Dataset Viewer
problem
string | hints
sequence | answer
string | corrects
sequence | scores
float64 |
|---|---|---|---|---|
Find the sum of all integer bases $b>9$ for which $17_b$ is a divisor of $97_b.$ | ["\n <note>\n <description>Any base‐representation of an integer in base b can be converted to(...TRUNCATED) | 70 | [
0,
1,
0,
0,
0,
0,
0,
1
] | 0.25 |
"In $\\triangle ABC$ points $D$ and $E$ lie on $\\overline{AB}$ so that $AD < AE < AB$, while points(...TRUNCATED) | ["\n <note>\n <description>Use the reflection property of a line segment: if a point P lies on a(...TRUNCATED) | 588 | [
0,
0,
0,
0,
0,
0,
0,
1
] | 0.125 |
"The $9$ members of a baseball team went to an ice-cream parlor after their game. Each player had a (...TRUNCATED) | ["\n <note>\n <description>When distributing n distinct objects into k distinct boxes with no em(...TRUNCATED) | 16 | [
0,
1,
0,
0,
0,
0,
0,
0
] | 0.125 |
"Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $1(...TRUNCATED) | ["\n <note>\n <description>Use the discriminant test for quadratic equations in two variables: f(...TRUNCATED) | 117 | [
0,
0,
0,
0,
1,
0,
0,
0
] | 0.125 |
"There are $8!= 40320$ eight-digit positive integers that use each of the digits $1, 2, 3, 4, 5, 6, (...TRUNCATED) | ["\n <note>\n <description>When a problem involves arranging a set of distinct objects into a se(...TRUNCATED) | 279 | [
0,
0,
0,
0,
0,
0,
0,
0
] | 0 |
"An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the(...TRUNCATED) | ["\n <note>\n <description>In a tangential quadrilateral (one with an incircle), the sums of the(...TRUNCATED) | 504 | [
0,
0,
0,
0,
0,
0,
0,
0
] | 0 |
"The twelve letters $A$,$B$,$C$,$D$,$E$,$F$,$G$,$H$,$I$,$J$,$K$, and $L$ are randomly grouped into s(...TRUNCATED) | ["\n <note>\n <description>When selecting items at random from a finite set, the total number of(...TRUNCATED) | 821 | [
0,
0,
0,
0,
0,
0,
0,
0
] | 0 |
"Let $k$ be a real number such that the system \\begin{align*} &|25 + 20i - z| = 5 \\ &|z - 4 - k| =(...TRUNCATED) | ["\n <note>\n <description>Interpret the modulus |w – a| as the distance from a point w to a f(...TRUNCATED) | 77 | [
0,
0,
1,
0,
0,
0,
0,
0
] | 0.125 |
"The parabola with equation $y = x^2 - 4$ is rotated $60^\\circ$ counterclockwise around the origin.(...TRUNCATED) | ["\n <note>\n <description>When a curve is rotated about the origin by an angle θ, its parametr(...TRUNCATED) | 62 | [
0,
0,
0,
0,
0,
0,
0,
0
] | 0 |
"The $27$ cells of a $3 \\times 9$ grid are filled in using the numbers $1$ through $9$ so that each(...TRUNCATED) | ["\n <note>\n <description>Use the Fundamental Counting Principle to multiply the number of choi(...TRUNCATED) | 81 | [
0,
0,
0,
0,
0,
0,
0,
0
] | 0 |
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