data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "Use the Horner's method to calculate the value of the polynomial $f(x) = 10 + 25x - 8x^2 + x^4 + 6x^5 + 2x^6$ at $x = -4$, then determine the value of $v_3$."
}
] | math | {
"style": "rule",
"ground_truth": "-36"
} | {
"index": 36700,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Use the Horner's method to calculate the value of the polynomial $f(x) = 12 + 35x - 8x^2 + 79x^3 + 6x^4 + 5x^5 + 3x^6$ at $x = -4$. What is the value of $V_4$?"
}
] | math | {
"style": "rule",
"ground_truth": "220"
} | {
"index": 36701,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Use the Horner's method to calculate the value of the polynomial $f(x) = 2x^5 + 5x^3 - x^2 + 9x + 1$ when $x = 3$. What is the value of $v_3$ in the third step?"
}
] | math | {
"style": "rule",
"ground_truth": "68"
} | {
"index": 36702,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Use the Horner's method to calculate the value of the polynomial $f(x) = 2x^5 - 3x^2 + 4x^4 - 2x^3 + x$ when $x=2$."
}
] | math | {
"style": "rule",
"ground_truth": "102"
} | {
"index": 36703,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Use the Horner's method to calculate the value of the polynomial $f(x) = 5x^5 + 2x^4 + 3.5x^3 - 2.6x^2 + 1.7x - 0.8$ when $x=1$ and find the value of $v_3$."
}
] | math | {
"style": "rule",
"ground_truth": "7.9"
} | {
"index": 36704,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Use the Horner's method to calculate the value of the polynomial $f(x) = 7x^7 + 6x^6 + 5x^5 + 4x^4 + 3x^3 + 2x^2 + x$ when $x = 3$, and find the value of $v_3$."
}
] | math | {
"style": "rule",
"ground_truth": "262"
} | {
"index": 36705,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Use the Horner's method to compute the value of the polynomial $f(x)=0.5x^{5}+4x^{4}-3x^{2}+x-1$ when $x=3$, and determine the first operation to perform."
}
] | math | {
"style": "rule",
"ground_truth": "5.5"
} | {
"index": 36706,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Use the Horner's method to write out the process of calculating the value of $f(x) = 1 + x + 0.5x^2 + 0.16667x^3 + 0.04167x^4 + 0.00833x^5$ at $x = -0.2$."
}
] | math | {
"style": "rule",
"ground_truth": "0.81873"
} | {
"index": 36707,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Use the angle addition formula for cosine to simplify the expression $\\cos 54^{\\circ}\\cos 24^{\\circ}+2\\sin 12^{\\circ}\\cos 12^{\\circ}\\sin 126^{\\circ}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{2}"
} | {
"index": 36708,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Use the bisection method to find an approximate solution for $f(x)=0$. Given that $f(1)=-2$, $f(3)=0.625$, and $f(2)=-0.984$, calculate the next $f(m)$, where $m =$ __________."
}
] | math | {
"style": "rule",
"ground_truth": "2.5"
} | {
"index": 36709,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Use the bisection method to find an approximate zero of the function $f(x) = \\log x + x - 3$, given that approximate solutions (accurate to 0.1) are $\\log 2.5 \\approx 0.398$, $\\log 2.75 \\approx 0.439$, and $\\log 2.5625 \\approx 0.409$."
}
] | math | {
"style": "rule",
"ground_truth": "2.6"
} | {
"index": 36710,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Use the digits from $0$ to $9$ to form three-digit numbers that are divisible by $5$ and do not have repeating digits. How many such numbers are there?"
}
] | math | {
"style": "rule",
"ground_truth": "136"
} | {
"index": 36711,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Use the five digits $0$, $1$, $2$, $3$, $4$ to form integers that satisfy the following conditions:\n(I) All four-digit integers;\n(II) Five-digit integers without repetition that are greater than $21000$."
}
] | math | {
"style": "rule",
"ground_truth": "66"
} | {
"index": 36712,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Use the method of random simulation experiments to estimate the probability of having exactly two days of rain in three days: First, use a calculator to generate random integers between \\\\(0\\\\) and \\\\(9\\\\), with \\\\(1\\\\), \\\\(2\\\\), \\\\(3\\\\), \\\\(4\\\\) represe... | math | {
"style": "rule",
"ground_truth": "0.25"
} | {
"index": 36713,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Use the method of random simulation to estimate the probability that it will rain on exactly two of the three days. Using a calculator, generate random integer values between 0 and 9, where 1, 2, 3, and 4 represent raining days and 5, 6, 7, 8, 9, and 0 signify non-raining days.... | math | {
"style": "rule",
"ground_truth": "0.25"
} | {
"index": 36714,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Use the six digits 0, 1, 2, 3, 4, 5 to form four-digit even numbers without repeating any digit. Calculate the total number of such numbers that can be formed."
}
] | math | {
"style": "rule",
"ground_truth": "156"
} | {
"index": 36715,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using $600$ cards, $200$ of them having written the number $5$ , $200$ having a $2$ , and the other $200$ having a $1$ , a student wants to create groups of cards such that the sum of the card numbers in each group is $9$ . What is the maximum amount of groups that ... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 36716,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using $1 \\times 2$ tiles to cover a $2 \\times 10$ grid, how many different ways are there to cover the grid?"
}
] | math | {
"style": "rule",
"ground_truth": "89"
} | {
"index": 36717,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using 1 digit of '1', 2 digits of '2', and 2 digits of '3', how many different four-digit numbers can be formed? Fill in the blank with the total number of different four-digit numbers."
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 36718,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using 6 different colors to paint the 4 cells in the picture, with each cell painted in one color, and requiring that at most 3 colors are used and no two adjacent cells have the same color, how many different coloring methods are there? (Answer using a number.)"
}
] | math | {
"style": "rule",
"ground_truth": "390"
} | {
"index": 36719,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using Green's theorem, evaluate the line integral \\( I = \\oint_{L} 2(x^{2}+y^{2}) \\, dx + (x+y)^{2} \\, dy \\) along the contour \\( L \\) of triangle \\( ABC \\) with vertices \\( A(1,1) \\), \\( B(2,2) \\), \\( C(1,3) \\)."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{4}{3}"
} | {
"index": 36720,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using a $4 \\times 4$ grid where points are spaced equally at 1 unit apart both horizontally and vertically, how many rectangles are there whose four vertices are points on this grid?"
}
] | math | {
"style": "rule",
"ground_truth": "101"
} | {
"index": 36721,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using a permutation of the numbers $10, 20, 30, 40$ for $A, B, C, D$, maximize the value of the expression $\\frac{1}{A-\\frac{1}{B+\\frac{1}{C-\\frac{1}{D}}}}$. Then, find the value of $A+2B+3C+4D$."
}
] | math | {
"style": "rule",
"ground_truth": "290"
} | {
"index": 36722,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using a table of a certain height, two identical blocks of wood are placed as shown in Figure 1. Length $r$ is found to be $32$ inches. After rearranging the blocks as in Figure 2, length $s$ is found to be $28$ inches. How high is the table?"
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 36723,
"solution": "Let's denote the height of the table as $h$, the length of each wood block as $l$, and the width of each wood block as $w$. All measurements are in inches.\n\nFrom the problem statement, we have two configurations:\n1. In Figure 1, the blocks are arranged such that the total length fr... |
DeepScaleR | [
{
"role": "user",
"content": "Using an electric stove with a power of $P=500 \\mathrm{W}$, a certain amount of water is heated. When the electric stove is turned on for $t_{1}=1$ minute, the water temperature increases by $\\Delta T=2^{\\circ} \\mathrm{C}$, and after turning off the heater, the temperature ... | math | {
"style": "rule",
"ground_truth": "2.38"
} | {
"index": 36724,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using arithmetic operation signs, write the largest natural number using two twos."
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"index": 36725,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using each of the digits 1-9 exactly once, form a two-digit perfect square, a three-digit perfect square, and a four-digit perfect square. What is the smallest four-digit perfect square among them?"
}
] | math | {
"style": "rule",
"ground_truth": "1369"
} | {
"index": 36726,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using equal-length toothpicks to form a rectangular diagram as shown, if the length of the rectangle is 20 toothpicks long and the width is 10 toothpicks long, how many toothpicks are used?"
}
] | math | {
"style": "rule",
"ground_truth": "430"
} | {
"index": 36727,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using five distinct digits, $1$, $4$, $5$, $8$, and $9$, determine the $51\\text{st}$ number in the sequence when arranged in ascending order.\nA) $51489$\nB) $51498$\nC) $51849$\nD) $51948$"
}
] | math | {
"style": "rule",
"ground_truth": "51849"
} | {
"index": 36728,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using five nines (9), arithmetic operations, and exponentiation, create the numbers from 1 to 13."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 36729,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using one each of the coins and bills of 1 jiao, 2 jiao, 5 jiao, 1 yuan, 2 yuan, and 5 yuan, how many different monetary values can be formed?"
}
] | math | {
"style": "rule",
"ground_truth": "63"
} | {
"index": 36730,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using only once each of the digits $1, 2, 3, 4, 5, 6, 7$ and $ 8$ , write the square and the cube of a positive integer. Determine what that number can be."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 36731,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using only pennies, nickels, dimes, and quarters, what is the smallest number of coins Freddie would need so he could pay any amount of money less than a dollar?"
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 36732,
"solution": "To solve this problem, we need to determine the minimum number of coins required to make any amount of money from 1 cent to 99 cents using pennies, nickels, dimes, and quarters.\n\n1. **Covering the first 25 cents:**\n - We use 4 pennies to cover amounts 1 cent to 4 cents.\n - We ... |
DeepScaleR | [
{
"role": "user",
"content": "Using only pennies, nickels, dimes, quarters, and half-dollars, determine the smallest number of coins needed to pay any amount of money less than a dollar and a half."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 36733,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using only the digits $2,3$ and $9$ , how many six-digit numbers can be formed which are divisible by $6$ ?"
}
] | math | {
"style": "rule",
"ground_truth": "81"
} | {
"index": 36734,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using only the digits 7, 8 and 9, how many positive seven-digit integers can be made that are palindromes?"
}
] | math | {
"style": "rule",
"ground_truth": "81"
} | {
"index": 36735,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using only the paths and the directions shown, how many different routes are there from $\\text{M}$ to $\\text{N}$?"
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"index": 36736,
"solution": "To solve this problem, we will use a systematic approach by counting the number of ways to reach $\\text{N}$ from each point, starting from the points closest to $\\text{N}$ and working backwards.\n\n1. **From $\\text{C}$ to $\\text{N}$**: There is only one direct path from $\\text{C}... |
DeepScaleR | [
{
"role": "user",
"content": "Using systematic sampling method to select 32 people from 960 for a questionnaire survey, they are randomly numbered from 1 to 960. After grouping, the number drawn by simple random sampling in the first group is 9. Among the 32 people drawn, those with numbers in the interval ... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 36737,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using systematic sampling to select 20 students from 1000, the students are randomly numbered from 000 to 999 and grouped: the first group ranges from 000 to 049, the second group from 050 to 099, ..., and the twentieth group from 950 to 999. If the number 122 from the third gr... | math | {
"style": "rule",
"ground_truth": "872"
} | {
"index": 36738,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using systematic sampling to select a sample of size 20 from 180 students, the students are randomly numbered from 1 to 180. They are then divided into 20 groups in order of their number (group 1: numbers 1-9, group 2: numbers 10-18, ..., group 20: numbers 172-180). If the numb... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"index": 36739,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using systematic sampling to select a sample of size \\\\(20\\\\) from \\\\(160\\\\) students, the \\\\(160\\\\) students are numbered from \\\\(1\\\\) to \\\\(160\\\\) and evenly divided into \\\\(20\\\\) groups (\\\\(1～8\\\\), \\\\(9～16\\\\), ..., \\\\(153～160\\\\)). If the n... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 36740,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using systematic sampling, \\\\(32\\\\) people are selected from \\\\(960\\\\) for a questionnaire survey. They are randomly numbered from \\\\(1\\\\) to \\\\(960\\\\), and then grouped. The number drawn by simple random sampling in the first group is \\\\(9\\\\). Among the \\\... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 36741,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using systematic sampling, extract a sample of size 12 from a population of 123 individuals. The sampling interval is ______."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 36742,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the 0.618 method to select a trial point, if the experimental interval is $[2, 4]$, with $x_1$ being the first trial point and the result at $x_1$ being better than that at $x_2$, then the value of $x_3$ is ____."
}
] | math | {
"style": "rule",
"ground_truth": "3.236"
} | {
"index": 36743,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the 3 vertices of a triangle and 7 points inside it (a total of 10 points), how many smaller triangles can the original triangle be divided into?\n\n(1985 Shanghai Junior High School Math Competition, China;\n1988 Jiangsu Province Junior High School Math Competition, Chin... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 36744,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the Horner's method (also known as Qin Jiushao's algorithm), calculate the value of the polynomial \\\\(f(x)=12+35x-8x^{2}+79x^{3}+6x^{4}+5x^{5}+3x^{6}\\\\) when \\\\(x=-4\\\\), and determine the value of \\\\(V_{3}\\\\)."
}
] | math | {
"style": "rule",
"ground_truth": "-57"
} | {
"index": 36745,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the Horner's method, calculate the value of the polynomial $f(x)=2x^{4}-x^{3}+3x^{2}+7$ at $x=3$, and find the corresponding value of $v_{3}$."
}
] | math | {
"style": "rule",
"ground_truth": "54"
} | {
"index": 36746,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the bar graph, what is the positive difference between the number of students at the school with the largest enrollment and the number of students at the school with the smallest enrollment?\n\n[asy]\nsize(250);\ndefaultpen(fontsize(9));\n\nfill((0,0)--(40,0)--(40,20)--(0... | math | {
"style": "rule",
"ground_truth": "650"
} | {
"index": 36747,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the data presented in the chart, what was the average daily high temperature in Brixton from September 15th, 2008 to September 21st, 2008, inclusive? The daily high temperatures in degrees Fahrenheit were recorded as 51, 64, 61, 59, 48, 63, and 55."
}
] | math | {
"style": "rule",
"ground_truth": "57.3"
} | {
"index": 36748,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the differential, calculate to an accuracy of 0.01 the increment of the function \\( y = x \\sqrt{x^{2} + 5} \\) at \\( x = 2 \\) and \\( \\Delta x = 0.2 \\)."
}
] | math | {
"style": "rule",
"ground_truth": "0.87"
} | {
"index": 36749,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits $0$, $1$, $2$, $3$, $4$ to form a five-digit number without repeating any digit, the probability that the number is even and the digits $1$, $2$ are adjacent is ______."
}
] | math | {
"style": "rule",
"ground_truth": "0.25"
} | {
"index": 36750,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits $0$, $1$, $2$, $3$, $4$ to form a four-digit number without repeating any digit, determine the total number of four-digit numbers less than $2340$."
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 36751,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits $0$, $1$, $2$, $3$, $4$, $5$, how many different five-digit even numbers greater than $20000$ can be formed without repetition?"
}
] | math | {
"style": "rule",
"ground_truth": "240"
} | {
"index": 36752,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits $1$, $2$, $3$, $5$, and $6$ exactly once, the five-digit positive integers are formed and arranged in ascending order. What is the $60^{\\text{th}}$ integer in this list?"
}
] | math | {
"style": "rule",
"ground_truth": "32651"
} | {
"index": 36753,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits $1, 2, 3, 4$, 24 unique four-digit numbers can be formed without repeating any digit. If these 24 four-digit numbers are arranged in ascending order, find the sum of the two middle numbers."
}
] | math | {
"style": "rule",
"ground_truth": "4844"
} | {
"index": 36754,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits $2, 4, 6$ to construct six-digit numbers, how many such numbers are there if no two consecutive digits in the number can both be 2 (for example, 626442 is allowed, but 226426 is not allowed)?"
}
] | math | {
"style": "rule",
"ground_truth": "448"
} | {
"index": 36755,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits 0 to 9, how many three-digit even numbers can be formed without repeating any digits?"
}
] | math | {
"style": "rule",
"ground_truth": "360"
} | {
"index": 36756,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits 0, 1, 2, 3, 4, 5 to form numbers without repeating any digit. Calculate: \n(1) How many six-digit numbers can be formed? \n(2) How many three-digit numbers can be formed that contain at least one even number? \n(3) How many three-digit numbers can be formed ... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 36757,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits 0, 1, 2, 3, 4, 5, if repetition of digits is not allowed, the number of different five-digit numbers that can be formed, which are divisible by 5 and do not have 3 as the hundred's digit, is ______."
}
] | math | {
"style": "rule",
"ground_truth": "174"
} | {
"index": 36758,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits 0, 1, 2, 3, 4, and 5, form six-digit numbers without repeating any digit. \n(1) How many such six-digit odd numbers are there? \n(2) How many such six-digit numbers are there where the digit 5 is not in the unit place? \n(3) How many such six-digit numbers a... | math | {
"style": "rule",
"ground_truth": "408"
} | {
"index": 36759,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits 0, 1, 2, 3, 4, how many even three-digit numbers can be formed if each digit can be used more than once, and the number must be greater than 200?"
}
] | math | {
"style": "rule",
"ground_truth": "45"
} | {
"index": 36760,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits 0, 1, 2, 3, and 4, how many even numbers can be formed without repeating any digits?"
}
] | math | {
"style": "rule",
"ground_truth": "163"
} | {
"index": 36761,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits 0, 2, 3, 5, 7, how many four-digit numbers divisible by 5 can be formed if:\n(1) Digits do not repeat;\n(2) Digits can repeat."
}
] | math | {
"style": "rule",
"ground_truth": "200"
} | {
"index": 36762,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits 1 to 6 to form the equation shown below, where different letters represent different digits, the two-digit number represented by $\\overline{A B}$ is what?\n$$\n\\overline{A B} \\times (\\overline{C D} - E) + F = 2021\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "32"
} | {
"index": 36763,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits 1, 2, 3, 4, 5, how many even four-digit numbers less than 4000 can be formed if each digit can be used more than once?"
}
] | math | {
"style": "rule",
"ground_truth": "150"
} | {
"index": 36764,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits 1, 2, 3, 4, 5, how many even three-digit numbers less than 500 can be formed if each digit can be used more than once?"
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 36765,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits 1, 2, 3, 4, how many distinct four-digit even numbers can be formed?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 36766,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits 1, 2, and 3 to form four-digit numbers, where each digit must appear, and identical digits cannot be adjacent, how many such four-digit numbers are there?"
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 36767,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the digits 3, 4, 7, and 8, form two two-digit numbers (each digit can only be used once and must be used) such that their product is maximized. What is the maximum product?"
}
] | math | {
"style": "rule",
"ground_truth": "6142"
} | {
"index": 36768,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the distinct digits \\( a, b, \\) and \\( c \\), Araceli wrote the number \\( abc \\), and Luana wrote the numbers \\( ab, bc, \\) and \\( ca \\). Find the digits \\( a, b, \\) and \\( c \\), knowing that the sum of the numbers written by Luana is equal to the number writ... | math | {
"style": "rule",
"ground_truth": "198"
} | {
"index": 36769,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the four arithmetic operators and parentheses, find a way to combine the numbers 10, 10, 4, and 2 such that the result is 24. What is the arithmetic expression?"
}
] | math | {
"style": "rule",
"ground_truth": "(2 + 4 \\div 10) \\times 10"
} | {
"index": 36770,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the letters $A$, $M$, $O$, $S$, and $U$, we can form five-letter \"words\". If these \"words\" are arranged in alphabetical order, then the \"word\" $USAMO$ occupies position"
}
] | math | {
"style": "rule",
"ground_truth": "115"
} | {
"index": 36771,
"solution": "To find the position of the word \"USAMO\" in the alphabetical order of all possible permutations of the letters $A$, $M$, $O$, $S$, and $U$, we can proceed as follows:\n\n1. **Count the permutations starting with each letter before 'U':**\n - The letters before 'U' in alphabetical ... |
DeepScaleR | [
{
"role": "user",
"content": "Using the method of base prime representation, where the place of each digit represents an exponent in the prime factorization (starting with the smallest prime on the right), convert the number $196$ into base prime."
}
] | math | {
"style": "rule",
"ground_truth": "2002"
} | {
"index": 36772,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the numbers $1$, $2$, $3$, $4$ to form a four-digit number without repeating digits, the number of four-digit numbers larger than $2134$ is _____. (Answer in digits)"
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"index": 36773,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the numbers $2, 4, 12, 40$ each exactly once, you can perform operations to obtain 24."
}
] | math | {
"style": "rule",
"ground_truth": "40 \\div 4 + 12 + 2"
} | {
"index": 36774,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the numbers 0, 1, 2, 3, 4, 5 to form unique three-digit numbers, determine the total number of even numbers that can be formed."
}
] | math | {
"style": "rule",
"ground_truth": "52"
} | {
"index": 36775,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the numbers 3, 0, 4, 8, and a decimal point to form decimals, the largest three-digit decimal is \\_\\_\\_\\_\\_\\_, the smallest decimal is \\_\\_\\_\\_\\_\\_, and their difference is \\_\\_\\_\\_\\_\\_."
}
] | math | {
"style": "rule",
"ground_truth": "8.082"
} | {
"index": 36776,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the numbers from 1 to 22 exactly once each, Antoine writes 11 fractions. For example, he could write the fractions \\(\\frac{10}{2}, \\frac{4}{3}, \\frac{15}{5}, \\frac{7}{6}, \\frac{8}{9}, \\frac{11}{19}, \\frac{12}{14}, \\frac{13}{17}, \\frac{22}{21}, \\frac{18}{16}, \\... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 36777,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the property that in finding the limit of the ratio of two infinitesimals, they can be replaced with their equivalent infinitesimals (property II), find the following limits:\n1) \\(\\lim _{x \\rightarrow 0} \\frac{\\sin 4 x}{\\sin 3 x}\\)\n2) \\(\\lim _{x \\rightarrow 0}... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{10}"
} | {
"index": 36778,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the same Rotokas alphabet, how many license plates of five letters are possible that begin with G, K, or P, end with T, cannot contain R, and have no letters that repeat?"
}
] | math | {
"style": "rule",
"ground_truth": "630"
} | {
"index": 36779,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the same relationships between ball weights, how many blue balls are needed to balance $5$ green, $3$ yellow, and $3$ white balls?"
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"index": 36780,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the seven digits $1, 2, 3, 4, 5, 6, 7$ to appropriately arrange them into a 7-digit number so that it is a multiple of 11, how many such numbers can be formed?"
}
] | math | {
"style": "rule",
"ground_truth": "576"
} | {
"index": 36781,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the side lengths 2, 3, 5, 7, and 11, how many different triangles with exactly two equal sides can be formed?"
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 36782,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the six digits $0$, $1$, $2$, $3$, $4$, $5$, form integers without repeating any digit. Determine how many such integers satisfy the following conditions:\n\n$(1)$ How many four-digit even numbers can be formed?\n\n$(2)$ How many five-digit numbers that are multiples of $... | math | {
"style": "rule",
"ground_truth": "270"
} | {
"index": 36783,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the six digits 0, 1, 2, 3, 4, 5 to form a six-digit number without repeating any digit, how many such numbers are there where the unit digit is less than the ten's digit?"
}
] | math | {
"style": "rule",
"ground_truth": "300"
} | {
"index": 36784,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the six digits 0, 1, 2, 3, 4, 5,\n(1) How many distinct three-digit numbers can be formed?\n(2) How many distinct three-digit odd numbers can be formed?"
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"index": 36785,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the six digits 0, 1, 2, 3, 4, 5, we can form _ _ _ _ _ different five-digit numbers that do not have repeating digits and are divisible by 5."
}
] | math | {
"style": "rule",
"ground_truth": "216"
} | {
"index": 36786,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the systematic sampling method to select 32 people for a questionnaire survey from 960 people, determine the number of people among the 32 whose numbers fall within the interval [200, 480]."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 36787,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the trapezoidal rule with an accuracy of 0.01, calculate $\\int_{2}^{3} \\frac{d x}{x-1}$."
}
] | math | {
"style": "rule",
"ground_truth": "0.6956"
} | {
"index": 36788,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the vertices of a cube as vertices, how many triangular pyramids can you form?"
}
] | math | {
"style": "rule",
"ground_truth": "58"
} | {
"index": 36789,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using the vertices of a single rectangular solid (cuboid), how many different pyramids can be formed?"
}
] | math | {
"style": "rule",
"ground_truth": "106"
} | {
"index": 36790,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using three different weights of 1 gram, 3 grams, and 9 grams, various weights of objects can be measured. Assuming the objects to be measured and the known weights can be placed on either side of the balance scale, how many different weights of objects can be measured?"
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 36791,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using three rectangular pieces of paper (A, C, D) and one square piece of paper (B), an area of 480 square centimeters can be assembled into a large rectangle. It is known that the areas of B, C, and D are all 3 times the area of A. Find the total perimeter of the four pieces o... | math | {
"style": "rule",
"ground_truth": "184"
} | {
"index": 36792,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using toothpicks of equal length, a rectangular grid is constructed. The grid measures 25 toothpicks in height and 15 toothpicks in width. Additionally, there is an internal horizontal partition at every fifth horizontal line starting from the bottom. Calculate the total number... | math | {
"style": "rule",
"ground_truth": "850"
} | {
"index": 36793,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Using two red, three blue, and four green small cubes, calculate the number of different towers that can be built using eight of these cubes."
}
] | math | {
"style": "rule",
"ground_truth": "1260"
} | {
"index": 36794,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Usually, I go up the escalator in the subway. I have calculated that when I walk up the moving escalator, I ascend 20 steps, and it takes me exactly 60 seconds. My wife walks up the stairs more slowly and only ascends 16 steps; therefore, her total time to ascend the escalator ... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 36795,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "V is the pyramidal region defined by the inequalities \\( x, y, z \\geq 0 \\) and \\( x + y + z \\leq 1 \\). Evaluate the integral:\n\n\\[ \\int_V x y^9 z^8 (1 - x - y - z)^4 \\, dx \\, dy \\, dz. \\"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9! 8! 4!}{25!}"
} | {
"index": 36796,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Vaccination is one of the important means to protect one's own and others' health and lives. In order to test the immune effect of a certain vaccine on the $C$ virus, researchers used white rabbits as experimental subjects and conducted the following experiments:<br/>Experiment... | math | {
"style": "rule",
"ground_truth": "80\\%"
} | {
"index": 36797,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Values for $A, B, C,$ and $D$ are to be selected from $\\{1, 2, 3, 4, 5, 6\\}$ without replacement (i.e. no two letters have the same value). How many ways are there to make such choices so that the two curves $y=Ax^2+B$ and $y=Cx^2+D$ intersect? (The order in which the curves ... | math | {
"style": "rule",
"ground_truth": "90"
} | {
"index": 36798,
"solution": "1. **Understanding the Problem**: We need to find the number of ways to choose values for $A, B, C, D$ from the set $\\{1, 2, 3, 4, 5, 6\\}$ without replacement such that the curves $y = Ax^2 + B$ and $y = Cx^2 + D$ intersect.\n\n2. **Condition for Intersection**: The curves intersect... |
DeepScaleR | [
{
"role": "user",
"content": "Van was asked to add 46 to 37 and round the result to the nearest ten. He figured that since he was going to have to round anyway, he might as well do it before adding the numbers. He rounded 46 to 50 and 37 to 40, thus getting an answer of $50+40=90$. This answer is not correc... | math | {
"style": "rule",
"ground_truth": "80"
} | {
"index": 36799,
"solution": ""
} |
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