messages listlengths 2 2 |
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[
{
"content": "## Task B-1.3.\n\nA ship traveling along a river has covered $24 \\mathrm{~km}$ upstream and $28 \\mathrm{~km}$ downstream. For this journey, it took half an hour less than for traveling $30 \\mathrm{~km}$ upstream and $21 \\mathrm{~km}$ downstream, or half an hour more than for traveling $15 \\ma... |
[
{
"content": "3. (6 points) A construction company was building a tunnel. When $\\frac{1}{3}$ of the tunnel was completed at the original speed, they started using new equipment, which increased the construction speed by $20 \\%$ and reduced the working hours to $80 \\%$ of the original. As a result, it took a ... |
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"content": "4. Given the three sides of an obtuse triangle are 3, $4, x$, then the range of values for $x$ is ( ).\n(A) $1<x<7$.\n(B) $5 \\ll x<7$.\n(C) $1<x<\\sqrt{7}$.\n(D) $5<x<7$ or $1<x<\\sqrt{7}$.",
"role": "user"
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"content": "<think>\nOkay, so I have this problem here where I need to fi... |
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{
"content": "1. Solve the equation: $\\frac{8 x+13}{3}=\\frac{19-12 x}{2}-\\left(16 x-\\frac{7-4 x}{6}\\right)$.",
"role": "user"
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"content": "<think>\nOkay, so I need to solve this equation: (8x + 13)/3 = (19 - 12x)/2 - (16x - (7 - 4x)/6). Hmm, that looks a bit complicated with all the fractio... |
[
{
"content": "Let $a_n\\ (n\\geq 1)$ be the value for which $\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)$ is maximal. Find $\\lim_{n\\to\\infty} \\ln a_n.$",
"role": "user"
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"content": "<think>\nOkay, so I need to find the limit as n approaches infinity of the natural logarithm of a_n, where a_n is the... |
[
{
"content": "Task B-4.2. Let $n$ be the number obtained by writing 2013 zeros between every two digits of the number 14641. Determine all solutions of the equation $x^{4}=n$ in the set $\\mathbb{C}$.",
"role": "user"
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"content": "<think>\nOkay, let's see. I need to find all complex solutions to... |
[
{
"content": "6. As shown in Figure 2, let $P$ be a point inside the equilateral $\\triangle ABC$ with side length 12. Draw perpendiculars from $P$ to the sides $BC$, $CA$, and $AB$, with the feet of the perpendiculars being $D$, $E$, and $F$ respectively. Given that $PD: PE: PF = 1: 2: 3$. Then, the area of qu... |
[
{
"content": "8.59 For each pair of real numbers $x, y$, the function $f$ satisfies the functional equation\n$$\nf(x)+f(y)=f(x+y)-x y-1 .\n$$\n\nIf $f(1)=1$, then the number of integers $n$ (where $n \\neq 1$) that satisfy $f(n)=n$ is\n(A) 0.\n(B) 1.\n(C) 2.\n(D) 3.\n(E) infinitely many.\n(30th American High Sc... |
[
{
"content": "Given $0 \\leqslant x, y, z \\leqslant 1$, solve the equation:\n$$\\frac{x}{1+y+z x}+\\frac{y}{1+z+x y}+\\frac{z}{1+x+y z}=\\frac{3}{x+y+z} .$$",
"role": "user"
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"content": "<think>\nAlright, so I have this equation to solve: \n\n\\[\n\\frac{x}{1 + y + z x} + \\frac{y}{1 + z + x y}... |
[
{
"content": "## Problem Statement\n\nCalculate the definite integral:\n\n$$\n\\int_{0}^{3 / 2} \\frac{x^{2} \\cdot d x}{\\sqrt{9-x^{2}}}\n$$",
"role": "user"
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"content": "<think>\nOkay, so I need to calculate the definite integral of x squared over the square root of (9 minus x squared) from 0 ... |
[
{
"content": "Example 6 The rules of a \"level-up game\" stipulate: On the $n$-th level, a die must be rolled $n$ times. If the sum of the points obtained from these $n$ rolls is greater than $2^{n}$, the level is considered passed. Questions:\n(1) What is the maximum number of levels a person can pass in this ... |
[
{
"content": "2. (9th Canadian Mathematical Competition) $N$ is an integer, its representation in base $b$ is 777. Find the smallest positive integer $b$ such that $N$ is a fourth power of an integer in decimal notation.",
"role": "user"
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"content": "<think>\nOkay, let's tackle this problem. So,... |
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"content": "Problem 6. (8 points) In the plane, there is a non-closed, non-self-intersecting broken line consisting of 31 segments (adjacent segments do not lie on the same straight line). For each segment, the line defined by it is constructed. It is possible for some of the 31 constructed lines to coincide.... |
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{
"content": "7.1. Solve the equation $\\frac{n!}{2}=k!+l!$ in natural numbers, where $n!=1 \\cdot 2 \\cdot \\ldots n$. If there are no solutions, write 0; if there is one solution, write $n$; if there are multiple solutions, write the sum of the values of $n$ for all solutions. Recall that a solution is a trip... |
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{
"content": "Example 1 (Question from the 13th \"Hope Cup\" Invitational Competition) The real roots of the equations $x^{5}+x+1=0$ and $x+\\sqrt[5]{x}+1=0$ are $\\alpha, \\beta$ respectively, then $\\alpha+\\beta$ equals ( ).\nA. -1\nB. $-\\frac{1}{2}$\nC. $\\frac{1}{2}$\nD. 1",
"role": "user"
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{
... |
[
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"content": "Example 5 Given that $x_{1}, x_{2}, \\cdots, x_{10}$ are all positive integers, and $x_{1}+x_{2}+\\cdots+x_{10}=2005$, find the maximum and minimum values of $x_{1}^{2}+x_{2}^{2}+\\cdots+x_{10}^{2}$.",
"role": "user"
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{
"content": "<think>\nOkay, let's see. I need to find the maximum... |
End of preview. Expand in Data Studio
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PredictionBench OpenR1 Math Filtered Data
Filtered data derived from open-r1/OpenR1-Math-220k default subset for PredictionBench.
- Filtering: token length <= 8192.
- Full train: 70,000 rows, stored on the Hub as 7 parquet shards under
train/. - Validation/test: 201 rows,
test.parquet. - Random subsets:
sub3500_seed{1,2,3}/train.parquet, each 3,500 rows.
Local source file train.parquet was sharded for upload reliability:
train/train-00000-of-00007.parquet
...
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