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jamesdborin
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Nemotron-Math-v2-prompt-only

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train

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The dataset generation failed

Error code:   DatasetGenerationError
Exception:    ArrowInvalid
Message:      Failed to parse string: '[{"function": {"description": "Call this function to execute Python code in a stateful Jupyter notebook environment. Python will respond with the output of the execution or time out after 120.0 seconds.", "name": "stateful_python_code_exec", "parameters": {"properties": {"code": {"description": "Code to execute", "type": "string"}}, "required": ["code"], "type": "object"}}, "type": "function"}]' as a scalar of type double
Traceback:    Traceback (most recent call last):
                File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1837, in _prepare_split_single
                  writer.write_table(table)
                  ~~~~~~~~~~~~~~~~~~^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/arrow_writer.py", line 765, in write_table
                  self._write_table(pa_table, writer_batch_size=writer_batch_size)
                  ~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.14/site-packages/datasets/arrow_writer.py", line 773, in _write_table
                  pa_table = table_cast(pa_table, self._schema)
                File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2369, in table_cast
                  return cast_table_to_schema(table, schema)
                File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2303, 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 1852, 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 2143, in cast_array_to_feature
                  return array_cast(
                      array,
                  ...<2 lines>...
                      allow_decimal_to_str=allow_decimal_to_str,
                  )
                File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 1854, in wrapper
                  return func(array, *args, **kwargs)
                File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2006, in array_cast
                  return array.cast(pa_type)
                         ~~~~~~~~~~^^^^^^^^^
                File "pyarrow/array.pxi", line 1147, in pyarrow.lib.Array.cast
                File "/usr/local/lib/python3.14/site-packages/pyarrow/compute.py", line 412, in cast
                  return call_function("cast", [arr], options, memory_pool)
                File "pyarrow/_compute.pyx", line 604, in pyarrow._compute.call_function
                File "pyarrow/_compute.pyx", line 399, in pyarrow._compute.Function.call
                  result = GetResultValue(
                File "pyarrow/error.pxi", line 155, in pyarrow.lib.pyarrow_internal_check_status
                File "pyarrow/error.pxi", line 92, in pyarrow.lib.check_status
                  raise convert_status(status)
              pyarrow.lib.ArrowInvalid: Failed to parse string: '[{"function": {"description": "Call this function to execute Python code in a stateful Jupyter notebook environment. Python will respond with the output of the execution or time out after 120.0 seconds.", "name": "stateful_python_code_exec", "parameters": {"properties": {"code": {"description": "Code to execute", "type": "string"}}, "required": ["code"], "type": "object"}}, "type": "function"}]' as a scalar of type double
              
              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 1683, 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 1869, in _prepare_split_single
                  raise DatasetGenerationError("An error occurred while generating the dataset") from e
              datasets.exceptions.DatasetGenerationError: An error occurred while generating the dataset

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dataset string	config string	split string	row_index int64	prompt string	prompt_source string	prompt_source_detail string	system_prompt null	system_source null	tools null	tools_source null	schema_str null	extraction_error null
nvidia/Nemotron-Math-v2	default	high_part00	0	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Beginning with simplification of the expressions, calculate the derivatives of the following functions. $f(x)=\left(\sqrt {1-x^4}+1\right): \left(\frac{1}{\sqrt {1+x^2}}+\sqrt {1-x^2}\right)$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	1	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. The ratio of the altitude of a cone to the radius of its circumscribed sphere is equal to $q$. Find the ratio of the volumes of these solids. For what $q$ is the problem solvable?	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	2	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Given that $a > 1$ and $\gcd(a, 6) = 1$, find the greatest value of $n$ in terms of $a$ such that the equation $a^2x + 6ay + 36z = n$ does not have natural roots $(x,y,z)$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	3	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Triangles $AMB$ and $AMC$ lie on different sides of the segment $AM$. It is known that $\angle BAM=30^\circ$, $\angle BMA=110^\circ$, $\angle CAM=20^\circ$, $\angle CMA=150^\circ$. Find the angles of triangle $BMC$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	4	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. A point is selected at random from the interior of a right triangle with legs of length $2\sqrt{3}$ and $4$. Let $p$ be the probability that the distance between the point and the nearest vertex is less than $2$. Then $p$ ...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	5	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. What is the probability that a hand of 13 cards randomly dealt from a pack of 52 contains exactly 2 aces?	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	6	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Let $ABC$ be a triangle with points $E$ and $F$ on sides $AC$ and $AB$ respectively. Rays $EF$ and $CB$ meet at $D$. Given that $CE = 4$, $EA = 2$, $DF = 3$, and $FE = 1$, find the ratios $AF/FB$ ...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	7	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Let $(a_i, b_i, c_i)$ be a permutation of $(1, 2, 3)$ for $i = 1, 2, 3, 4, 5$. Find the maximum and minimum values of $P = \prod_{i=1}^{5} a_i + \prod_{i=1}^{5} b_i + \prod_{i=1}^{5} c_i$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	8	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Calculate the integral $ f(x) := \int_{0}^{1} \frac{4t\sqrt{t(1-t)}}{x-4t} \, dt $ for $ x > 4 $.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	9	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Let $a, b, c$ be real numbers such that the equation $x^3 + ax^2 + bx + c = 0$ has three positive real roots $x_1, x_2, x_3$, and $x_1 - x_2 = \lambda > 0$, $x_1 > \frac{x_2 + x_3}{2}$. Find the maximum of \(\fra...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	10	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. The altitude of a right prism is 1 m, its base is a rhombus with side equal to 2 m and an acute angle of $30^\circ$. A secant plane is drawn through a side of the base which is at an angle of $60^\circ$ to the plane of the...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	11	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Joey is 1 year older than Chloe, and Zoe is exactly 1 year old today. Today is the first of the 9 birthdays on which Chloe's age will be an integral multiple of Zoe's age. What will be the sum of the two digits of Joey's a...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	12	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Ellie has two lists, each consisting of 6 consecutive positive integers. The smallest integer in the first list is $a$, the smallest integer in the second list is $b$, and $a < b$. She makes a third list which consis...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	13	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Compute the sum $ \sin^2 0^\circ + \sin^2 1^\circ + \sin^2 2^\circ + \sin^2 3^\circ + \sin^2 4^\circ + \ldots + \sin^2 99^\circ $.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	14	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Given a regular quadrangular pyramid $SABCD$ with vertex $S$. A plane is drawn through the midpoints of the edges $AB$, $AD$ and $CS$. In what ratio does the plane divide the volume of the pyramid?	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	15	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. In triangle $ABC$, point $M$ is the midpoint of $[BC]$, $H$ is the orthocenter, and $O$ is the circumcenter. Point $N$ is the reflection of $M$ with respect to $H$. Given that $\|OA\| = \|ON\| = 11$ and \(\|OH...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	16	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Consider the projection of a cube with edge $a$ onto a plane perpendicular to a diagonal of the cube. What is the ratio of the area of this projection to the area of the section of the cube by the plane passing through the...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	17	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. In quadrilateral $ABCD$, $AB = 12$, $BC = 16$, $CD = 7$, and $\angle ABC = 90^\circ$. If $AD$ has an integral length, find the sum of all possible lengths of $AD$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	18	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. For which positive integers $a$ and $b$ does the equation $ax - by = xy$ have positive integer solutions?	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	19	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Solve the following inequalities. $\tan x+\cot x<-3$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	20	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Find integers $ n, x, $ and $ y $ such that $ 2n-1 = x^2 $ and $ 2n^4-1 = y^2 $.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	21	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Calculate the minimum possible value of the perimeter of triangle $ABC$ given that: - $\angle A = 2 \angle B$ - $\angle C > 90^\circ$ - The sides $a, b, c$ of the triangle are integers.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	22	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Find all permutations $\{a_1,a_2,a_3,a_4,a_5,a_6,a_7,a_8,a_9\}$ of $\{-3,-2,-1,1,2,3,4,5,6\}$ such that $$a_1a_2\le a_2a_3\le\cdots{}\le a_7a_8\le a_8a_9.$$	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	23	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Using (1) and (2) and the formulas for the sums of $n$ terms of an arithmetic and a geometric progression, calculate the following limits: $\lim\limits_{n\to \infty } \left(\frac{1}{a_1a_2}+\frac{1}{a_2a_3} +\ldots +\frac{...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	24	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. How many ways are there to arrange the integers 1 through $ N^2 $ in an $ N \times N $ matrix such that (a) the diagonal elements increase from left to right and (b) each diagonal element is the smallest in its respect...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	25	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Consider two points $A(-1, 1)$ and $B(1, -1)$ on the coordinate plane. Let $P$ be a point such that the absolute value of the $x$-coordinate of $P$ is less than or equal to 1. Find the area of the domain of points $P$ sati...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	26	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Find the integer solutions of $x^y = y^x$ where $x \ne y$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	27	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. $\sin x\cos x-6\sin x+6\cos x+6=0$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	28	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. A square has sides of length 2. Set $\cal S$ is the set of all line segments that have length 2 and whose endpoints are on adjacent sides of the square. The midpoints of the line segments in set $\cal S$ enclose a region w...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	29	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Calculate the integral $ f(x) := \int_{0}^{1} \frac{4t\sqrt{t(1-t)}}{x-4t} \, dt $ for $ x > 4 $.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	30	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. How many subspaces of each dimension are there in $ F_p^4 $?	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	31	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. An aquarium has the shape of a rectangular parallelepiped with width $\ell$, length $L$, and height $h = 30$ cm, where $\ell < h < L$. When the aquarium is rotated around one of the two longest edges of its base until the ...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	32	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Determine the smallest rank $ n $ such that the terms of the sequence $ (a_n)_{n \ge 0} $ defined by $ a_n = \frac{2^n + 3n + 2}{3 \cdot 2^{n+1}} $ belong to the neighborhood \( \left( \frac{5}{36}, \frac{7}{36} \rig...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	33	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Given the constraints $x \ge 4$, $y \ge 5$, $6 \le z \le 6$, and $x^2 + y^2 + z^2 = 90$, find the minimum value of the expression $A = x + y + z$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	34	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Determine whether the sequence $ U_n = \sum_{k=1}^n \frac{1}{\sqrt{n^2 + k}} $ is increasing or decreasing.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	35	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Find all ordered pairs of real numbers $(x, y)$ that are solutions to the following system of equations: \[ x^4 + 2x^3 - y = -\frac{1}{4} + \sqrt{3} \] \[ y^4 + 2y^3 - x = -\frac{1}{4} - \sqrt{3} \]	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	36	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Let $a$, $b$, $c$, $d$, $a + b + c + 18 + d$, $a + b + c + 18 - d$, $b + c$, and $c + d$ be distinct prime numbers such that $a + b + c = 2010$, $a, b, c \geq 3$, and $6d \leq 50$. Find the maximum va...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	37	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Find the number of triples $(a, b, c)$ such that $b$ is divisible by $a$, $c$ is divisible by $b$, and $1 \leq a \leq b \leq c \leq 100$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	38	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Compute the degree of the field extension $ [F(t) : F(s)] $.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	39	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Evaluate the integral $$\int_0^{\frac{\pi}{2}} \ln \left\| \Gamma \left[ c + ix - \ln \left( 2 \cos x \right) \right] \right\| \text{d}x.$$	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	40	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. The total probability that Aasma will choose the highest ranking prospect among the 1000 prospects is the sum of the probability for each possible value of m+1 with m+1 ranging between k+1 and 1000. Find the sum. To simpli...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	41	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Workers $A$ and $B$ have been working the same number of days. If $A$ worked one day less and $B$ 7 days less then $A$ would earn 72 roubles and $B$ 64 roubles 80 kopecks. If, conversely, $A$ worked 7 days less and $B$ one...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	42	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Generalize the problem by considering a balanced set with $ m+n $ real numbers $ a_1 < a_2 < \cdots < a_{m+n} $ such that $ a_1, \ldots, a_m $ form an arithmetic progression with common difference $ p $ and \( a_m,...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	43	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Simplify the following expressions: $\frac{\sqrt {a^3b}\sqrt [3]{a^4b^3}:\sqrt [6]{a}}{(b^2-ab-2a^2)\sqrt {ab}} -a^{-\frac{2}{3}}\left(\frac{3a^2}{3b-6a+2ab-b^2}:\frac{a+b}{3a-ab} -\frac{ab}{a+b}\right)$	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	44	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Let $ T = TNYWR $. The graph of the equation $ y = 2Tx^3 + 2018Tx^2 + x - T^2 $ passes through collinear points $(20, a)$, $(17, b)$, and $(r, c)$ for some real number $ r $. Compute $ r $.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	45	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Let $a_1,a_2,\ldots ,a_n$ (where $n\ge 2$) be positive numbers. Determine the number of real solutions of the system of equations $$x_1x_2=a_1, x_2x_3=a_2,\ldots , x_{n-1}x_n=a_{n-1}, x_nx_1=a_n.$$	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	46	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Find all polynomials $P(x)$ such that $P(x^2) = -P(x)P(x+1)$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	47	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Bob starts at 1 kg and eats 1 apple a day. For every apple he eats, he gains 1/7 of his current weight. As Bob grows in weight, he eats $\lfloor x \rfloor$ apples when he weighs $x$ kg. After how many days will Bob weigh 1...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	48	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Determine the multiplicity of $Char(R(\pi_{n-k}))$ in the formal character of $\Lambda^k V$, where $V=R(\pi_1+2\pi_n)$ is an irreducible module over the Lie algebra $A_n$ with the highest weight $\pi_1+2\pi_n$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	49	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Find the angle between the planes (a) $\begin{array}[t]{lll} 2x+y-z=2,\medskip \\ x+2y-z=1; \end{array}$ (b) $\begin{array}[t]{lll} 3x-y-2z=1,\medskip \\ 2x+3y-z=2; \end{array}$ (c) $\begin{array}[t]{lll} x-y+3z=2,\medskip...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	50	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Given a cube $ABCDA_1B_1C_1D_1$ $(AA_1\\| BB_1\\| CC_1\\| DD_1)$. Find the distance from the vertex $A$ to the plane passing through the vertices $A_1$, $B$, $D$ if the edge of the cube is equal to $a$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	51	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. In a regular heptagon $ABCDEFG$, let the intersection of $AE$ and $CF$ be $H$. If $7\angle AHC = m^\circ$, find $m$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	52	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Given a permutation $\pi = \{\lambda_1, \lambda_2, \lambda_3, \ldots, \lambda_{2018}, \lambda_{2019}\}$ of the set $\{1, 2, 3, \ldots, 2018, 2019\}$, compute the remainder when the largest possible value of the expression ...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	53	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Given that $ n + m = 2014 $, find the maximum and minimum values of $ n! \cdot m! $.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	54	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Find all positive integers $ x $ and $ y $ such that $ y^x = x^{50} $.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	55	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Solve the following equations applying the methods presented above. $\tan x+\cot 2x=2\cot 4x$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	56	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Determine how many ways there are to pick thirteen cards from a standard deck of 52 cards such that all ranks are included but no "straight flush" exists among them. A "straight flush" is defined as two cards of the same s...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	57	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Given the matrix $ A = \begin{pmatrix} -1 & 4 & -2 \\ 1 & -1 & 1 \\ 3 & -6 & 4 \end{pmatrix} $, find the matrix $ X $ such that $ X^2 = A $ and $ X \neq A $ and $ X \neq -A $.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	58	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Let $C$ be a circle with radius 5 centered at the origin. Given points $A(0, 7)$ and $B(1, 6)$, denote by $C(P)$ the circle passing through points $A$ and $B$ and centered at point $P(\alpha, \beta)$. Find the ranges of $\...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	59	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Given an integer $ n > 2 $, consider a finite sequence $ a_1, a_2, \ldots, a_n $ that satisfies the following conditions: 1. $ a_1 = 1 $ and $ a_2 = 2 $ 2. $ a_1 < a_2 < \cdots < a_n $ 3. For any integer $ k $ ...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	60	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Given a right triangle $ABC$ with the right vertex angle $C$. The angle $CAB$ is equal to $\alpha $. The bisector of $\angle ABC$ cuts the leg $AC$ at a point $K$. A circle which cuts the hypotenuse $AB$ at a point $M$ is...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	61	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Lukas is playing pool on an equilateral triangle table with each side 16 feet long. The pockets are at the corners labeled C, H, and T. Lukas shoots a ball from corner C such that on the second bounce, the ball hits 2 feet...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	62	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Given $a$, $b$, and $c$ are positive, find the minimum value of the expression: \[ P = \frac{19a}{b+c} + \frac{4b}{c+a} + \frac{2009c}{a+b} \]	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	63	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. A circle with center $A$ has radius $10$. Point $B$ is in the same plane such that $AB=20$. Let $k$ and $l$ be lines tangent to the circle at points $P$ and $Q$ respectively, which intersect at $B$. Segment $CD$ with $C$ o...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	64	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. In the right triangle $ABC$ the angle $B$ is a right angle, ($\| AB \| = 3$, $\| BC \| = 4$). Calculate the angle between the medians $AM$ and $BD$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	65	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Determine the values of $n$ for which an $n \times n$ square can be tiled with L-shaped trominoes (pieces consisting of three unit squares forming an L-shape).	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	66	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. In a building with floors numbered from 1 to 8, the builder wants to place elevators such that for every choice of two floors, there are at least three elevators that stop on those floors. Each elevator can stop at a maxim...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	67	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. When moving in a circle in the same direction, two points meet every 12 minutes, the first point completing the circle 10 seconds faster than the second point. What part of the circumference does each point cover per secon...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	68	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Find all pairs of natural numbers $(m,n)$, $m \leq n$, such that there exists a table with $m$ rows and $n$ columns filled with the numbers 1 and 0, satisfying the following property: If a cell contains a 0 (respectively a...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	69	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Evaluate the integral \[ \int_0^1 \int_0^1 \int_0^1 \frac{x^4 y^3 z^2}{(x + y + z)(x^2 + y^2 + z^2) - (x^3 + y^3 + z^3)} \, dx \, dy \, dz. \]	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	70	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. An inscribed and circumscribed $n$-gon is divided by a line into two inscribed and circumscribed polygons with different numbers of sides. Find $n$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	71	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Find all pairs $(m, n) \in (\mathbb{N}^*)^2$ such that $mn \mid 2^{m!} + 5^{n!}$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	72	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Evaluate the limit \[\lim_{n\to \infty} n\ln \left[\sum_{k=2}^n\log_{\frac{1}{3}}\left(1-\frac{2}{k(k+1)}\right)\right].\]	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	73	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Simplify the expression $\frac{\displaystyle\prod_{n = 2}^{10}\frac{2n - 2}{n + 2}}{\displaystyle\prod_{n = 0}^{10}\frac{2n - 1}{n + 1}}$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	74	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. A point $O$ is taken outside the right angle with vertex $C$ on the extension of its bisector such that $\| OC \| = \sqrt 2$. A circle of radius 2 with center at the point $O$ is constructed. Find the area of the figure boun...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	75	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Let $a$, $b$, and $c$ be distinct complex numbers such that $a + b + c \neq 0$. Compute the greatest possible number of unordered pairs of different polynomials in the set \[ \left\{ ax^2 + bx + c, ax^2 + cx + b, b...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	76	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Through the edge of the base of a regular quadrangular pyramid is drawn a plane which cuts from the opposite face a triangle of area $a^2$. Find the lateral surface area of a pyramid that is cut out of the given pyramid by...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	77	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. In triangle $ABC$, the perpendicular bisector of side $AC$ intersects segment $BC$ at point $D$ and ray $AB$ at point $E$. Points $M$ and $N$ are the midpoints of segments $AC$ and $DE$, respectively. For what values of $\...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	78	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. A positive integer $ n $ is added to the numerator and denominator of $ S(2) $ such that the value of the resulting fraction is $ \frac{1}{2} $. Compute $ n $.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	79	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Solve the given systems of equations: $\left\{\begin{array}{lll} \frac{\sqrt [3]{2x+y}}{y}+\frac{\sqrt [3]{2x+y}}{2x}=\frac{81}{182}\medskip \\ \frac{\sqrt [3]{2x-y}}{y}-\frac{\sqrt [3]{2x-y}}{2x}=\frac{1}{182}. \end{array...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	80	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Find the residue at $ z = 0 $ of the function $ f(z) = \frac{\cos(1/z)}{\sin z} $.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	81	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Two trains started simultaneously from points $A$ and $B$ towards each other. At first each of them traveled with uniform acceleration (the initial speeds of the trains are zero, the accelerations are different), and then...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	82	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Determine all natural numbers $ n $ such that $ 1 + n + \frac{n^2}{2!} + \frac{n^3}{3!} + \frac{n^4}{4!} + \frac{n^5}{5!} + \frac{n^6}{6!} $ is an integer, where $ n < 2023 $.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	83	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Find positive integers $ x $ and prime $ p $ such that $ 2^x p^2 = a^5 $, where $ a $ is a positive integer.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	84	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Solve the differential equation $y'=-\frac{y}{\sqrt{x^2+y^2}}$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	85	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Determine all possible values of $f(101)$ for functions $f:\mathbb{N}\to\mathbb{N}$ such that $$mn+1 \text{ divides } f(m)f(n)+1$$ for all positive integers $m$ and $n$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	86	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Given $ a, b, c > 0 $ and $ abc = 8 $, find the maximum and minimum values of $ k = \frac{1}{\sqrt{a+1}} + \frac{1}{\sqrt{b+1}} + \frac{1}{\sqrt{c+1}} $.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	87	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Find a prime $ p $ that divides the number $ 9999999 + 1999000 $.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	88	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. 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?	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	89	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Solve the inequality $ x^{\log_4(x + 1)} > 256x $.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	90	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Determine the digits $ x $, $ y $, and $ z $ if the equation \[ \sqrt{\underbrace{\overline{xx \ldots x}}_{2n\text{ digits}}} - \underbrace{\overline{yy\ldots y}}_{n\text{ digits}} = \underbrace{\overline{zz \ldots ...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	91	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Let $n$ be a positive integer. On a $2 \times 3n$ board, we mark some squares such that any square (marked or not) is adjacent to at most two other distinct marked squares. What is the greatest possible number of marke...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	92	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Given a set of several different vectors in the plane. It is known that each vector of the set is equal to the sum of several others from this set. Find the smallest possible number of vectors in the set.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	93	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Solve the indicated equations: $x^{(\log _3 x)^2-3\log _3 x}=3^{8-3\log _{2\sqrt 2}4}$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	94	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. A rectangle is cut into 10 squares, with the side of the smallest square being 3. Find the dimensions of the rectangle.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	95	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Determine the ages of Euler and Gauss given the following information: - If you take Gauss's age, subtract Euler's age, and subtract Gauss's son's age, you get the same result as if you subtract Gauss's son's age from Eule...	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	96	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Solve the equation: $\frac{1}{\cos{x}}+\frac{1}{\cos{2x}}+\frac{1}{\cos{3x}}=\frac{1}{4\cos{\frac{x}{2}}\cos{x}\cos{\frac{3x}{2}}-1}$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	97	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Rationalize the denominator of $\frac{2}{1+\sqrt{6}+\sqrt{15}}$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	98	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. In triangle $ABC$, the angle bisector $AK$ is drawn. The center of the circle inscribed in triangle $AKC$ coincides with the center of the circumscribed circle around triangle $ABC$. Determine the angles of triangle $ABC$.	messages	first_user_message	null	null	null	null	null	null
nvidia/Nemotron-Math-v2	default	high_part00	99	Solve the following math problem. Make sure to put the answer (and only answer) inside \boxed{}. Evaluate the Cauchy principal value of the integral $\mathbb{PV} \int_{0}^{1} \frac{1}{(\pi^2 + \ln^2{x})(1 - x^2)} \, dx$.	messages	first_user_message	null	null	null	null	null	null

End of preview.

Nemotron-Math-v2-prompt-only

Prompt-only extraction from nvidia/Nemotron-Math-v2.

Files:

prompts.csv: one prompt extraction record per source row. Records include prompt, separated system_prompt, and structured tools when the source row defines available tools. Nested values are JSON-encoded inside CSV cells.
summary.md: source row counts, extracted row counts, count deltas, and failed prompt counts.
null_or_empty_rows.md: row indexes where prompt extraction produced a null or empty prompt.

Summary:

extracted rows: 7085839
failed prompt rows: 0
row count delta: 0

Uploaded under jamesdborin from the Nemotron Post-Training v3 prompt extractor workflow.

Downloads last month: 71

Total file size:

7.94 GB

Collection including jamesdborin/Nemotron-Math-v2-prompt-only

Nemotron-Post-Training-v3 Prompt-Only

Collection

51 items • Updated 6 days ago