S3-CoT: Self-Sampled Succinct Reasoning Enables Efficient Chain-of-Thought LLMs
Paper • 2602.01982 • Published
instruction stringlengths 87 4.38k | gold_answer stringlengths 0 159 | chain_0.0 stringlengths 1.69k 65.6k | chain_-0.1 stringlengths 1.28k 60.7k | chain_-0.3 stringlengths 294 44.3k | chain_-0.5 stringlengths 227 39.9k | tokens_len_0.0 int64 346 16.4k | tokens_len_-0.1 int64 432 16.4k | tokens_len_-0.3 int64 151 16.4k | tokens_len_-0.5 int64 62 16.4k | ratios_0.0 float64 1 1 | ratios_-0.1 float64 0.14 16.4 | ratios_-0.3 float64 0.04 11.7 | ratios_-0.5 float64 0.03 4.93 | answer_0.0 stringlengths 0 168 ⌀ | answer_-0.1 stringlengths 0 166 ⌀ | answer_-0.3 stringlengths 0 168 ⌀ | answer_-0.5 stringlengths 0 168 ⌀ | is_correct_0.0 bool 2
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Let $x$ , $y$ and $z$ all exceed $1$ and let $w$ be a positive number such that $\log_xw=24$ , $\log_y w = 40$ and $\log_{xyz}w=12$ . Find $\log_zw$ . Please reason step by step, and put your final answer within \boxed{}. | 60 | Okay, I have this problem here, and I need to find log_z w. The problem gives me some logarithmic equations involving x, y, z, and w. Let me write them down to organize my thoughts:
1. log_x w = 24
2. log_y w = 40
3. log_{xyz} w = 12
All x, y, z are greater than 1, and w is a positive number. So, I need to use these ... | Okay, I have this problem here, and I need to find log_z w. The problem gives me some logarithmic equations involving x, y, z, and w. Let me write them down to organize my thoughts:
1. log_x w = 24
2. log_y w = 40
3. log_{xyz} w = 12
And I need to find log_z w.
Hmm, I remember that logarithmic equations can often be... | Okay, I have this problem here, and I need to find log_z w. The problem gives me that log_x w = 24, log_y w = 40, and log_{xyz} w = 12. Let me write down these equations so I can see them clearly.
So, log_x w = 24 means that x^24 = w. Similarly, log_y w = 40 means y^40 = w, and log_{xyz} w = 12 means (xyz)^12 = w.
H... | Okay, I have this problem here, and I need to find log_z w. The problem gives me that log_x w = 24, log_y w = 40, and log_{xyz} w = 12. Let me write down these equations:
log_x w = 24 → means x^{24} = w.
Similarly, log_y w = 40 → y^{40} = w.
And log_{xyz} w = 12 → (xyz)^{12} = w.
Since all three expressions equal w... | 2,513 | 2,660 | 1,787 | 1,469 | 1 | 1.058496 | 0.711102 | 0.58456 | 60 | 60 | 60 | 60 | true | true | true | true | true | true | true | true |
Let $f(x)=|x-p|+|x-15|+|x-p-15|$ , where $0 < p < 15$ . Determine the minimum value taken by $f(x)$ for $x$ in the interval $p \leq x\leq15$ . Please reason step by step, and put your final answer within \boxed{}. | 15 | Okay, I need to find the minimum value of the function \( f(x) = |x - p| + |x - 15| + |x - p -15| \) where \( 0 < p < 15 \). The problem specifies that we should consider \( x \) in the interval \( p \leq x \leq 15 \). Hmm, okay, so I guess I should analyze this function step by step.
First, let me rewrite the functio... | Okay, I need to find the minimum value of the function \( f(x) = |x - p| + |x - 15| + |x - p - 15| \) where \( 0 < p < 15 \). The minimum should be found specifically within the interval \( p \leq x \leq 15 \). Hmm, let me think about how to approach this.
First, since it's a function involving absolute values, it's p... | Okay, I need to find the minimum value of the function \( f(x) = |x - p| + |x - 15| + |x - p - 15| \) where \( 0 < p < 15 \) and \( x \) is in the interval \( [p, 15] \).
First, let me understand what this function represents. It's the sum of three absolute value functions. The points where the expression inside the a... | Okay, I need to find the minimum value of the function \( f(x) = |x - p| + |x - 15| + |x - p -15| \) where \( 0 < p < 15 \). The interval for \( x \) is from \( p \) to 15. Hmm, since the function consists of absolute values, it's probably piecewise linear, and the minimum occurs at a point where the "kinks" happen, th... | 2,863 | 3,000 | 1,575 | 3,856 | 1 | 1.047852 | 0.550122 | 1.346839 | 15 | 15 | 15 | 15 | true | true | true | true | true | true | true | true |
What is the product of the real roots of the equation $x^2 + 18x + 30 = 2 \sqrt{x^2 + 18x + 45}$ ? Please reason step by step, and put your final answer within \boxed{}. | 20 | Okay, I have this equation to solve: x² + 18x + 30 = 2√(x² + 18x + 45). Hmm, that looks a bit complicated with the square root. Let me see how I can approach this.
First, maybe I can simplify the equation by making a substitution. I notice that both sides have similar expressions inside the square root and on the left... | Okay, I have this equation to solve: x² + 18x + 30 = 2√(x² + 18x + 45). Hmm, that looks a bit complicated with the square root. Let me see how I can approach this.
First, maybe I can simplify the equation by making a substitution. I notice that both sides have similar expressions inside the square root and on the left... | Okay, I have this equation to solve: x² + 18x + 30 = 2√(x² + 18x + 45). Hmm, it looks a bit complicated because of the square root. Maybe I can simplify it by substituting some expression.
Let me let y = x² + 18x. Then the equation becomes y + 30 = 2√(y + 45). That seems manageable. Now, I can square both sides to eli... | Okay, I need to find the product of the real roots of the equation \( x^2 + 18x + 30 = 2 \sqrt{x^2 + 18x + 45} \). Hmm, let me figure out how to approach this.
First, I notice the equation has a square root on the right side, which makes it a bit tricky. Maybe I can make a substitution to simplify it. Let me let \( y ... | 2,425 | 1,562 | 1,181 | 1,157 | 1 | 0.644124 | 0.48701 | 0.477113 | 20 | 20 | 20 | 20 | true | true | true | true | true | true | true | true |
A machine-shop cutting tool has the shape of a notched circle, as shown. The radius of the circle is $\sqrt{50}$ cm, the length of $AB$ is $6$ cm and that of $BC$ is $2$ cm. The angle $ABC$ is a right angle. Find the square of the distance (in centimeters) from $B$ to the center of the circle. [asy] size(150); defaultp... | 26 | Okay, I'm looking at this geometry problem about a machine-shop cutting tool shaped like a notched circle. Let me try to visualize it. There's a circle with radius √50 cm. Points A, B, and C are on or related to this circle. AB is 6 cm long, BC is 2 cm, and angle ABC is a right angle. I need to find the square of the d... | Okay, I'm looking at this geometry problem about a machine-shop cutting tool shaped like a notched circle. Let me try to visualize it. There's a circle with radius √50 cm. Points A, B, and C are such that AB is 6 cm, BC is 2 cm, and angle ABC is a right angle. I need to find the square of the distance from point B to t... | Okay, I need to find the square of the distance from point B to the center of the circle in this machine-shop cutting tool problem. Let me think about how to approach this step by step.
First, let me visualize the setup. The tool is a notched circle, which from the Asymptote code seems to be a circle with radius √50 c... | Okay, I need to find the square of the distance from point B to the center of the circle in this machine-shop cutting tool. The circle has a radius of √50 cm, and there's a right-angled triangle ABC where AB is 6 cm, BC is 2 cm, and angle ABC is a right angle. Point C is on the circle.
Let me visualize this: There's a... | 10,731 | 9,346 | 5,693 | 3,964 | 1 | 0.870935 | 0.530519 | 0.369397 | 26 | 26 | 26 | 26 | true | true | true | true | true | true | true | true |
"Suppose that the sum of the squares of two complex numbers $x$ and $y$ is $7$ and the sum of the cu(...TRUNCATED) | 4 | "Okay, I have this problem here: the sum of the squares of two complex numbers x and y is 7, and the(...TRUNCATED) | "Okay, I have this problem here: the sum of the squares of two complex numbers x and y is 7, and the(...TRUNCATED) | "Okay, I have this problem where two complex numbers \\( x \\) and \\( y \\) satisfy \\( x^2 + y^2 =(...TRUNCATED) | "Okay, I have this problem where two complex numbers \\( x \\) and \\( y \\) satisfy \\( x^2 + y^2 =(...TRUNCATED) | 11,385 | 3,147 | 1,731 | 1,161 | 1 | 0.276416 | 0.152042 | 0.101976 | 4 | 4 | 4 | 4 | true | true | true | true | true | true | true | true |
"Let $a_n=6^{n}+8^{n}$ . Determine the remainder on dividing $a_{83}$ by $49$ . Please reason step b(...TRUNCATED) | 35 | "Okay, I need to find the remainder when \\( a_{83} = 6^{83} + 8^{83} \\) is divided by 49. Hmm, 49 (...TRUNCATED) | "Okay, I need to find the remainder when \\( a_{83} = 6^{83} + 8^{83} \\) is divided by 49. Hmm, 49 (...TRUNCATED) | "Okay, I need to find the remainder when \\( a_{83} = 6^{83} + 8^{83} \\) is divided by 49. Hmm, 49 (...TRUNCATED) | "Okay, I need to find the remainder when \\( a_{83} = 6^{83} + 8^{83} \\) is divided by 49. Hmm, 49 (...TRUNCATED) | 7,488 | 2,716 | 2,338 | 1,829 | 1 | 0.362714 | 0.312233 | 0.244257 | 35 | 35 | 35 | 35 | true | true | true | true | true | true | true | true |
"Twenty five of King Arthur's knights are seated at their customary round table. Three of them are c(...TRUNCATED) | 57 | "Okay, so I need to figure out the probability that at least two of three chosen knights from a roun(...TRUNCATED) | "Okay, so I need to find the probability that at least two of the three chosen knights are sitting n(...TRUNCATED) | "Okay, so I need to find the probability that at least two of the three chosen knights are sitting n(...TRUNCATED) | "Okay, I need to find the probability that at least two of the three chosen knights from a round tab(...TRUNCATED) | 3,251 | 4,802 | 3,868 | 2,144 | 1 | 1.477084 | 1.189788 | 0.659489 | 57 | 57 | 57 | 57 | true | true | true | true | true | true | true | true |
"What is the largest $2$ -digit prime factor of the integer $n = {200\\choose 100}$ ? Please reason (...TRUNCATED) | 61 | "Okay, so I need to find the largest two-digit prime factor of the binomial coefficient \\( n = \\db(...TRUNCATED) | "Okay, so I need to find the largest two-digit prime factor of the binomial coefficient \\( n = \\db(...TRUNCATED) | "Okay, I need to find the largest two-digit prime factor of the binomial coefficient \\( {200 \\choo(...TRUNCATED) | "Okay, I need to find the largest two-digit prime factor of \\( \\dbinom{200}{100} \\). Hmm, let me (...TRUNCATED) | 11,082 | 6,178 | 4,884 | 10,793 | 1 | 0.557481 | 0.440715 | 0.973922 | 61 | 61 | 61 | 101 | true | true | true | false | true | true | true | true |
"Find the minimum value of $\\frac{9x^2\\sin^2 x + 4}{x\\sin x}$ for $0 < x < \\pi$ . Please reason (...TRUNCATED) | 12 | "Okay, I need to find the minimum value of the function \\( \\frac{9x^2 \\sin^2 x + 4}{x \\sin x} \\(...TRUNCATED) | "Okay, I need to find the minimum value of the function \\( \\frac{9x^2 \\sin^2 x + 4}{x \\sin x} \\(...TRUNCATED) | "Okay, I need to find the minimum value of the function \\( \\frac{9x^2 \\sin^2 x + 4}{x \\sin x} \\(...TRUNCATED) | "Okay, I need to find the minimum value of the function \\( \\frac{9x^2 \\sin^2 x + 4}{x \\sin x} \\(...TRUNCATED) | 4,292 | 1,993 | 1,763 | 1,310 | 1 | 0.464352 | 0.410764 | 0.305219 | 12 | 12 | 12 | 12 | true | true | true | true | true | true | true | true |
"The numbers $1447$ , $1005$ and $1231$ have something in common: each is a $4$ -digit number beginn(...TRUNCATED) | 432 | "Okay, I need to find how many four-digit numbers start with 1 and have exactly two identical digits(...TRUNCATED) | "Okay, I need to find how many four-digit numbers start with 1 and have exactly two identical digits(...TRUNCATED) | "Okay, I need to find how many 4-digit numbers start with 1 and have exactly two identical digits. L(...TRUNCATED) | "Okay, I need to find how many 4-digit numbers start with 1 and have exactly two identical digits. L(...TRUNCATED) | 13,043 | 6,263 | 8,260 | 10,062 | 1 | 0.480181 | 0.63329 | 0.771448 | 459 | 432 | 432 | 486 | false | true | true | false | true | true | true | true |
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Dataset Overview
We release a new self-sampled variable-length reasoning dataset based on DeepSeek-R1-Distill-Qwen-7B.
The seed problems are collected from three high-quality datastes: MATH500, LIMO-v2, and AIME problems released before 2023.
The data are used for efficient cot learning in our paper (S3-CoT: Self-Sampled Succinct Reasoning Enables Efficient Chain-of-Thought LLMs).
For each instruction (problem), we provide multiple reasoning traces generated under different activation-steering ratios, together with token-length statistics and answer extraction based on \boxed{} parsing.
This dataset is designed to support research on efficient reasoning, reasoning-length control, and length–accuracy trade-offs.
For more details about the data construction process, sampling configuration, and metadata fields, please refer to the V1 release: S3-CoT-Self-Sampled-Data.
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