AStar-Thought-V2
Collection
4 items • Updated
Datasets:
system stringclasses 1
value | latent_conversations listlengths 2 2 | original_conversations listlengths 2 2 | steps listlengths 1 300 | chosen_steps_flag listlengths 1 300 |
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"value": "## 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 ... | [
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"value": "## 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 ... | [
"We need to solve a problem about a ship traveling upstream and downstream. The problem states:",
"A ship traveling along a river has covered 24 km upstream and 28 km downstream. For this journey, it took half an hour less than for traveling 30 km upstream and 21 km downstream, or half an hour more than for trave... | [
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"value": "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 ... | [
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"value": "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 ... | [
"We are given a problem: A construction company was building a tunnel. When 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 complet... | [
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"value": "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 $1<x<\\sqrt{7}$."
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"value": "<think>\n\nWe are given: three sides of ... | [
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"value": "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 $1<x<\\sqrt{7}$."
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"value": "<think>We are given: three sides of an o... | [
"We are given: three sides of an obtuse triangle are 3, 4, x. We need the range of values for x such that a triangle with sides 3, 4, x is obtuse (i.e., has an angle greater than 90 degrees). Also the triangle must be valid (triangle inequality). So we need to find x satisfying triangle inequality and the condition... | [
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"value": "1. Solve the equation: $\\frac{8 x+13}{3}=\\frac{19-12 x}{2}-\\left(16 x-\\frac{7-4 x}{6}\\right)$."
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"value": "<think>\n\nWe are asked to solve the equation:\n\n(8x + 13)/3 = (19 - 12x)/2 - (16x - (7 - 4x)/6)\n\n<latent><latent_1></latent>\n\... | [
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"value": "1. Solve the equation: $\\frac{8 x+13}{3}=\\frac{19-12 x}{2}-\\left(16 x-\\frac{7-4 x}{6}\\right)$."
},
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"value": "<think>We are asked to solve the equation:\n\n(8x + 13)/3 = (19 - 12x)/2 - (16x - (7 - 4x)/6)\n\nWe need to solve for x. Let's rewr... | [
"We are asked to solve the equation:",
"(8x + 13)/3 = (19 - 12x)/2 - (16x - (7 - 4x)/6)",
"We need to solve for x. Let's rewrite clearly.",
"Equation:",
"(8x + 13)/3 = (19 - 12x)/2 - [16x - (7 - 4x)/6]",
"We need to simplify both sides. Let's start by simplifying the right-hand side (RHS). There is a term... | [
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"value": "Let $a_n\\ (n\\geq 1)$ be the value for which $\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)$ is maximal. Find $\\lim_{n\\to\\infty} \\ln a_n.$"
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"value": "<think>\n\nWe are given: Let a_n (n ≥ 1) be the value for which ∫_x^{2x} e^{-t^n} dt (x ≥ 0) is ... | [
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"value": "Let $a_n\\ (n\\geq 1)$ be the value for which $\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)$ is maximal. Find $\\lim_{n\\to\\infty} \\ln a_n.$"
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"value": "<think>We are given: Let a_n (n ≥ 1) be the value for which ∫_x^{2x} e^{-t^n} dt (x ≥ 0) is maxi... | [
"We are given: Let a_n (n ≥ 1) be the value for which ∫_x^{2x} e^{-t^n} dt (x ≥ 0) is maximal. Find lim_{n→∞} ln a_n.",
"Interpretation: For each n, define f_n(x) = ∫_x^{2x} e^{-t^n} dt, for x ≥ 0. We need to find the x that maximizes f_n(x) (presumably unique, but we are told \"a_n be the value for which ... is ... | [
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"value": "11. Given that the internal angles $A, B, C$ of $\\triangle ABC$ have opposite sides $a, b, c$ respectively, and $\\sqrt{3} b \\cos \\frac{A+B}{2}=c \\sin B$.\n(1) Find the size of $\\angle C$;\n(2) If $a+b=\\sqrt{3} c$, find $\\sin A$."
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"value": "11. Given that the internal angles $A, B, C$ of $\\triangle ABC$ have opposite sides $a, b, c$ respectively, and $\\sqrt{3} b \\cos \\frac{A+B}{2}=c \\sin B$.\n(1) Find the size of $\\angle C$;\n(2) If $a+b=\\sqrt{3} c$, find $\\sin A$."
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"We are given: √3 b cos((A+B)/2) = c sin B.",
"We need to find angle C first.",
"Recall that in triangle ABC, A+B+C = π, so (A+B)/2 = (π - C)/2 = π/2 - C/2.",
"Thus cos((A+B)/2) = cos(π/2 - C/2) = sin(C/2).",
"So left side: √3 b * sin(C/2).",
"Right side: c sin B.",
"Thus equation: √3 b sin(C/2) = c sin... | [
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"value": "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 $\\mathbb{C}$."
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"value": "<think>\n\nWe have to parse the problem: \"L... | [
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"value": "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 $\\mathbb{C}$."
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"value": "<think>We have to parse the problem: \"Let n... | [
"We have to parse the problem: \"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 C.\" So we need to find all complex fourth roots of n.",
"First, what is n? The number 14641 has digits: 1,4,6,4,1. \"Writing... | [
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[{"from":"user","value":"6. As shown in Figure 2, let $P$ be a point inside the equilateral $\\trian(...TRUNCATED) | [{"from":"user","value":"6. As shown in Figure 2, let $P$ be a point inside the equilateral $\\trian(...TRUNCATED) | ["We are given an equilateral triangle ABC with side length 12. Point P is inside. Perpendiculars PD(...TRUNCATED) | [1,1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1(...TRUNCATED) | |
[{"from":"user","value":"8.59 For each pair of real numbers $x, y$, the function $f$ satisfies the f(...TRUNCATED) | [{"from":"user","value":"8.59 For each pair of real numbers $x, y$, the function $f$ satisfies the f(...TRUNCATED) | ["We are given a functional equation: for all real numbers x, y, f(x) + f(y) = f(x+y) - x y - 1. So (...TRUNCATED) | [
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[{"from":"user","value":"Given $0 \\leqslant x, y, z \\leqslant 1$, solve the equation:\n$$\\frac{x}(...TRUNCATED) | [{"from":"user","value":"Given $0 \\leqslant x, y, z \\leqslant 1$, solve the equation:\n$$\\frac{x}(...TRUNCATED) | ["We need to solve the equation:","For $0 \\le x,y,z \\le 1$, solve:","$$\\frac{x}{1+y+zx} + \\frac{(...TRUNCATED) | [1,0,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,0,1,0,1,1(...TRUNCATED) |
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AStar-Thought-V2-OpenR1-Math-3k
This dataset is the training data used for the A-Thought-V2* models presented in A*-Thought-V2: Efficient Latent Reasoning via Geometric Dynamics of LLM.
It is built from OpenR1-Math-3k and compressed using the A*-Thought-V2 pipeline, which interleaves explicit text reasoning with implicit latent tokens guided by the geometric dynamics of the LLM. Each example includes a system prompt, latent conversations, original conversations, segmented steps, and a chosen_steps_flag indicating which reasoning steps were retained as explicit text.
- Paper: A*-Thought-V2
- Code: https://github.com/AI9Stars/AStar-Thought
- Models & Datasets collection: https://huggingface.co/collections/xxang/astar-thought-v2
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