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The dataset generation failed because of a cast error
Error code: DatasetGenerationCastError
Exception: DatasetGenerationCastError
Message: An error occurred while generating the dataset
All the data files must have the same columns, but at some point there are 3 new columns ({'ks', 'num_samples', 'pass_at_ks'}) and 9 missing columns ({'stopped_early', 'num_generations', 'num_correct', 'accuracy', 'question_idx', 'per_question_bools', 'sample', 'generations_actually_run', 'idx'}).
This happened while the json dataset builder was generating data using
hf://datasets/adimnaku/qwen3_4b_polaris_full/summary.json (at revision bf71012ca80f35996b2ee661b447e08fa8bad352), [/tmp/hf-datasets-cache/medium/datasets/45885713401576-config-parquet-and-info-adimnaku-qwen3_4b_polaris-79fd9023/hub/datasets--adimnaku--qwen3_4b_polaris_full/snapshots/bf71012ca80f35996b2ee661b447e08fa8bad352/question_results.jsonl (origin=hf://datasets/adimnaku/qwen3_4b_polaris_full@bf71012ca80f35996b2ee661b447e08fa8bad352/question_results.jsonl), /tmp/hf-datasets-cache/medium/datasets/45885713401576-config-parquet-and-info-adimnaku-qwen3_4b_polaris-79fd9023/hub/datasets--adimnaku--qwen3_4b_polaris_full/snapshots/bf71012ca80f35996b2ee661b447e08fa8bad352/summary.json (origin=hf://datasets/adimnaku/qwen3_4b_polaris_full@bf71012ca80f35996b2ee661b447e08fa8bad352/summary.json)]
Please either edit the data files to have matching columns, or separate them into different configurations (see docs at https://hf.co/docs/hub/datasets-manual-configuration#multiple-configurations)
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1887, in _prepare_split_single
writer.write_table(table)
File "/usr/local/lib/python3.12/site-packages/datasets/arrow_writer.py", line 674, in write_table
pa_table = table_cast(pa_table, self._schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2272, in table_cast
return cast_table_to_schema(table, schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2218, in cast_table_to_schema
raise CastError(
datasets.table.CastError: Couldn't cast
ks: list<item: int64>
child 0, item: int64
num_samples: int64
pass_at_ks: struct<1: double, 3: double, 5: double, 10: double>
child 0, 1: double
child 1, 3: double
child 2, 5: double
child 3, 10: double
to
{'idx': Value('int64'), 'question_idx': Value('int64'), 'sample': {'idx': Value('int64'), 'question_idx': Value('int64'), 'question': Value('string'), 'answer': Value('string'), 'environment_feedback_level': Value('string'), 'solution': Value('string')}, 'num_correct': Value('int64'), 'num_generations': Value('int64'), 'generations_actually_run': Value('int64'), 'stopped_early': Value('bool'), 'accuracy': Value('float64'), 'per_question_bools': List(Value('bool'))}
because column names don't match
During handling of the above exception, another exception occurred:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1347, in compute_config_parquet_and_info_response
parquet_operations = convert_to_parquet(builder)
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 980, in convert_to_parquet
builder.download_and_prepare(
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 884, in download_and_prepare
self._download_and_prepare(
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 947, in _download_and_prepare
self._prepare_split(split_generator, **prepare_split_kwargs)
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1736, in _prepare_split
for job_id, done, content in self._prepare_split_single(
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1889, in _prepare_split_single
raise DatasetGenerationCastError.from_cast_error(
datasets.exceptions.DatasetGenerationCastError: An error occurred while generating the dataset
All the data files must have the same columns, but at some point there are 3 new columns ({'ks', 'num_samples', 'pass_at_ks'}) and 9 missing columns ({'stopped_early', 'num_generations', 'num_correct', 'accuracy', 'question_idx', 'per_question_bools', 'sample', 'generations_actually_run', 'idx'}).
This happened while the json dataset builder was generating data using
hf://datasets/adimnaku/qwen3_4b_polaris_full/summary.json (at revision bf71012ca80f35996b2ee661b447e08fa8bad352), [/tmp/hf-datasets-cache/medium/datasets/45885713401576-config-parquet-and-info-adimnaku-qwen3_4b_polaris-79fd9023/hub/datasets--adimnaku--qwen3_4b_polaris_full/snapshots/bf71012ca80f35996b2ee661b447e08fa8bad352/question_results.jsonl (origin=hf://datasets/adimnaku/qwen3_4b_polaris_full@bf71012ca80f35996b2ee661b447e08fa8bad352/question_results.jsonl), /tmp/hf-datasets-cache/medium/datasets/45885713401576-config-parquet-and-info-adimnaku-qwen3_4b_polaris-79fd9023/hub/datasets--adimnaku--qwen3_4b_polaris_full/snapshots/bf71012ca80f35996b2ee661b447e08fa8bad352/summary.json (origin=hf://datasets/adimnaku/qwen3_4b_polaris_full@bf71012ca80f35996b2ee661b447e08fa8bad352/summary.json)]
Please either edit the data files to have matching columns, or separate them into different configurations (see docs at https://hf.co/docs/hub/datasets-manual-configuration#multiple-configurations)Need help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
idx int64 | question_idx int64 | sample dict | num_correct int64 | num_generations int64 | generations_actually_run int64 | stopped_early bool | accuracy float64 | per_question_bools list |
|---|---|---|---|---|---|---|---|---|
4 | 24,565 | {
"idx": 4,
"question_idx": 24565,
"question": "A school has 2400 students, each student has 5 classes every day, each teacher teaches 4 classes every day, and each class is taught by one teacher for 30 students. How many teachers are there in the school?",
"answer": "100",
"environment_feedback_level": "full... | 1 | 64 | 1 | true | 0.015625 | [
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1 | 6,539 | {
"idx": 1,
"question_idx": 6539,
"question": "Jori has 3 gallons of distilled water. She uses 5/4 gallons in the first science experiment and 1/3 gallon in a second experiment. How much distilled water does she have left after both experiments?",
"answer": "\\frac{17}{12}",
"environment_feedback_level": "ful... | 1 | 64 | 1 | true | 0.015625 | [
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20 | 29,969 | {
"idx": 20,
"question_idx": 29969,
"question": "Given data: $2$, $5$, $7$, $9$, $11$, $8$, $7$, $8$, $10$, the $80$th percentile is ______.",
"answer": "10",
"environment_feedback_level": "full_solution",
"solution": "N/A"
} | 1 | 64 | 1 | true | 0.015625 | [
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32 | 13,013 | {
"idx": 32,
"question_idx": 13013,
"question": "In right triangle $DEF$, $DE=15$, $DF=9$, and $EF=12$ units. What is the distance from $F$ to the midpoint of segment $DE$?",
"answer": "7.5",
"environment_feedback_level": "full_solution",
"solution": "N/A"
} | 1 | 64 | 1 | true | 0.015625 | [
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3 | 30,269 | {
"idx": 3,
"question_idx": 30269,
"question": "The stem-and-leaf plot shows the number of minutes and seconds of one ride on each of the $17$ top-rated roller coasters in the world. In the stem-and-leaf plot, $2 \\ 20$ represents $2$ minutes, $20$ seconds, which is the same as $140$ seconds. What is the median o... | 1 | 64 | 1 | true | 0.015625 | [
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16 | 13,698 | {
"idx": 16,
"question_idx": 13698,
"question": "How many four-digit numbers can be formed using three 1s, two 2s, and five 3s?",
"answer": "71",
"environment_feedback_level": "full_solution",
"solution": "N/A"
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31 | 32,133 | {
"idx": 31,
"question_idx": 32133,
"question": "Three not necessarily integer numbers are given. If each of these numbers is increased by 1, the product of the numbers also increases by 1. If each of these numbers is increased by 2, their product also increases by 2. Find these numbers.",
"answer": "-1",
"en... | 1 | 64 | 1 | true | 0.015625 | [
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12 | 23,172 | {
"idx": 12,
"question_idx": 23172,
"question": "Let $ABCD$ be an isosceles trapezoid with bases $AB=92$ and $CD=19$. Suppose $AD=BC=x$ and a circle with center on $\\overline{AB}$ is tangent to segments $\\overline{AD}$ and $\\overline{BC}$. If $m$ is the smallest possible value of $x$, then $m^2$=\n$\\text{(A) ... | 1 | 64 | 1 | true | 0.015625 | [
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25 | 48,930 | {
"idx": 25,
"question_idx": 48930,
"question": "There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:\n - Each person has a unique name: `Arnold`, `Eric`, `... | 1 | 64 | 1 | true | 0.015625 | [
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0 | 22,679 | {
"idx": 0,
"question_idx": 22679,
"question": "Kristýna chose a certain odd natural number divisible by three. Jakub and David then examined triangles with a perimeter in millimeters equal to the number chosen by Kristýna, where the sides have lengths in millimeters expressed as mutually distinct integers.\n\nJa... | 1 | 64 | 1 | true | 0.015625 | [
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14 | 9,818 | {
"idx": 14,
"question_idx": 9818,
"question": "Given the function $f(x)=( \\frac {1}{3})^{x}$, the sum of the first $n$ terms of the geometric sequence $\\{a\\_n\\}$ is $f(n)-c$, and the first term of the sequence $\\{b\\_n\\}_{b\\_n > 0}$ is $c$. The sum of the first $n$ terms, $S\\_n$, satisfies $S\\_n-S_{n-1}... | 1 | 64 | 1 | true | 0.015625 | [
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34 | 4,589 | {
"idx": 34,
"question_idx": 4589,
"question": "Vasya wrote twenty threes in a row on a board. By placing \"+\" signs between some of them, Vasya found that the sum equals 600. How many plus signs did Vasya place?",
"answer": "9",
"environment_feedback_level": "full_solution",
"solution": "N/A"
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37 | 2,903 | {
"idx": 37,
"question_idx": 2903,
"question": "Three positive reals \\( x \\), \\( y \\), and \\( z \\) are such that\n\\[\n\\begin{array}{l}\nx^{2}+2(y-1)(z-1)=85 \\\\\ny^{2}+2(z-1)(x-1)=84 \\\\\nz^{2}+2(x-1)(y-1)=89\n\\end{array}\n\\]\nCompute \\( x + y + z \\).",
"answer": "18",
"environment_feedback_leve... | 1 | 64 | 1 | true | 0.015625 | [
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35 | 49,810 | {
"idx": 35,
"question_idx": 49810,
"question": "Jonathan discovers that his ideal match is Sara Lark. To increase his chances of finding a girlfriend, he is open to dating any girl whose name is an anagram of \"Sara Lark,\" provided that the name includes both a first and last name with at least one letter each.... | 1 | 64 | 1 | true | 0.015625 | [
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17 | 11,562 | {
"idx": 17,
"question_idx": 11562,
"question": "Find the smallest natural number ending in the digit 2 such that it doubles when this digit is moved to the beginning.",
"answer": "105263157894736842",
"environment_feedback_level": "full_solution",
"solution": "N/A"
} | 1 | 64 | 1 | true | 0.015625 | [
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26 | 2,628 | {
"idx": 26,
"question_idx": 2628,
"question": "For a real number $x$ , let $f(x)=\\int_0^{\\frac{\\pi}{2}} |\\cos t-x\\sin 2t|\\ dt$ .\n\n(1) Find the minimum value of $f(x)$ .\n\n(2) Evaluate $\\int_0^1 f(x)\\ dx$ .\n\n*2011 Tokyo Institute of Technology entrance exam, Problem 2*",
"answer": "\\frac{1}{4}... | 1 | 64 | 1 | true | 0.015625 | [
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13 | 34,527 | {
"idx": 13,
"question_idx": 34527,
"question": "3. As shown in Figure 4, the parabola $y=a x^{2}+b x-3$ intersects the $x$-axis at points $A$ and $B$, and intersects the $y$-axis at point $C$, and $O B=O C=3 O A$. The line $y=-\\frac{1}{3} x+1$ intersects the $y$-axis at point $D$, and $E$ is the vertex of the p... | 1 | 64 | 1 | true | 0.015625 | [
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40 | 15,774 | {
"idx": 40,
"question_idx": 15774,
"question": "The expression $\\lfloor x\\rfloor$ denotes the greatest integer less than or equal to $x$. Find the value of $$\\left\\lfloor\\frac{2002!}{2001!+2000!+1999!+\\cdots+1!}\\right\\rfloor.$$",
"answer": "2000",
"environment_feedback_level": "full_solution",
"sol... | 1 | 64 | 1 | true | 0.015625 | [
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33 | 29,899 | {
"idx": 33,
"question_idx": 29899,
"question": "Given that $\\{a_n\\}$ is a geometric sequence with a common ratio of $q$, and $a_m$, $a_{m+2}$, $a_{m+1}$ form an arithmetic sequence.\n\n(Ⅰ) Find the value of $q$; \n(Ⅱ) Let the sum of the first $n$ terms of the sequence $\\{a_n\\}$ be $S_n$. Determine whether $... | 1 | 64 | 1 | true | 0.015625 | [
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11 | 44,275 | {
"idx": 11,
"question_idx": 44275,
"question": "A QR-like code consists of a $5 \\times 5$ grid with either black or white squares. Every valid code must contain at least one square of each color. A code is termed $\\textit{symmetric}$ if it looks the same when rotated by multiples of $90^\\circ$ around the grid... | 1 | 64 | 1 | true | 0.015625 | [
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29 | 52,668 | {
"idx": 29,
"question_idx": 52668,
"question": "13. (GDR 1) Find whether among all quadrilaterals whose interiors lie inside a semicircle of radius \\( r \\) there exists one (or more) with maximal area. If so, determine their shape and area.",
"answer": "\\dfrac{3\\sqrt{3}}{4} r^2",
"environment_feedback_le... | 1 | 64 | 1 | true | 0.015625 | [
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15 | 35,592 | {
"idx": 15,
"question_idx": 35592,
"question": "26. In the diagram below, $A B C D$ is a cyclic quadrilateral with $A B=A C$. The line $F G$ is tangent to the circle at the point $C$, and is parallel to $B D$. If $A B=6$ and $B C=4$, find the value of $3 A E$.",
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49 | 1,353 | {
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"question": "Given $|\\vec{a}|=1$, $|\\vec{b}|=6$, and $\\vec{a}\\cdot(\\vec{b}-\\vec{a})=2$, calculate the angle between $\\vec{a}$ and $\\vec{b}$.",
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19 | 29,832 | {
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2 | 18,904 | {
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"question": "Two spheres touch the plane of triangle \\( A B C \\) at points \\( A \\) and \\( B \\) and are located on opposite sides of this plane. The sum of the radii of these spheres is 11, and the distance between their centers is \\( \\sqrt{481} \\). The center of a third... | 1 | 64 | 1 | true | 0.015625 | [
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6 | 50,155 | {
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"question": "The modified Fibonacci sequence $F_n$ is defined by $F_0 = 4, F_1 = 3$, and $F_n = F_{n-1} + F_{n-2}$ for $n \\geq 2$. Find the units digit of $F_{F_{10}}$.",
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39 | 21,116 | {
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"question": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\frac{2\\pi}{3}} \\frac{\\cos^2 x \\, dx}{(1 + \\cos x + \\sin x)^2}\n$$",
"answer": "\\frac{\\sqrt{3}}{2} - \\ln 2",
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18 | 37,422 | {
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"question": "Do either (1) or (2):\n\n(1) Let \\( a_i = \\sum_{n=0}^{\\infty} \\frac{x^{3n+i}}{(3n+i)!} \\). Prove that \\( a_0^3 + a_1^3 + a_2^3 - 3 a_0 a_1 a_2 = 1 \\).\n\n(2) Let \\( O \\) be the origin, \\( \\lambda \\) a positive real number, \\( C \\) be the conic \\( ax^... | 1 | 64 | 1 | true | 0.015625 | [
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23 | 24,772 | {
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"question": "We marked the midpoints of all sides and diagonals of a regular 1976-sided polygon. What is the maximum number of these points that can lie on a single circle?",
"answer": "1976",
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51 | 42,140 | {
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58 | 9,053 | {
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"question": "In $\\triangle ABC$, $\\angle A=55^\\circ$, $\\angle C=75^\\circ$, $D$ is on side $\\overline{AB}$ and $E$ is on side $\\overline{BC}$. If $DB=BE$, then $\\angle{BED} =$",
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50 | 38,511 | {
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"question": "\n3. Let $P(x)=x^{2}+\\frac{1}{2} x+b$ and $Q(x)=x^{2}+c x+d$ be two polynomials with real coefficients such that $P(x) Q(x)=Q(P(x))$ for all real $x$. Find all the real roots of $P(Q(x))=0$.",
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22 | 17,214 | {
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"question": "For 155 boxes containing red, yellow, and blue balls, there are three classification methods: for each color, classify the boxes with the same number of balls of that color into one category. If every natural number from 1 to 30 is the number of boxes in some categ... | 1 | 64 | 1 | true | 0.015625 | [
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52 | 42,353 | {
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"question": "There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:\n - Each person has a unique name: `Peter`, `Bob`, `Ar... | 1 | 64 | 1 | true | 0.015625 | [
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65 | 2,082 | {
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"question": "Given that the random variable $ξ$ follows a normal distribution $N(1,σ^{2})$, and $P(ξ\\leqslant 4)=0.79$, determine the value of $P(-2\\leqslant ξ\\leqslant 1)$.",
"answer": "0.29",
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55 | 47,279 | {
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"question": "There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:\n - Each person has a unique name: `Bob`, `Arnold`, `P... | 1 | 64 | 1 | true | 0.015625 | [
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53 | 36,742 | {
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"question": "Given 100 distinct prime numbers \\( p_{1}, p_{2}, \\cdots, p_{100} \\), let \\( N=p_{1}^{2}+p_{2}^{2}+\\cdots+p_{100}^{2} \\). What is the remainder when \\( N \\) is divided by 3?",
"answer": "1",
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62 | 38,677 | {
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"question": "There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:\n - Each person has a unique name: `Alice`, `Arnold`, ... | 1 | 64 | 1 | true | 0.015625 | [
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57 | 9,884 | {
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"question": "On the hypotenuse $AB$ of the right triangle $ABC$, points $M$ and $N$ are taken such that $BC = BM$ and $AC = AN$.\n\nProve that $\\angle MCN = 45^\\circ$.",
"answer": "45",
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"solution": "N/A"
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54 | 18,934 | {
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"question": "In triangle \\(ABC\\), the altitude \\(BM\\), the angle bisector \\(BN\\), and the median \\(BL\\) are drawn. It is known that \\(AM = MN = NL\\). Find the tangent of angle \\(A\\) of this triangle.",
"answer": "\\sqrt{7}",
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42 | 50,697 | {
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"question": "A table tennis club hosts a series of doubles matches following several rules:\n1. Each player belongs to two pairs at most.\n2. Every two distinct pairs play one game against each other at most.\n3. Players in the same pair do not play against each other when they... | 1 | 64 | 1 | true | 0.015625 | [
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41 | 597 | {
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"question": "In an acute-angled triangle \\( A B C \\) on a plane, circles with diameters \\( A B \\) and \\( A C \\) intersect the altitude from \\( C \\) at points \\( M \\) and \\( N \\), and intersect the altitude from \\( B \\) at points \\( P \\) and \\( Q \\). Prove that t... | 1 | 64 | 1 | true | 0.015625 | [
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69 | 31,683 | {
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"question": "Alina and Masha wanted to create an interesting version of the school tour of the Olympiad. Masha proposed several problems and rejected every second problem of Alina (exactly half). Alina also proposed several problems and only accepted every third problem of Mash... | 1 | 64 | 1 | true | 0.015625 | [
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7 | 52,702 | {
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"question": "8. For any real number $x$, $[x]$ represents the greatest integer not exceeding $x$. When $0 \\leqslant x \\leqslant 100$, the range of $f(x)=[3 x]+[4 x]+[5 x]+[6 x]$ contains $\\qquad$ different integers.",
"answer": "1201",
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68 | 47,223 | {
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"question": "283 Find the unit digit of $\\left(\\frac{5+\\sqrt{21}}{2}\\right)^{2010}$.\n\nTranslate the above text into English, please keep the original text's line breaks and format, and output the translation result directly.",
"answer": "7",
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73 | 11,664 | {
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"question": "Poplar, willow, locust, birch, and phoenix trees are planted in a row, with a distance of 1 meter between any two adjacent trees. The distance between the poplar and both the willow and locust trees is equal. The distance between the birch and both the poplar and l... | 1 | 64 | 1 | true | 0.015625 | [
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44 | 47,687 | {
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48 | 37,188 | {
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"question": "Let \\( x, y, z \\) be distinct positive integers such that \\( xyz \\mid (xy-1)(yz-1)(zx-1) \\). Find all possible values of \\( x, y, z \\).",
"answer": "(2,3,5)",
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59 | 14,559 | {
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79 | 40,364 | {
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"question": "A filmmaker releases a music video that is 4 minutes long. A dedicated viewer watches the video 5 times, pausing every 30 seconds to analyze each frame for hidden meanings and symbolism. If it takes the viewer an additional 2 minutes to analyze each paused frame, h... | 1 | 64 | 1 | true | 0.015625 | [
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77 | 374 | {
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"question": "There are 200 candies. What is the minimum number of schoolchildren that these candies can be distributed to so that, no matter how the candies are distributed, there are always at least two schoolchildren who receive the same number of candies (possibly none)?",
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71 | 32,686 | {
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"question": "Let segments $KN,KL$ be tangent to circle $C$ at points $N,L$ , respectively. $M$ is a point on the extension of the segment $KN$ and $P$ is the other meet point of the circle $C$ and the circumcircle of $\\triangle KLM$ . $Q$ is on $ML$ such that... | 1 | 64 | 1 | true | 0.015625 | [
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38 | 45,605 | {
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"question": "There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:\n - Each person has a unique name: `Eric`, `Peter`, `A... | 1 | 64 | 2 | true | 0.015625 | [
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82 | 34,293 | {
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"question": "The numbers $1447$, $1005$ and $1231$ have something in common: each is a $4$-digit number beginning with $1$ that has exactly two identical digits. How many such numbers are there?\n",
"answer": "432",
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81 | 39,658 | {
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"question": "Jar #1 contains five red marbles, three blue marbles, and one green marble. Jar #2 contains five blue marbles, three green marbles, and one red marble. Jar #3 contains five green marbles, three red marbles, and one blue marble.\n\nYou randomly select one marble fro... | 1 | 64 | 1 | true | 0.015625 | [
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8 | 17,522 | {
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"question": "The quadrilateral \\(ABCD\\) is inscribed in a circle. It is known that \\(BC = CD, \\angle BCA = 64^\\circ,\\) and \\(\\angle ACD = 70^\\circ\\). A point \\(O\\) is marked on the segment \\(AC\\) such that \\(\\angle ADO = 32^\\circ\\). What is the measure of the a... | 1 | 64 | 2 | true | 0.015625 | [
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56 | 14,847 | {
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"question": "Given that \\(2 \\cdot 50N\\) is an integer and its representation in base \\(b\\) is 777, find the smallest positive integer \\(b\\) such that \\(N\\) is a fourth power of an integer.",
"answer": "18",
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83 | 20,969 | {
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"question": "Andrea flips a fair coin repeatedly, continuing until she either flips two heads in a row (the sequence $H H$ ) or flips tails followed by heads (the sequence $T H$ ). What is the probability that she will stop after flipping $H H$ ?",
"answer": "1/4",
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74 | 27,563 | {
"idx": 74,
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"question": "Determine the prime numbers $p$ for which the number $a = 7^p - p - 16$ is a perfect square.\n\nLucian Petrescu",
"answer": "3",
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86 | 38,358 | {
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"question": "During training target practice, each soldier fired 10 times. One of them was successful and scored 90 points in total. How many times did he score 7 points if he scored 10 points 4 times and the results of the remaining shots were 7, 8, and 9 points? Note that the... | 1 | 64 | 1 | true | 0.015625 | [
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80 | 3,080 | {
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"question": "In the quadrilateral \\(ABCD\\), it is known that \\(AB = BD\\) and \\(\\angle ABD = \\angle DBC\\), with \\(\\angle BCD = 90^\\circ\\). A point \\(E\\) on segment \\(BC\\) is such that \\(AD = DE\\). What is the length of segment \\(BD\\), given that \\(BE = 7\\) a... | 1 | 64 | 1 | true | 0.015625 | [
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9 | 52,815 | {
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"question": "The score on a certain 150-point test varies directly with the square of the time a student spends preparing for the test. If a student receives 90 points on a test for which she spent 2 hours preparing, what score would she receive on the next test if she spent 3 h... | 1 | 64 | 7 | true | 0.015625 | [
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87 | 51,951 | {
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"question": "There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:\n - Each person has a unique name: `Eric`, `Arnold`, `... | 1 | 64 | 1 | true | 0.015625 | [
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85 | 29,434 | {
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"question": "In the diagram, the rectangular wire grid contains 15 identical squares. The length of the rectangular grid is 10. What is the length of wire needed to construct the grid?",
"answer": "76",
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"solution": "N/A"
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91 | 28,490 | {
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"question": "Amy, Beth, and Jo listen to four different songs and discuss which ones they like. No song is liked by all three. Furthermore, for each of the three pairs of the girls, there is at least one song liked by those two girls but disliked by the third. In how many diffe... | 1 | 64 | 1 | true | 0.015625 | [
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89 | 5,989 | {
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"question": "In a magic square, the sum of the three entries in any row, column, or diagonal is the same value. The figure below shows four of the entries of a magic square. Find $x$.\n[asy]\nsize(2cm);\nfor (int i=0; i<=3; ++i) draw((i,0)--(i,3)^^(0,i)--(3,i));\nlabel(\"$x$\",(... | 1 | 64 | 1 | true | 0.015625 | [
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93 | 21,408 | {
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"question": "Given that $a > 0$ and $b > 0$, they satisfy the equation $3a + b = a^2 + ab$. Find the minimum value of $2a + b$.",
"answer": "3 + 2\\sqrt{2}",
"environment_feedback_level": "full_solution",
"solution": "N/A"
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94 | 46,278 | {
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"question": "4. (8 points) A cruise ship travels from upstream location $A$ to downstream location $B$ in 1 hour. On the return trip, the ship doubles its speed and still takes 1 hour. Therefore, if the cruise ship also doubles its speed when departing from $A$, it will take $\... | 1 | 64 | 3 | true | 0.015625 | [
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64 | 7,660 | {
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"question": "Brian writes down four integers $w > x > y > z$ whose sum is $44$. The pairwise positive differences of these numbers are $1, 3, 4, 5, 6,$ and $9$. What is the sum of the possible values for $w$?",
"answer": "31",
"environment_feedback_level": "full_solution",
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97 | 22,350 | {
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"question": "Triangle $ ABC$ has fixed vertices $ B$ and $ C$ , so that $ BC \\equal{} 2$ and $ A$ is variable. Denote by $ H$ and $ G$ the orthocenter and the centroid, respectively, of triangle $ ABC$ . Let $ F\\in(HG)$ so that $ \\frac {HF}{FG} \\equal{} 3$ ... | 1 | 64 | 1 | true | 0.015625 | [
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99 | 39,120 | {
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"question": "2. Given the functions $y=2 \\cos \\pi x(0 \\leqslant x \\leqslant 2)$ and $y=2(x \\in$ $R$ ) whose graphs enclose a closed plane figure. Then the area of this figure is $\\qquad$ .",
"answer": "4",
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100 | 11,965 | {
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"question": "Let $f(x)=e^{x}$, and $f(x)=g(x)-h(x)$, where $g(x)$ is an even function, and $h(x)$ is an odd function. If there exists a real number $m$ such that the inequality $mg(x)+h(x)\\geqslant 0$ holds for $x\\in [-1,1]$, determine the minimum value of $m$.",
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88 | 2,487 | {
"idx": 88,
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"question": "Find all functions $f : R \\to R$ satisfying the conditions:\n1. $f (x + 1) \\ge f (x) + 1$ for all $x \\in R$ \n2. $f (x y) \\ge f (x)f (y)$ for all $x, y \\in R$ ",
"answer": "f(x)=x",
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95 | 18,453 | {
"idx": 95,
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"question": "The circles \\( K_1 \\) and \\( K_2 \\) share a common point \\( A \\). Three lines are drawn through point \\( A \\): two passing through the centers of the circles and intersecting them at points \\( B \\) and \\( C \\), and the third line is parallel to \\( BC \... | 1 | 64 | 1 | true | 0.015625 | [
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76 | 19,056 | {
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"question": "Suppose that $x$ and $y$ are complex numbers such that $x+y=1$ and that $x^{20}+y^{20}=20$. Find the sum of all possible values of $x^{2}+y^{2}$.",
"answer": "-90",
"environment_feedback_level": "full_solution",
"solution": "N/A"
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96 | 47,920 | {
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"question": "2. The product of five numbers is not equal to zero. Each of these numbers was decreased by one, yet their product remained unchanged. Provide an example of such numbers.",
"answer": "2",
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"solution": "N/A"
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105 | 10,531 | {
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"question": "Given that \\( x \\) is a positive real number and \\( x \\cdot 3^{x} = 3^{18} \\). If \\( k \\) is a positive integer and \\( k < x < k + 1 \\), find the value of \\( k \\).",
"answer": "15",
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"solution": "N/A"
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92 | 10,486 | {
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"question": "On the complex plane, consider the parallelogram formed by the points 0, $z,$ $\\frac{1}{z},$ and $z + \\frac{1}{z}$ where the area of the parallelogram is $\\frac{24}{25}.$ If the real part of $z$ is positive, determine the smallest possible value of $\\left| z + ... | 1 | 64 | 1 | true | 0.015625 | [
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109 | 17,756 | {
"idx": 109,
"question_idx": 17756,
"question": "Which of the following is the sum of three consecutive integers?\n(A) 17\n(B) 11\n(C) 25\n(D) 21\n(E) 8",
"answer": "21",
"environment_feedback_level": "full_solution",
"solution": "N/A"
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110 | 10,623 | {
"idx": 110,
"question_idx": 10623,
"question": "\\(A, B, C\\) are three prime numbers less than 20, and \\(A + B + C = 30\\). Find these three prime numbers.",
"answer": "2,11,17",
"environment_feedback_level": "full_solution",
"solution": "N/A"
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98 | 19,480 | {
"idx": 98,
"question_idx": 19480,
"question": "Given a machine that transforms a positive integer \\( N \\) based on the rule: if \\( N = 7 \\), the machine outputs \\( 3 \\times 7 + 1 = 22 \\).\n\nBy inputting the result back into the machine and repeating five times, the output sequence is:\n\\[ 7 \\rightarro... | 1 | 64 | 1 | true | 0.015625 | [
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104 | 27,329 | {
"idx": 104,
"question_idx": 27329,
"question": "A sequence $(a_n)$ of positive integers is defined by $a_0=m$ and $a_{n+1}= a_n^5 +487$ for all $n\\ge 0$ . \nFind all positive integers $m$ such that the sequence contains the maximum possible number of perfect squares.",
"answer": "9",
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75 | 9,976 | {
"idx": 75,
"question_idx": 9976,
"question": "Given a function \\( f : \\mathbf{R} \\rightarrow \\mathbf{R} \\) that satisfies the following conditions:\n1. For all \\( x, y \\in \\mathbf{R} \\), \\( f(x) + f(y) + 1 \\geqslant f(x + y) \\geqslant f(x) + f(y) \\).\n2. For all \\( x \\in [0,1) \\), \\( f(0) \\geq... | 1 | 64 | 2 | true | 0.015625 | [
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28 | 24,956 | {
"idx": 28,
"question_idx": 24956,
"question": "From the set of numbers \\( 1, 2, 3, 4, \\cdots, 1982 \\), remove some numbers so that in the remaining numbers, no number is equal to the product of any two other numbers. What is the minimum number of numbers that need to be removed to achieve this? How can this ... | 1 | 64 | 6 | true | 0.015625 | [
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108 | 4,378 | {
"idx": 108,
"question_idx": 4378,
"question": "Given the ratio of length $AD$ to width $AB$ of the rectangle is $4:3$ and $AB$ is 40 inches, determine the ratio of the area of the rectangle to the combined area of the semicircles.",
"answer": "\\frac{16}{3\\pi}",
"environment_feedback_level": "full_solution... | 1 | 64 | 1 | true | 0.015625 | [
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43 | 32,920 | {
"idx": 43,
"question_idx": 32920,
"question": "Given that the first term of a geometric sequence $\\{a\\_n\\}$ is $\\frac{3}{2}$, and the sum of the first $n$ terms is $S\\_n$, where $n \\in \\mathbb{N}^*$. Also, $-2S\\_2$, $S\\_3$, and $4S\\_4$ form an arithmetic sequence.\n\n1. Find the general term formula f... | 1 | 64 | 4 | true | 0.015625 | [
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107 | 12,972 | {
"idx": 107,
"question_idx": 12972,
"question": "Given that \\( F \\) is the right focus of the hyperbola \\( x^{2} - y^{2} = 1 \\), \\( l \\) is the right directrix of the hyperbola, and \\( A \\) and \\( B \\) are two moving points on the right branch of the hyperbola such that \\( A F \\perp B F \\). The proj... | 1 | 64 | 1 | true | 0.015625 | [
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118 | 9,249 | {
"idx": 118,
"question_idx": 9249,
"question": "How many natural numbers greater than 6 but less than 60 are relatively prime to 15?",
"answer": "29",
"environment_feedback_level": "full_solution",
"solution": "N/A"
} | 1 | 64 | 1 | true | 0.015625 | [
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101 | 49,707 | {
"idx": 101,
"question_idx": 49707,
"question": "2. How many six-digit numbers of the form $\\overline{a b c a c b}$ are divisible by 23?",
"answer": "42",
"environment_feedback_level": "full_solution",
"solution": "N/A"
} | 1 | 64 | 2 | true | 0.015625 | [
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120 | 12,065 | {
"idx": 120,
"question_idx": 12065,
"question": "In \\( \\triangle ABC \\), if \\( |\\overrightarrow{AB}| = 2 \\), \\( |\\overrightarrow{BC}| = 3 \\), and \\( |\\overrightarrow{CA}| = 4 \\), find the value of \\( \\overrightarrow{AB} \\cdot \\overrightarrow{BC} + \\overrightarrow{BC} \\cdot \\overrightarrow{CA} ... | 1 | 64 | 1 | true | 0.015625 | [
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47 | 52,394 | {
"idx": 47,
"question_idx": 52394,
"question": "The increasing sequence of positive integers $a_1, a_2, a_3, \\dots$ follows the recursive formula\n\\[a_{n + 2} = a_{n + 1} + a_n\\]\nfor all $n \\geq 1$. If $a_7 = 210$, determine $a_8$.",
"answer": "340",
"environment_feedback_level": "full_solution",
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113 | 48,455 | {
"idx": 113,
"question_idx": 48455,
"question": "4. 199 A car departs from point $O$ along a straight highway, maintaining a constant speed $v$. At the same time the car starts, a person on a bicycle departs from a point that is a distance $a$ from $O$ and a distance $b$ from the highway, aiming to deliver a let... | 1 | 64 | 2 | true | 0.015625 | [
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30 | 36,560 | {
"idx": 30,
"question_idx": 36560,
"question": "Let $n$ be a positive integer. Find the largest nonnegative real number $f(n)$ (depending on $n$ ) with the following property: whenever $a_1,a_2,...,a_n$ are real numbers such that $a_1+a_2+\\cdots +a_n$ is an integer, there exists some $i$ such that ... | 1 | 64 | 5 | true | 0.015625 | [
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123 | 30,901 | {
"idx": 123,
"question_idx": 30901,
"question": "Draw a tangent line MN to the circle $(x-2)^2+(y-2)^2=1$ at point N, where N is the point of tangency. If $|MN|=|MO|$ (where O is the origin), then the minimum value of $|MN|$ is \\_\\_\\_\\_\\_\\_.",
"answer": "\\frac{7\\sqrt{2}}{8}",
"environment_feedback_le... | 1 | 64 | 1 | true | 0.015625 | [
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121 | 46,114 | {
"idx": 121,
"question_idx": 46114,
"question": "Inside a circle with radius $6$ lie four smaller circles with centres $A,B,C$ and $D$ . The circles touch each other as shown. The point where the circles with centres $A$ and $C$ touch each other is the centre of the big circle. Calculate the area of qua... | 1 | 64 | 1 | true | 0.015625 | [
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117 | 31,397 | {
"idx": 117,
"question_idx": 31397,
"question": "A regular octahedron has side length $1$. A plane parallel to two of its opposite faces cuts the octahedron into the two congruent solids. The polygon formed by the intersection of the plane and the octahedron has area $\\frac {a\\sqrt {b}}{c}$, where $a$, $b$, an... | 1 | 64 | 1 | true | 0.015625 | [
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124 | 21,779 | {
"idx": 124,
"question_idx": 21779,
"question": "Please fold a long rope in half, then fold it in half again along the middle of the folded rope, and continue to fold it in half 5 times in total. Finally, cut the rope along the middle after it has been folded 5 times. At this point, the rope will be cut into ___... | 1 | 64 | 1 | true | 0.015625 | [
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128 | 14,059 | {
"idx": 128,
"question_idx": 14059,
"question": "Given a rectangle \\(ABCD\\), different points are chosen on two of its sides: five points on \\(AB\\) and six points on \\(BC\\). How many different triangles can be formed with vertices at the chosen points?",
"answer": "135",
"environment_feedback_level": "... | 1 | 64 | 1 | true | 0.015625 | [
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119 | 26,228 | {
"idx": 119,
"question_idx": 26228,
"question": "Consider a unit cube in a coordinate system with vertices $A(0,0,0)$, $A'(1,1,1)$, and other vertices placed accordingly. A regular octahedron has vertices placed at fractions $\\frac{1}{3}$ and $\\frac{2}{3}$ along the segments connecting $A$ with $A'$'s adjacent... | 1 | 64 | 1 | true | 0.015625 | [
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130 | 46,840 | {
"idx": 130,
"question_idx": 46840,
"question": "Alex is a politically moderate civil servant who organizes a community event to promote civil discourse on important topics. He plans to set up a series of discussion tables, each with a different topic. Alex orders 5 tables and places 8 chairs around each table f... | 1 | 64 | 1 | true | 0.015625 | [
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