, not a complete tool interaction environment. Each source retains its own license, not a choice of dual licenses: NVIDIA sources declare CC-BY-4.0; APPS and GSM8K declare MIT. Attribution: NVIDIA, APPS dataset authors Dan Hendrycks and collaborators, codeparrot, OpenAI/GSM8K authors and upstream contributors. Source cards: https://huggingface.co/datasets/nvidia/Nemotron-Post-Training-Dataset-v1 ; https://huggingface.co/datasets/nvidia/SWE-Zero-openhands-trajectories ; https://huggingface.co/datasets/codeparrot/apps ; https://github.com/openai/grade-school-math . Attribution: NVIDIA and the upstream dataset contributors; source revisions are in manifest.json. Preserve upstream repository license obligations recorded in provenance.
Cached DiffusionGemma tokenizer IDs; original native system/user messages; no assistant targets, solutions or tool outputs. Train/dev task groups are disjoint and lexically screened. This is not universal contamination clearance. SWE entries are static task starts, not an executable repository environment. Broader benchmark adapters and full 8-H100 performance admission remain pending.
- Downloads last month
- 106