evals-prompt-only
Collection
Prompt-only evaluation datasets with generic Doubleword batch request JSONL. • 4 items • Updated
custom_id stringlengths 12 12 | method stringclasses 1
value | url stringclasses 1
value | body dict |
|---|---|---|---|
27a6a176c38d | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Find the sum of all integer bases $b>9$ for which $17_b$ is a divisor of $97_b.$"
}
]
} |
c1f39ffa66e4 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "On $\\triangle ABC$ points $A, D, E$, and $B$ lie in that order on side $\\overline{AB}$ with $AD = 4$, $DE = 16$, $EB = 8$. Points $A, F, G$ and $C$ lie in that order on side $\\overline{AC}$ with $AF = 13$, $FG = 52$, and $GC = 26$.... |
1d9e0d2b7e20 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "The 9 members of a baseball team went to an ice-cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who cho... |
1a5067356e5c | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^2-xy-6y^2=0$."
}
]
} |
2b0413f7abb2 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "There are $8!= 40320$ eight-digit positive integers that use each of the digits 1, 2, 3, 4, 5, 6, 7, 8 exactly once. Let N be the number of these integers that are divisible by $22$. Find the difference between $N$ and 2025."
}
... |
c87f0c5135f1 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is $3$, and the area of the trapezoid is $72$. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq ... |
0addab1dd7e2 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "The twelve letters $A$,$B$,$C$,$D$,$E$,$F$,$G$,$H$,$I$,$J$,$K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and... |
94ab8888a47d | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Let $k$ be a real number such that the system\n\\begin{align*} |25+20i-z|&=5\\\\ |z-4-k|&=|z-3i-k| \\\\ \\end{align*}\nhas exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n},$ where... |
3528385d7501 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "The parabola with equation $y = x^2 - 4$ is rotated $60^\\circ$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a - \\sqrt{b}}{... |
d5c3dc404d6f | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "The $27$ cells of a $3 \\times 9$ grid are filled in using the numbers $1$ through $9$ so that each row contains $9$ different numbers, and each of the three $3 \\times 3$ blocks heavily outlined in the example below contains $9$ diff... |
057850181302 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "A piecewise linear function is defined by\n\\[f(x) = \\begin{cases} x & \\text{if } x \\in [-1, 1) \\\\ 2 - x & \\text{if } x \\in [1, 3)\\end{cases}\\]\nand $f(x + 4) = f(x)$ for all real numbers $x.$ The graph of $f(x)$ has the sawt... |
b2ac42b16439 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "The set of points in $3$-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities\n$$x-yz<y-zx<z-xy$$\nforms three disjoint convex regions. Exactly one of those regions has finite area. ... |
8c8bffcdcc50 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws $25$ more lines segments through the disk, drawing each segment by selecting two points at random on the perimet... |
6a53c69d773a | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Let $ABCDE$ be a convex pentagon with $AB=14$, $BC=7$, $CD=24$, $DE=13$, $EA=26$, and $\\angle B=\\angle E=60^{\\circ}$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expresse... |
8d54e4108214 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Let $N$ denote the numbers of ordered triples of positive integers $(a, b, c)$ such that $a, b, c \\le 3^6$ and $a^3 + b^3 + c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$."
}
]
} |
a0f21f676ab3 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Six points $A, B, C, D, E$ and $F$ lie in a straight line in that order. Suppose that $G$ is a point not on the line and that $AC = 26$, $BD = 22$, $CE = 31$, $DF = 33$, $AF = 73$, $CG = 40$, and $DG = 30$. Find the area of $\\triangl... |
2b7adcfcb612 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Find the sum of all positive integers $n$ such that $n+2$ divides the product $3(n+3)(n^2+9)$."
}
]
} |
b4440f3c8764 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Four unit squares form a $2\\times 2$ grid. Each of the $12$ unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has $2$ red sides and $2$ blue sides. One example is sh... |
5194aff55768 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "The product\n$$\\prod_{k=4}^{63} \\frac{\\log_k \\left(5^{k^2 - 1}\\right)}{\\log_{k+1} \\left(5^{k^2 - 4}\\right)} = \\frac{\\log_4 (5^{15})}{\\log_5 (5^{12})} \\cdot \\frac{\\log_5 (5^{24})}{\\log_6 (5^{21})} \\cdot \\frac{\\log_6 (... |
bb4f4a75bea2 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Suppose $\\triangle ABC$ has angles $\\angle BAC = 84^\\circ$, $\\angle ABC = 60^\\circ$, and $\\angle ACB = 36^\\circ$. Let $D$, $E$, and $F$ be the midpoints of sides $\\overline{BC}$, $\\overline{AC}$, and $\\overline{AB}$, respect... |
5302bc39e7f6 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Circle $\\omega_1$ with radius $6$ centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius $15$. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\o... |
b19ff77f8fa8 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Let $A$ be the set of positive integer divisors of $2025$. Let $B$ be a randomly selected subset of $A$. The probability that $B$ is a nonempty set with the property that the least common multiple of its elements is $2025$ is $\\frac{... |
59eb0940d0ee | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "From an unlimited supply of $1$-cent coins, $10$-cent coins, and $25$-cent coins, Silas wants to find a collection of coins that has a total value of $N$ cents, where $N$ is a positive integer. He uses the so-called \\textit{greedy al... |
70eb83eb94bf | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "There are $n$ values of $x$ in the interval $0 < x < 2\\pi$ where $f(x) = \\sin\\left(7\\pi \\cdot \\sin(5x)\\right) = 0$. For $t$ of these $n$ values of $x$, the graph of $y = f(x)$ is tangent to the $x$-axis. Find $n + t$."
}
... |
1d21228fa491 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $N$ be the number of subsets of the 16 chairs that could be selected. Find the remainder when ... |
3d5a2cc101b1 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Let $S$ be the set of vertices of a regular $24$-gon. Find the number of ways to draw $12$ segments of equal lengths so that each vertex in $S$ is an endpoint of exactly one of the $12$ segments."
}
]
} |
f9833a3e61be | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Let $A_1 A_2 A_3 \\ldots A_{11}$ be an $11$-sided non-convex simple polygon with the following properties:\n\n\\begin{itemize}\n\\item For every integer $2 \\le i \\le 10$, the area of $\\triangle A_i A_{1} A_{i+1}$ is equal to $1$.... |
95f19e24c3cc | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Let $x_1, x_2, x_3, \\ldots$ be a sequence of rational numbers defined by $x_1 = \\frac{25}{11}$ and\n$$x_{k+1} = \\frac{1}{3}\\left(x_k + \\frac{1}{x_k} - 1\\right)$$\nfor all $k \\ge 1$. Then $x_{2025}$ can be expressed as $\\frac{m... |
a2aa4b0b6507 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "Let $\\triangle ABC$ be a right triangle with $\\angle A = 90^\\circ$ and $BC = 38$. There exist points $K$ and $L$ inside the triangle such that\n$$AK = AL = BK = CL = KL = 14.$$\nThe area of the quadrilateral $BKLC$ can be expressed... |
cc500ca9e344 | POST | /v1/chat/completions | {
"model": "[MODEL]",
"messages": [
{
"role": "user",
"content": "There are exactly three positive real numbers $k$ such that the function\n$$f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x}$$\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $x... |
- Downloads last month
- 48