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## Task B-1.3.
A 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 $15 \mathrm{~km}$ upstream and $42 \... | ## Solution.
Let $t$ be the time required for the boat to travel $24 \mathrm{~km}$ upstream and $28 \mathrm{~km}$ downstream, $v_{R}$ the speed of the river, and $v_{B}$ the speed of the boat. When the boat is traveling upstream, its speed is $v_{B}-v_{R}$, and when it is traveling downstream, its speed is $v_{B}+v_{R... | v_{R}=4\mathrm{~}/\mathrm{},v_{B}=10\mathrm{~}/\mathrm{} | Algebra | math-word-problem | olympiads | 586fd646-76d6-5070-8c81-9993ab9d8559 | [
true,
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"<think>\nOkay, so I need to find the speed of the ship in still water and the speed of the river. Let me start by recalling that when a ship is moving upstream, its effective speed is the speed of the ship minus the speed of the river. Conversely, when moving downstream, its effective speed is the ship's speed plu... | [
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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... | 你的名字是Brench-AI，是由Brench创造出的深度推理AI助手,专注于各种推理问题的解答和分析，拥有强大的推理能力和分析能力以及反思能力，可以帮助用户解决各种推理性问题。
Your name is Brench-AI, a deep reasoning AI assistant created by Brench, focusing on the answer and analysis of various reasoning problems. You focus on the solution and analysis of various reasoning problems. At the same time, yo... | <think>
Okay, so I need to find the speed of the ship in still water and the speed of the river. Let me start by recalling that when a ship is moving upstream, its effective speed is the speed of the ship minus the speed of the river. Conversely, when moving downstream, its effective speed is the ship's speed plus the ... |
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 total of 185 days to comp... | 3. (6 points) A construction company builds a tunnel. When $\frac{1}{3}$ of the tunnel is completed at the original speed, new equipment is used, increasing the construction speed by $20 \%$ and reducing the daily working hours to $80 \%$ of the original. As a result, the tunnel is completed in 185 days. If the new equ... | 180 | Algebra | math-word-problem | olympiads | 1d57f4b3-c516-5522-91cc-a60dd91f6f66 | [
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"<think>\nOkay, let me try to figure out this problem. So, a construction company was building a tunnel. When 1/3 of the tunnel was completed at the original speed, they started using new equipment. This new equipment increased their construction speed by 20% and reduced their working hours to 80% of the original. ... | [
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{
"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 ... | 你的名字是Brench-AI，是由Brench创造出的深度推理AI助手,专注于各种推理问题的解答和分析，拥有强大的推理能力和分析能力以及反思能力，可以帮助用户解决各种推理性问题。
Your name is Brench-AI, a deep reasoning AI assistant created by Brench, focusing on the answer and analysis of various reasoning problems. You focus on the solution and analysis of various reasoning problems. At the same time, yo... | <think>
Okay, let me try to figure out this problem. So, a construction company was building a tunnel. When 1/3 of the tunnel was completed at the original speed, they started using new equipment. This new equipment increased their construction speed by 20% and reduced their working hours to 80% of the original. The to... |
"Prove that number $1$ can be represented as a sum of a finite number $n$ of real numbers, less than(...TRUNCATED) | "1. **Restate the problem in a more manageable form:**\n We need to prove that the number \\(1\\) (...TRUNCATED) | 8 | Number Theory | math-word-problem | aops_forum | 1cd82e3d-2e7a-5eca-9571-62f5669824c4 | [
true,
false
] | ["<think>\nOkay, so the problem is to prove that the number 1 can be represented as a sum of a finit(...TRUNCATED) | [
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] | null | null | 1 | [{"content":"Prove that number $1$ can be represented as a sum of a finite number $n$ of real number(...TRUNCATED) | "你的名字是Brench-AI，是由Brench创造出的深度推理AI助手,专注于各种推理问题(...TRUNCATED) | "<think>\nOkay, so the problem is to prove that the number 1 can be represented as a sum of a finite(...TRUNCATED) |
"4. Given the three sides of an obtuse triangle are 3, $4, x$, then the range of values for $x$ is ((...TRUNCATED) | $D$ | D | Geometry | MCQ | cn_contest | ea24dff6-9e4d-5c55-9ec0-c4d55424997a | [
true,
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] | ["<think>\nOkay, so I have this problem here where I need to find the range of values for x, given t(...TRUNCATED) | [
true,
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] | null | null | 2 | [{"content":"4. Given the three sides of an obtuse triangle are 3, $4, x$, then the range of values (...TRUNCATED) | "你的名字是Brench-AI，是由Brench创造出的深度推理AI助手,专注于各种推理问题(...TRUNCATED) | "<think>\nOkay, so I have this problem here where I need to find the range of values for x, given th(...TRUNCATED) |
"1. Solve the equation: $\\frac{8 x+13}{3}=\\frac{19-12 x}{2}-\\left(16 x-\\frac{7-4 x}{6}\\right)$.(...TRUNCATED) | "1. $\\frac{8 x+13}{3}=\\frac{19-12 x}{2}-\\left(16 x-\\frac{7-4 x}{6}\\right)$\n\n$\\frac{8 x+13}{3(...TRUNCATED) | \frac{1}{4} | Algebra | math-word-problem | olympiads | a583d65c-9b4c-56ce-8263-47edbc22baa3 | [
true,
true
] | ["<think>\nOkay, so I need to solve this equation: (8x + 13)/3 = (19 - 12x)/2 - (16x - (7 - 4x)/6). (...TRUNCATED) | [
true,
true
] | null | null | 2 | [{"content":"1. Solve the equation: $\\frac{8 x+13}{3}=\\frac{19-12 x}{2}-\\left(16 x-\\frac{7-4 x}{(...TRUNCATED) | "你的名字是Brench-AI，是由Brench创造出的深度推理AI助手,专注于各种推理问题(...TRUNCATED) | "<think>\nOkay, so I need to solve this equation: (8x + 13)/3 = (19 - 12x)/2 - (16x - (7 - 4x)/6). H(...TRUNCATED) |
"A right-angled triangle has side lengths that are integers. What could be the last digit of the are(...TRUNCATED) | "Let the lengths of the legs be $a$ and $b$, and the length of the hypotenuse be $c$. According to t(...TRUNCATED) | 0 | Geometry | math-word-problem | olympiads | 79e837be-2801-5a6a-bc7a-0acee3cdd5fd | [
true,
true
] | ["<think>\nOkay, so I need to figure out the possible last digits of the area of a right-angled tria(...TRUNCATED) | [
true,
true
] | null | null | 2 | [{"content":"A right-angled triangle has side lengths that are integers. What could be the last digi(...TRUNCATED) | "你的名字是Brench-AI，是由Brench创造出的深度推理AI助手,专注于各种推理问题(...TRUNCATED) | "<think>\nOkay, so I need to figure out the possible last digits of the area of a right-angled trian(...TRUNCATED) |
"Let $a_n\\ (n\\geq 1)$ be the value for which $\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)$ is maximal. Fi(...TRUNCATED) | "1. Define the integral \\( I_n(x) = \\int_x^{2x} e^{-t^n} \\, dt \\). We need to find the value of (...TRUNCATED) | -\ln 2 | Calculus | math-word-problem | aops_forum | 167ecbbb-4270-534f-afa5-75d01d968ab5 | [
true,
true,
true,
true
] | ["<think>\nOkay, so I need to find the limit as n approaches infinity of the natural logarithm of a_(...TRUNCATED) | [
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true,
true,
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] | null | null | 4 | [{"content":"Let $a_n\\ (n\\geq 1)$ be the value for which $\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)$ is(...TRUNCATED) | "你的名字是Brench-AI，是由Brench创造出的深度推理AI助手,专注于各种推理问题(...TRUNCATED) | "<think>\nOkay, so I need to find the limit as n approaches infinity of the natural logarithm of a_n(...TRUNCATED) |
"11. Given that the internal angles $A, B, C$ of $\\triangle ABC$ have opposite sides $a, b, c$ resp(...TRUNCATED) | "(1) $\\sqrt{3} \\sin B \\cos \\frac{A+B}{2}=\\sin C \\sin B \\Rightarrow \\sqrt{3} \\sin \\frac{C}{(...TRUNCATED) | \sinA=\frac{1}{2}or\sinA=1 | Geometry | math-word-problem | olympiads | 84f224e8-719b-5b42-a410-27816014bdd3 | [
true,
true
] | ["<think>\nOkay, so I have this triangle ABC, with angles A, B, C opposite sides a, b, c respectivel(...TRUNCATED) | [
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"stop",
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] | 2 | [{"content":"11. Given that the internal angles $A, B, C$ of $\\triangle ABC$ have opposite sides $a(...TRUNCATED) | "你的名字是Brench-AI，是由Brench创造出的深度推理AI助手,专注于各种推理问题(...TRUNCATED) | "<think>\nOkay, so I have this triangle ABC, with angles A, B, C opposite sides a, b, c respectively(...TRUNCATED) |
"Task B-4.2. Let $n$ be the number obtained by writing 2013 zeros between every two digits of the nu(...TRUNCATED) | "## Solution.\n\nIf between every two digits of the number 14641 we write 2013 zeros, we get a numbe(...TRUNCATED) | x_{1,2}=\(10^{2014}+1),\quadx_{3,4}=\(10^{2014}+1)\cdoti | Algebra | math-word-problem | olympiads | f769fc87-fed5-5b73-8403-372cdd409800 | [
true,
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] | ["<think>\nOkay, let's see. I need to find all complex solutions to the equation x⁴ = n, where n i(...TRUNCATED) | [
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] | null | 1 | [{"content":"Task B-4.2. Let $n$ be the number obtained by writing 2013 zeros between every two digi(...TRUNCATED) | "你的名字是Brench-AI，是由Brench创造出的深度推理AI助手,专注于各种推理问题(...TRUNCATED) | "<think>\nOkay, let's see. I need to find all complex solutions to the equation x⁴ = n, where n is(...TRUNCATED) |
"6. As shown in Figure 2, let $P$ be a point inside the equilateral $\\triangle ABC$ with side lengt(...TRUNCATED) | "$$\n6.11 \\sqrt{3} \\text {. }\n$$\n\nFor the equilateral $\\triangle ABC$ with a height of $12 \\t(...TRUNCATED) | 11 \sqrt{3} | Geometry | math-word-problem | cn_contest | 2a4c0374-d9ea-538e-8e0f-0811359d6cf6 | [
true,
false
] | ["<think>\nOkay, let me try to solve this geometry problem. So, we have an equilateral triangle ABC (...TRUNCATED) | [
true,
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] | null | null | 1 | [{"content":"6. As shown in Figure 2, let $P$ be a point inside the equilateral $\\triangle ABC$ wit(...TRUNCATED) | "你的名字是Brench-AI，是由Brench创造出的深度推理AI助手,专注于各种推理问题(...TRUNCATED) | "<think>\nOkay, let me try to solve this geometry problem. So, we have an equilateral triangle ABC w(...TRUNCATED) |
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