prompt listlengths 2 2 | metadata dict |
|---|---|
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"If the ratio of the areas of two similar polygons is 4:9, what is the ratio of their perimeters? Express your answer as a ratio.",
"An alloy weighing 48 ounces has a certain percentage of gold. To create an alloy that is 40% gold, 12 ounces of pure gold must be added. W... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given: $a$ and $b$ are opposite numbers, $c$ and $d$ are reciprocals. When $x=2$, find the value of the algebraic expression $\\left(cd\\right)^{2015}\\cdot x^{2}+\\left(a+b\\right)^{2015}$.",
"Cindy leaves school at the same time every day. If she cycles at 20 km/h, sh... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"There are ten more newborn elephants than baby hippos. An entire herd starts with some elephants and 35 hippos, and the female hippos, whose number is 5/7 of the total number of hippos, give birth to 5 new baby hippos each. There are altogether 315 animals. How many elephan... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given the lines $l_{1}$: $ax+3y+1=0$ and $l_{2}$: $x+\\left(a-2\right)y+a=0$, find the necessary and sufficient condition for $l_{1} \\parallel l_{2}$. Express your answer as a single value or condition.",
"For positive integers $n$, let $f(n)$ be the product of the dig... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Among $a$, $b$, $c$, $d$, $e$—a total of $5$ people—select $1$ as the team leader and $1$ as the deputy team leader, but $a$ cannot be the deputy team leader. The total number of different selection methods is ______.",
"Let \\\\(f(x)= \\sqrt {3}\\sin 3x+\\cos 3x\\\\), ... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Mary owns a store and sells three types of items: Item A has a cost price of $180, Item B has a cost price of $220, and Item C has a cost price of $130. She wants to sell Item A at a 15% profit, Item B at a 20% profit, and Item C at a 25% profit. Additionally, a 5% tax rate... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"A rectangle measures 8 cm in length and has a certain diagonal measurement. The perimeter of the rectangle is 46 cm. What is the length of the diagonal?",
"Given $|a-1|+(2+b)^2=0$, then $(a+b)^{2009}=$ ?",
"During a survey about whether high school students have eve... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"The function $f(x)=\\begin{cases}2-x, & x\\leqslant 0,\\\\ \\sqrt{4-x^2}, & 0 < x\\leqslant 2,\\end{cases}$, then the value of $\\int_{-2}^{2}f(x)dx$ is ______.",
"Amiyah is cutting some trees to build a cow shade. For every tree she cuts, she plants 5 new trees. If the... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"If some typists can type 48 letters in 20 minutes, then 30 typists working at the same rate can complete 216 letters in 1 hour. How many typists were in the initial group?",
"Calculate the value of $\\cos \\left( -\\frac{79\\pi}{6} \\right)$. Express your answer as a fr... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"At a certain point in the past, Shane was a multiple times older than Garret is now. Garret is currently 12. That point in the past was 20 years ago, and Shane is now 44 years old. How many times older was Shane than Garret's current age at that time?",
"What is the sma... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"The entire exterior of a solid $6 \\times 6 \\times 3$ rectangular prism is painted. Then, the prism is cut into $1 \\times 1 \\times 1$ cubes. How many of these cubes have no painted faces?",
"Simplify the following expression:\n\\[ \\frac{\\left(a b (x^{2}+y^{2}) + x ... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"The table below reflects the relationship between the remaining fuel $y$ in the fuel tank of a car traveling at a constant speed on a highway and the time $x$ in hours during the journey. This relationship can be represented as ______.\n\n| Time $x$ (hours) | $0$ | $1$ | $2... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Simplify and evaluate the expression:\n$$\n\\frac{x}{x^2 - 2x + 1} \\div \\left( \\frac{x + 1}{x^2 - 1} + 1 \\right)\n$$\nwhere $x = \\sqrt{3} + 1$.",
"If point $P$ is a moving point on the ellipse $\\frac{x^2}{2}+y^2=1$, then the maximum distance from $P$ to the line $... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given that the product of two numbers x and y is equal to their sum, express x in terms of y. Provide your answer in the form of an algebraic expression.",
"Given the sequence \\(\\{a_n\\}\\) with initial terms \\(a_1 = 3\\), \\(a_2 = 6\\), and the recursive relationshi... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Let the sides of the rectangle be x and y, such that its perimeter P = 2x + 2y and its diagonal D satisfies x^2 + y^2 = D^2. Given P = 14 and D = 5, find the maximum or minimum area of the rectangle using calculus and optimization.",
"Let $A=\\{x|x(4-x)\\geqslant 3\\}$,... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"What is the area of rectangle \\( PQRS \\) if the perimeter of rectangle \\( TVWY \\) is 60?",
"In a test, there are $m$ questions and $n$ students taking part, where $m$ and $n$ are given integers with $m, n \\geqslant 2$. The scoring rule for each question is: if exac... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given that $P\\left(\\sin \\theta,\\cos \\theta \\right)$ is a point on the terminal side of an angle $-\\frac{\\pi}{3}$, calculate the value of $\\tan \\theta$. Express your answer as a fraction or decimal.",
"Given the equation of the parabola $y^2 = 4x$, find the dis... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given that the function f(x) satisfies f(x-1) = x^2 + 1, find the value of f(-1). Express your answer as a single number.",
"Given vectors $\\overrightarrow{a}=(1,-2)$ and $\\overrightarrow{b}=(m,m-2)$, find the value of $m$ such that $\\overrightarrow{a}\\bot \\overrig... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given that the foci of an ellipse are on the $x$-axis, and the distance from a point on the ellipse with the same $x$-coordinate as the focus to the $x$-axis is equal to $\\frac{2}{3}$ of the minor axis length, find the eccentricity of the ellipse.",
"Given that line $a... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given the expansion of the equation \\\\((x^{2}+x+1)(2x-a)^{5}=a\\_{0}+a\\_{1}x+a\\_{2}x^{2}+…+a\\_{7}x^{7}\\\\), where \\\\(a\\_{0}=-32\\\\), find the value of \\\\(a\\_{0}+a\\_{1}+a\\_{2}+…+a\\_{7}\\\\).",
"Given that $f(x)$ is an even function defined on the domain $... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"A railway freight station is organizing and dispatching 8 coal freight trains into two groups, each containing 4 trains. The conditions are that trains A and B cannot be in the same group, train A departs first, and train B departs last. If the group containing train A depa... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"If the complex number $z$ satisfies $3+zi=z-3i$ (where $i$ is the imaginary unit), then the modulus of the complex number $z$, denoted $|z|=$ ______.",
"The function $f$ is defined by \\[f(x) = \\lfloor|x|\\rfloor - |\\lfloor x \\rfloor|\\]for all real numbers $x$, wher... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"In triangle \\( \\triangle ABC \\), \\( AB = 6 \\) and \\( BC = 4 \\). The length of the median on side \\( AC \\) is \\( \\sqrt{10} \\). Calculate the value of \\( \\sin^6 \\frac{A}{2} + \\cos^6 \\frac{A}{2} \\).",
"Find all real functions \\( f, g, h: \\mathbf{R} \\ri... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"In a zoo, there are 30 penguins, 22 zebras, and 8 tigers with 12 zookeepers. The total number of heads is less than the number of feet. If there are 12 zookeepers, what is the difference between the number of heads and the number of feet?",
"Find all natural numbers tha... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Fans trying to find out the age of the soccer star Aaron were told by Aaron teasingly, \"As for my age, the cube is a four-digit number, and the square of the square is a six-digit number, which together just happen to include all the digits from 0 to 9.\" So, Aaron is actu... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Arthur removes some pencils from a jar. There were originally 87 pencils in the jar, and now there are 83 pencils left. How many pencils did Arthur remove?",
"Let \\( Q(x) = a_{0} + a_{1} x + \\cdots + a_{n} x^{n} \\) be a polynomial with integer coefficients, and \\( 0... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Find the greatest positive integer \\( k \\) such that \\( 3^k \\) divides \\( 2^{3^m} + 1 \\) for any positive integer \\( m \\).",
"A dealer has some hard candy worth 2 dollars a pound and some worth 3 dollars a pound. He wishes to make a mixture that he can sell for ... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"The speed of a bus increases by 2 km after every one hour. If the distance travelling in the first one hour was 35 km, what was the total distance travelled in 12 hours?",
"The income and expenditure of a person are in a certain ratio. If the income of the person is Rs.... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given the function y = a^(x - 1) + 3 with conditions a > 0 and a!= 1, find a point (x, y) that must lie on the graph of the function. Express your answer as an ordered pair.",
"After recess, Buddy changed clothes for gym class. Down at the gym, all the students were div... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given that $\\tan (\\pi-\\alpha)=2$, find the value of $\\tan 2\\alpha$.",
"Let $f(n) = 1+ \\frac{1}{2}+ \\frac{1}{3}+…+ \\frac{1}{3n-1}$ $(n \\in \\mathbb{N}^*)$. Calculate the difference $f(n+1)-f(n)$.",
"What number, when added to ten times its square root, equal... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"A school bus traveled for 42 minutes at a certain speed. The distance the bus traveled is 35 miles. What is the speed of the bus in mph?",
"Express 1.36 billion in scientific notation. Provide your answer in the form of a number between 1 and 10 multiplied by a power of... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"A rectangular floor has a length that is more than its breadth by 450%. If Rs. 1360 is required to paint the floor at the rate of Rs. 5 per sq m, then what would be the length of the floor?",
"Let \\( n \\geq 3 \\) and \\( k \\geq 1 \\). Determine the smallest integer \... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given that the intersecting lines $l$ and $m$ are both within plane $\\alpha$ and neither is within plane $\\beta$, if $p$: at least one of $l$, $m$ intersects with $\\beta$; $q$: $\\alpha$ intersects with $\\beta$, then $p$ is a $\\boxed{\\text{necessary and sufficient con... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"The ratio of pens to pencils is some ratio. There are 6 more pencils than pens. There are 36 pencils. What is the ratio of pens to pencils?",
"Express $3.\\overline{7}$ as a common fraction.",
"A retailer purchases shirts from a wholesaler and then sells the shirts ... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"A committee of three students met with the principal today and agreed that Rachel will report to the principal every $9$ days, Jessica every $12$ days, and Richard every $15$ days. What is the least number of days before all three will again report to the principal on the s... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"if two - third of a bucket is filled in 100 seconds then the time taken to fill the bucket completely will be .",
"Given vectors $\\overrightarrow {a}=(1,2)$, $\\overrightarrow {b}=(1,0)$, and $\\overrightarrow {c}=(3,4)$, find the real number $\\lambda$ such that $(\\o... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Among the numbers $\\frac{22}{7}$, $\\pi$, $0$, $\\sqrt{\\frac{4}{9}}$, $0.6$, $0.1212212221\\ldots$ (where the number of 2s between adjacent 1s increases by 1 each time), how many are irrational numbers? Express your answer as a whole number.",
"In the zoo's swamp area... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Andrew, Annie's other friend, was assigned with the preparation of appetizers. He decided to bring some hotdogs on sticks, 20 pieces of bite-sized cheese pops and 40 pieces of chicken nuggets. Andrew brought 90 portions of appetizers in all. How many hotdogs on sticks did A... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Tabby is training for a triathlon, which includes swimming, cycling and running. She swims at a speed of 1 mile per hour, cycles at a speed of 18 miles per hour, and runs at a speed of 6 miles per hour. She spends 2 hours swimming, 3 hours cycling, and 2 hours running. How ... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"andy solves problems 70 to 125 inclusive in a math exercise . how many problems does he solve ?",
"In a group of ducks and cows, the total number of legs are 16 more than twice the number of heads. Find the total number of buffaloes.",
"The sequence is $\\frac{1}{2}... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given that $\\overrightarrow {a}$=(2,−1,2) and $\\overrightarrow {b}$=(-4,2,x), and $\\overrightarrow {a}$ is parallel to $\\overrightarrow {b}$, find the value of x.",
"How many inches are in a certain number of millimeters, rounded to the nearest hundredth of an inch?... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"What is the maximum number of square inches in the area of a rectangle with a perimeter of 12 inches?",
"A number when divided by a certain divisor left remainder 241, when twice the number was divided by the same divisor, the remainder was a different value. The diviso... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given two fixed points $O$ and $G$ in the plane. Find the locus of the vertices of triangles whose circumcenters and centroids are $O$ and $G$ respectively.",
"The equation of the tangent line to the curve $f(x)=2x-e^{x}$ at $x=0$ is ______________.",
"Deter... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Mary is baking a cake. The recipe calls for 12 cups of flour, 5 cups of sugar, and 49 cups of salt. She already put in some cups of flour and needs to add 1 more cup. How many cups of flour has she already put in?",
"The function f(x) is defined as follows:\n\n$$\nf(x) ... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Jenna is hemming her prom dress. The dress's hem is 3 feet long. Each stitch Jenna makes is a certain length. If Jenna makes 24 stitches per minute, and it takes her 6 minutes to hem her dress, how long is each stitch in inches?",
"Given the set B = {-1, 1, 4}, find the... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Suppose that the measurement of time during the day is converted to the metric system so that each day has $10$ metric hours, and each metric hour has $100$ metric minutes. Digital clocks would then be produced that would read $\\text{9:99}$ just before midnight, $\\text{0:... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Jake's neighbors hire him to mow their lawn and plant some flowers. Mowing the lawn takes 1 hour and pays a certain amount. If Jake wants to make $20/hour working for the neighbors, and planting the flowers takes 2 hours, Jake should charge $45 in total for planting the flo... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given the hyperbola $\\frac{{x}^{2}}{{a}^{2}}-\\frac{{y}^{2}}{{b}^{2}}=1$ ($a > 0$, $b > 0$) with an eccentricity of $2$, and one of its foci coincides with the focus of the parabola ${y}^{2}=4x$. Calculate the value of $ab$. Express your answer as a single value in the for... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"A ladder is standing vertically against a high wall of a house. Someone pulls the bottom end of the ladder 4 meters away from the wall. As a result, the top end of the ladder drops to $\\frac{1}{5}$ of its length. What is the length of the ladder?",
"Let $f(x) = 1 - 2x^... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"A vertical line divides the triangle with vertices (0,0), (1,1), and (9,1) in the xy-plane into two regions of equal area. Find the equation of the line in the form x = k, where k is a single number.",
"Given the arithmetic sequence $\\{a_{n}\\}$ satisfies $a_{5}+a_{6}=... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Define the sequences $\\left\\{a_{n}\\right\\}$ and $\\left\\{b_{n}\\right\\}$ as follows:\n$$\n\\begin{array}{l}\na_{1}=b_{1}=1, \\quad a_{2}=2, \\quad b_{2}=7, \\\\\na_{n+2}=4a_{n+1}-a_{n}, \\quad b_{n+2}=6b_{n+1}-b_{n} \\quad (n \\in \\mathbf{Z}_{+}).\n\\end{array}\n$$\n... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"If the function $f(x) = 2x - 1$, then $f(3) =$",
"A single bench section at a school event can hold either $7$ adults or $11$ children. When $N$ bench sections are connected end to end, an equal number of adults and children seated together will occupy all the bench spa... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Let $n\\geq 4$ be a positive integer.Out of $n$ people,each of two individuals play table tennis game(every game has a winner).Find the minimum value of $n$ ,such that for any possible outcome of the game,there always exist an ordered four people group $(a_{1},a_{2},a... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given that $f(0)=1$ and $f(n)=nf(n-1)$ for all positive integers $n$, find the value of $f(4)$.",
"\\(8.424 \\cos x + \\sqrt{\\sin ^{2} x - 2 \\sin 2 x + 4 \\cos ^{2} x} = 0\\)",
"Given that $a$ and $b$ are opposites, $c$ and $d$ are reciprocals, and $x$ is a square... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Calculate the value of $(-1)^{2002}$. Express your answer as an integer.",
"Given that the function f(x) is monotonically decreasing on (-∞,+∞) and is an odd function, and given f(1) = -1, find the range of x such that -1 ≤ f(x-2) ≤ 1. Express your answer as an interval... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given points \\( A(-1, 5) \\) and \\( B(3, -7) \\). Find the distance from the origin to the midpoint of segment \\( AB \\).",
"A sample has a capacity of $80$. After grouping, the frequency of the second group is $0.15$. Then, the frequency of the second group is _____... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given that $a$, $b$, and $c$ are distinct real numbers, find the slope angle of the line passing through the points $P(b, b+c)$ and $C(a, c+a)$.",
"Calculate: $$\\frac {3}{x}+ \\frac {2}{y}$$.",
"In a school located at the heart of the city, there are only 2 wheeler... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"If some number ^ x = 2 ^ 9, and x is 3, what is that number?",
"Given that $α \\in (0, \\frac{π}{2})$ and $β \\in (0, \\frac{π}{2})$, if $\\tan (α + β) = 2 \\tan β$, then when $α$ takes the maximum value, $\\tan 2α = \\_\\_\\_\\_\\_\\_$.",
"Xiao Ming participated in... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"If 6 years are subtracted from the present age of Arun and the remainder is divided by 18, then the present age of his grandson Gokul is obtained. Gokul is 2 years younger to Madan whose age is a certain number of years. The age of Arun is 60 years. What is Madan's age?",
... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"When $6y^3+5y^2-16y+8$ is divided by $2y+3$ the quotient is $3y^2+cy+\\frac{5}{2}c$. What is the remainder?",
"I drew the smallest circle enclosing a rhombus and the smallest square enclosing the circle. If the side of this square is 16 centimeters (cm), what is the are... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"In $\\triangle ABC$, $\\angle B = 46^{\\circ}$. Point $D$ is on side $BC$ such that $\\angle BAD = 21^{\\circ}$. Given that $AB = CD$, find the measure of $\\angle CAD$.",
"In the trapezoid shown in the given figure, \\(AB\\) is parallel to \\(DC\\), \\(AD = AB = BC = 1... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"In $\\triangle ABC$, $BC=1$, $B= \\frac {2\\pi}{3}$, and the area of $\\triangle ABC$, $S= \\sqrt {3}$, then the length of side $AC$ is ______.",
"Given that the domain of the function $y=f(x+1)$ is $[-2, 3]$, determine the domain of the function $y=f(x)$. Express your ... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Dilan, Martha, Phillip, and Veronica went to the park together to have some fun. They all had a different number of marbles: Dilan had 14 marbles, Martha had 20 marbles, Phillip had 19 marbles and finally, Veronica had only 7 marbles. They wanted to redistribute the marbles... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"In the game of *Winners Make Zeros*, a pair of positive integers $(m,n)$ is written on a sheet of paper. Then the game begins, as the players make the following legal moves:\n\n\n- If $m\\geq n$ , the player choose a positive integer $c$ such that $m-cn\\geq 0$ , and... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given the motion equation of an object is $S=24t-3t^{2}$ ($S$ is in meters and $t$ is in seconds), then the average velocity of the object over the time interval $\\left[0,6\\right]$ is equal to the instantaneous velocity at time $t=$____$s.",
"The area of a triangle is... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"A university intends to understand the intentions of its undergraduate students regarding participation in a certain social practice activity. It plans to use stratified sampling to draw a sample of 300 students from undergraduates across four grades. It is known that the r... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"The speed of a boat in still water is 20 kmph. What is the speed of the stream if the boat can cover 48 km downstream or 24 km upstream in the same time?",
"A set of 10 distinct integers $S$ is chosen. Let $M$ be the number of nonempty subsets of $S$ whose element... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"There are some girls and 8 boys in the school play. If both parents of each kid attend the premiere, there will be 28 parents in the auditorium. How many girls are in the school play?",
"Amit can do a work in 10 days, and Ananthu can do the same work in some days. Amit ... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"If the function $f(x)= \\begin{cases} 2x-a, & x\\geqslant 1 \\\\ \\ln (1-x), & x < 1\\end{cases}$ has two zeros, then the range of the real number $a$ is \\_\\_\\_\\_\\_.",
"4 and a certain number are factors of 60 n, and the minimum value of n is 8. What is the other f... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"On our last vacation, I bought 5 times as many tetras as Tim bought clowns. Tim bought twice as many clowns as Rick bought guppies. Rick bought 3 times as many guppies as Jane bought angelfish. Jane bought 10 more angelfish than Alex bought cichlids, and Alex bought half th... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Mark bought a shirt, pants, and shoes. The price of the pants is $120, knowing that the price of a shirt is three-quarters of the price of the pants and that the price of a shoe is ten dollars more than the price of the pants. What is the total cost of the shirt, pants, and... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"There are 4 children in the classroom, each student will get a certain number of pencils. The teacher would have to give out 8 pencils. How many pencils will each student get?",
"If the radius of the circle obtained by cutting the sphere $O$ with the plane $\\alpha$ is ... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"From the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, two numbers are drawn successively without replacement. Let event A be \"the first number drawn is odd\", and event B be \"the second number drawn is odd\". Calculate P(B|A), expressing your answer as a simplified fraction.",
... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Jessy plans to finish reading a 140-page book in one week. She decides to read a certain number of times daily, 6 pages each time, every day of the week. She needs to read 2 more pages per day to actually achieve her goal. How many times does she initially plan to read dail... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Simplify first, then evaluate: $2({x-2y})-\\frac{1}{3}({3x-6y})+2x$, where $x=2$ and $y=-\\frac{1}{4}$.",
"Claire wants to make 2 cakes for her mother. Two packages of flour are required for making a cake. If 1 package of flour is $3, how much does she pay for the flour... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"The quotient of one number divided by another is an integer, which is half of one of them and 6 times the other. Find this quotient.",
"Given the function $f(x) = \\begin{cases} -x^{2} & ;x < 0 \\\\ g(x) & ;x > 0 \\end{cases}$, where $f(x)$ is an odd function, calculate... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"A charity organization is preparing backpacks filled with school supplies to donate to children in need. They have 150 pencils, 255 notebooks, and 315 pens. If they want to make all the backpacks the same, with no school supplies left over, what is the greatest number of ba... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"The square $A B C D$ is enlarged from vertex $A$ resulting in the square $A B^{\\prime} C^{\\prime} D^{\\prime}$. The intersection point of the diagonals of the enlarged square is $M$. It is given that $M C = B B^{\\prime}$. What is the scale factor of the enlargement?",
... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given propositions p: \"For all $x$ in the interval [1,2], $x^2 - a \\geq 0$\", and q: \"There exists an $x$ in $\\mathbb{R}$ such that $x^2 + 2ax + (2-a) = 0$\", if the compound proposition \"p and q\" is true, determine the range of the real number $a$.",
"Estevan has... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Brianna is using part of the money she earned on her weekend job to buy several equally-priced CDs. She used one fifth of her money to buy one third of the CDs. What fraction of her money will she have left after she buys all the CDs?",
"Among the numbers -1, -2, 1, and... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given the set of numbers {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}, determine which number must be removed so that the mean (average) of the remaining numbers is 6.1. Express your answer as a single integer.",
"A man is purchasing a pair of sneakers at a club store where he r... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"In the complex plane, the point corresponding to the complex number z has coordinates (1,2). Express z as a complex number and calculate the product zi. Provide your answer in the form a + bi, where a and b are real numbers.",
"A merry-go-round has a circular platform w... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"In every cell of a table with $n$ rows and $m$ columns is written one of the letters $a$ , $b$ , $c$ . Every two rows of the table have the same letter in at most $k\\geq 0$ positions and every two columns coincide at most $k$ positions. Find $m$ , $n$ , $k$ ... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Soda is sold in packs of 6, 12 and 24 cans. What is the minimum number of packs needed to buy exactly 90 cans of soda?",
"Given the inequality 1/m + 2/(1-2m) >= k, where 0 < m < 1/2, find the maximum value of k. Express your answer as a single number.",
"Selene buys... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Given that the sum of the first $n$ terms of the sequence $\\{a_{n}\\}$ is $S_{n}=3^{n}-2$, find $a_{n}$.",
"Given that $\\tan \\alpha=3$ and $\\tan \\beta= \\frac {4}{3}$, find the value of $\\tan (\\alpha-\\beta)$.",
"Given a sequence $\\left\\{a_{n}\\right\\}$ wh... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"At the Bertolli Farm, they grow 2073 tomatoes, 4112 cobs of corn, and 985 onions. How many fewer onions are grown than tomatoes and corn together?",
"I put another number into my machine. The machine added 15 and then subtracted 6. The number 35 came out of the machine.... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Brielle has a unique wall clock that rings at different intervals. On the first day, it rings every 3 hours, starting at 1 A.M. On the second day, it rings every 4 hours, starting at 2 A.M. On the third day, it rings every 5 hours, starting at 3 A.M. How many times will the... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Determine the coordinates of the center \\( O \\) and the radius \\( r \\) of the circle defined by the equation: \\( x^2+y^2+4x=0 \\).",
"The sequence $\\left\\{a_{n}\\right\\}$ satisfies $a_{0} = 0, a_{n+1} = k a_{n} + \\sqrt{\\left(k^{2} - 1\\right) a_{n}^{2} + 1}$ f... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Find a two-digit number whose digits are different and whose square is equal to the cube of the sum of its digits.",
"Given that line $l$ is tangent to the curve $y=x^{2}+3x-1$ at point $(1,3)$, determine the slope of line $l$. Express your answer as a single numerical ... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Everyday Jonathan spends 8 hours on his phone. A certain portion of this time is spent on social media. He spends 28 hours on social media in a week. What is the ratio of the time spent on social media to the total time spent on his phone daily?",
"In the sequence $\\{a... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"If the wheel is 14 cm in diameter, how many revolutions does it need to make to cover a distance of 1408 cm?",
"A mass of 15 kg is halfway between 10 kg and 20 kg on the vertical axis. What is the age of the cod when its mass is 15 kg?",
"Find all positive integer v... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"In a triangular pyramid, sections are made parallel to its two non-intersecting edges. Find the section with the largest area.",
"Given that the first three terms of an arithmetic sequence $\\{a_n\\}$ are 2, 4, and 6, respectively, find the value of $a_4$. Express your ... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"In an isosceles trapezoid, the length of the longer base is equal to the length of its diagonals, and the length of the shorter base is equal to the height. Find the ratio of the length of the shorter base to the longer base. Express your answer as a ratio.",
"Given tha... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Reeya obtained 65, 67, 76, 80, and 95 out of 100 in different subjects. What will be her average score?",
"The area of the right triangle ABC ( $\\angle C=90^{\\circ}$ ) is 6, and the radius of the circumcircle around it is $\\frac{5}{2}$. Find the radius of the circle ... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"If 20 liters of chemical x are added to 80 liters of a mixture that is 20% chemical x and 80% chemical y, then what percentage of the resulting mixture is chemical x?",
"Jar X is 1/2 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. Jar Z... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"There are four different styles of jackets and three different colors of trousers. If a pair of trousers is matched with a jacket to form a set, calculate the total number of different selection methods.",
"Determine all positive integers $m$ satisfying the condition ... |
[
{
"content": "This is a K-armed bandit task with the following configuration.\nThe user will tell you the number of arms (K) and the maximum number of trials (T_max).\n\nThe <answer>...</answer> tags should contain only your action (this is the arm index).\nThe user will provide the reward for your action.\n\nY... | {
"T_max_problems": 5,
"problems": [
"Grant has four times as many vacations as Kelvin has classes. If Kelvin has 90 classes, how many vacations and classes do Grant and Kelvin have altogether?",
"Given that a positive integer N divided by 60 leaves a remainder of 49, find the remainder when N is divided by... |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 4