Datasets:
dataset_name stringclasses 1
value | method stringclasses 1
value | model_size stringclasses 1
value | experiment_dir stringclasses 1
value | source_file stringclasses 19
values | step int64 5 95 | sample_index int64 0 23 | split stringclasses 1
value | prompt stringlengths 256 13.8k | completion stringlengths 381 4.27k |
|---|---|---|---|---|---|---|---|---|---|
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 0 | train | <|im_start|>user
Problem: Given the function \( f(x) = x + \cos x \), where \( x \in \left[0, \frac{\pi}{2} \right] \), find the maximum value of \( f(x) \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|endoftext|>... | We are given the function:
$$
f(x) = x + \cos x, \quad x \in \left[0, \frac{\pi}{2} \right]
$$
Our goal is to **find the maximum value** of this function on the interval $ \left[0, \frac{\pi}{2} \right] $.
---
### Step 1: Understand the function
The function is the sum of two parts:
- $ x $: a linear function tha... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 1 | train | <|im_start|>user
Problem: What is the sum of all three-digit numbers \( n \) such that \( \frac{3n+2}{5n+1} \) is not in simplest form?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endofte... | We are given the expression:
$$
\frac{3n + 2}{5n + 1}
$$
We are to find **all three-digit numbers** $ n $ such that the fraction is **not in simplest form**, and then find the **sum** of those $ n $.
---
### Step 1: Understand what it means for a fraction to be in **simplest form**
A fraction $ \frac{a}{b} $ is in... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 2 | train | <|im_start|>user
Problem: On the day when Dima was congratulated on his birthday by his brother and sister, Dima said: "Look how interesting, I am now twice as old as my brother and three times as old as my sister!" "And your average age is 11 years," added their father. How old is Dima?
Please reason step by step, an... | We are given a problem where Dima is being celebrated on his birthday. His brother and sister also join in, and Dima makes a few statements about his age compared to his siblings, and then their father mentions that the **average age** of the three of them is 11 years.
---
### Step 1: Define variables
Let:
- Dima's ... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 3 | train | <|im_start|>user
Problem: Consider a large rectangle of size $m$ by $n$, divided into small squares with side length 1.
How many ways are there to go from the bottom left corner to the top right corner by moving only along the grid, and only upward or to the right?
Please reason step by step, and put your final answe... | We are given a grid that is $ m \times n $, meaning it has $ m $ rows and $ n $ columns, and we are to count the number of paths from the **bottom-left corner** to the **top-right corner**, moving **only right or up** at each step.
---
### Step-by-step Breakdown:
1. **Grid Structure**:
- A grid of size $ m \times... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 4 | train | <|im_start|>user
Problem: What is the remainder when $2x^2-17x+47$ is divided by $x-5$?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|end... | We are asked to find the **remainder** when the polynomial
$$
P(x) = 2x^2 - 17x + 47
$$
is divided by $ x - 5 $.
---
### Step 1: Use the **Remainder Theorem**
The **Remainder Theorem** states that when a polynomial $ P(x) $ is divided by $ x - a $, the **remainder** is
$$
P(a)
$$
So, to find the remainder whe... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 5 | train | <|im_start|>user
Problem: Determine the prime numbers $p$ and $q$ for which $p^{q} + q^{p}$ is also a prime number.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|e... | We are asked to find **prime numbers** $ p $ and $ q $ such that:
$$
p^q + q^p
$$
is also a **prime number**.
---
### **Step 1: Understand the problem**
We are to find **prime numbers** $ p, q $ such that:
$$
p^q + q^p \text{ is also a prime number.}
$$
We'll try small prime numbers $ p, q $ and evaluate $ p^q +... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 6 | train | <|im_start|>user
Problem: Let \( g(x) \) be a strictly increasing function defined for all \( x \geq 0 \). It is known that the range of \( t \) satisfying
\[ g(2t^2 + t + 5) < g(t^2 - 3t + 2) \]
is \( b < t < a \). Find \( a - b \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im... | We are given that $ g(x) $ is a **strictly increasing** function defined for all $ x \geq 0 $. That is, if $ x_1 < x_2 $, then $ g(x_1) < g(x_2) $.
We are told that the **range of $ t $** satisfying:
$$
g(2t^2 + t + 5) < g(t^2 - 3t + 2)
$$
is $ b < t < a $, and we are to find $ a - b $.
---
### Step 1: Use the prope... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 7 | train | <|im_start|>user
Problem: Given that $\mathbf{a}$ and $\mathbf{b}$ are nonzero vectors such that $\|\mathbf{a} + \mathbf{b}\| = \|\mathbf{a} - \mathbf{b}\|,$ find the angle between $\mathbf{a}$ and $\mathbf{b},$ in degrees.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>as... | We are given that:
$$
\|\mathbf{a} + \mathbf{b}\| = \|\mathbf{a} - \mathbf{b}\|
$$
We are to find the angle $\theta$ between the nonzero vectors $\mathbf{a}$ and $\mathbf{b}$.
---
### Step 1: Use the property of vector norms
Recall that the square of the magnitude of a vector is:
$$
\|\mathbf{v}\|^2 = \mathbf{v} ... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 8 | train | <|im_start|>user
Problem: At breakfast, lunch, and dinner, Joe randomly chooses with equal probabilities either an apple, an orange, or a banana to eat. On a given day, what is the probability that Joe will eat at least two different kinds of fruit?
Please reason step by step, and put your final answer within \boxed{}... | We are told that Joe eats **three meals** each day: **breakfast, lunch, and dinner**. At each meal, he randomly chooses one of three fruits: **apple, orange, or banana**, with **equal probability** of $ \frac{1}{3} $ for each.
We are to find the **probability that Joe eats at least two different kinds of fruit** on a ... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 9 | train | <|im_start|>user
Problem: Calculate the length of the arc of the curve \( x = 0.25 y^{2} - 0.5 \ln y \), enclosed between the points \( y = 1 \) and \( y = 1.5 \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|endof... | We are given the curve:
$$
x = 0.25 y^2 - 0.5 \ln y
$$
and asked to compute the **arc length** of this curve between $ y = 1 $ and $ y = 1.5 $.
---
### **Step 1: Use the arc length formula for a curve expressed as $ x = f(y) $**
If $ x = f(y) $, the formula for the **arc length** of the curve from $ y = a $ to $ y... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 10 | train | <|im_start|>user
Problem:
Let \(\xi, \xi_{1}, \xi_{2}, \ldots\) be a sequence of random variables.
(a) Show that
$$
\forall \varepsilon>0: \mathrm{P}\left(\left|\xi_{n}-\xi\right| \geqslant \varepsilon \text { infinitely often }\right)=0 \Leftrightarrow \xi_{n} \rightarrow \xi \text { almost surely }
$$
(b) Prove t... | We are given a problem involving **almost sure convergence** of a sequence of random variables and its relationship to other modes of convergence. Let's break down each part step by step.
---
### **(a) Show that:**
$$
\forall \varepsilon>0: \mathrm{P}\left(\left|\xi_{n}-\xi\right| \geqslant \varepsilon \text{ infinit... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 11 | train | <|im_start|>user
Problem: In parallelogram $ABCD$ holds $AB=BD$ . Let $K$ be a point on $AB$ , different from $A$ , such that $KD=AD$ . Let $M$ be a point symmetric to $C$ with respect to $K$ , and $N$ be a point symmetric to point $B$ with respect to $A$ . Prove that $DM=DN$
Please reason step by ... | We are given a **parallelogram** $ABCD$ with the property that $AB = BD$, and we need to show that:
- $K$ is a point on $AB$ (not $A$), such that $KD = AD$,
- $M$ is the **reflection** of $C$ over $K$,
- $N$ is the **reflection** of $B$ over $A$,
- Then, show that:
$$
DM = DN
$$
---
### **Step 1: Understand ... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 12 | train | <|im_start|>user
Problem: A motorcyclist left city A for city B. If he travels at a speed of 50 km/h, he will arrive in city B one hour earlier than the scheduled time. If he travels at a speed of 35 km/h, he will be 2 hours late. Find the distance between cities A and B.
Please reason step by step, and put your final... | We are given a problem involving a motorcyclist traveling between city A and city B. The motorcyclist arrives at different times depending on the speed at which he travels.
---
### Step 1: Define variables
Let:
- $ d $ = distance between cities A and B (in km)
- $ t $ = the **scheduled time** (in hours) that the mot... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 13 | train | <|im_start|>user
Problem: We call a pair of natural numbers \((a, p)\) good if the number \(a^3 + p^3\) is divisible by \(a^2 - p^2\), with \(a > p\).
(a) (1 point) Specify any possible value of \(a\) for which the pair \((a, 13)\) is good.
(b) (3 points) Find the number of good pairs for which \(p\) is a prime numbe... | We are given a definition for "good" pairs:
A pair $(a, p)$ is **good** if the number $a^3 + p^3$ is divisible by $a^2 - p^2$, with $a > p$.
We will solve both parts step by step.
---
### **(a) (1 point): Specify any possible value of $a$ for which the pair $(a, 13)$ is good.**
Let’s analyze the condition for the... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 14 | train | <|im_start|>user
Problem: Given the expression $\frac{1}{x}+\frac{1}{y}+\frac{1}{xy}$, where $x$ and $y$ are natural numbers. If the number $x$ is increased by 4, and the number $y$ is decreased by 4, the value of this expression does not change. Prove that $xy + 4$ is a square of an integer.
Please reason step by ste... | We are given the expression:
$$
E = \frac{1}{x} + \frac{1}{y} + \frac{1}{xy}
$$
where $ x $ and $ y $ are **natural numbers**.
It is given that if $ x $ is increased by 4, and $ y $ is decreased by 4, the value of the expression **does not change**:
$$
\frac{1}{x+4} + \frac{1}{y-4} + \frac{1}{(x+4)(y-4)} = \frac{1}... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 15 | train | <|im_start|>user
Problem: Compare the numbers: \( A = 2011 \cdot 20122012 \cdot 201320132013 \) and \( B = 2013 \cdot 20112011 \cdot 201220122012 \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|endoftext|><|endoft... | We are given:
$$
A = 2011 \cdot 20122012 \cdot 201320132013
$$
$$
B = 2013 \cdot 20112011 \cdot 201220122012
$$
Our goal is to **compare** $ A $ and $ B $ and determine which one is **larger**.
---
### Step 1: Understand the structure of the numbers
Let's first analyze the form of the numbers:
Each of these numbe... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 16 | train | <|im_start|>user
Problem: Given that the modulus of the complex number \( z \) is 1, if \( |z + 1 + \mathrm{i}| \) attains its maximum value and minimum value respectively when \( z = z_1 \) and \( z = z_2 \), then \( z_1 - z_2 = \quad \) .
Please reason step by step, and put your final answer within \boxed{}.<|im_end... | We are given that the **modulus** of a complex number $ z $ is 1, meaning:
$$
|z| = 1
$$
This defines the **unit circle** in the complex plane. The complex number $ z $ can be written as:
$$
z = e^{i\theta} = \cos\theta + i\sin\theta \quad \text{for } \theta \in [0, 2\pi)
$$
We are also given that:
$$
|z + 1 + i|
... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 17 | train | <|im_start|>user
Problem: If we line up in rows of ten people, one person will be left over. If we line up in rows of nine people, again one person will be leftover. The same will happen if we line up in rows of eight, seven, six, five, four, three, and finally two people. There are, of course, fewer than five thousand... | We are given that:
- If we line up in rows of **10**, **9**, **8**, **7**, **6**, **5**, **4**, **3**, or **2** people, **one person will always be left over**.
- So the **remainder is always 1** when the number of people is divided by any of these numbers: **2, 3, 4, 5, 6, 7, 8, 9, 10**.
- The total number of people ... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 18 | train | <|im_start|>user
Problem: Find the cosine of the angle between vectors $\overrightarrow{A B}$ and $\overrightarrow{A C}$.
$A(2, -8, -1), B(4, -6, 0), C(-2, -5, -1)$
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|end... | We are given three points in 3D space:
- $ A(2, -8, -1) $
- $ B(4, -6, 0) $
- $ C(-2, -5, -1) $
We are to find the **cosine of the angle** between vectors $ \vec{AB} $ and $ \vec{AC} $.
---
### Step 1: Find the vectors $ \vec{AB} $ and $ \vec{AC} $
Recall that the vector from point $ P $ to point $ Q $ is:
$$
\ve... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_10.json | 10 | 19 | train | <|im_start|>user
Problem: From time $t=0$ to time $t=1$ a population increased by $i\%$, and from time $t=1$ to time $t=2$ the population increased by $j\%$. Therefore, from time $t=0$ to time $t=2$ the population increased by
$\text{(A) (i+j)\%} \quad \text{(B) } ij\%\quad \text{(C) } (i+ij)\%\quad \text{(D) } \left(i... | We are given the following:
- From time $ t = 0 $ to $ t = 1 $, the population increased by $ i\% $.
- From time $ t = 1 $ to $ t = 2 $, the population increased by $ j\% $.
We are to find the **total percentage increase** from $ t = 0 $ to $ t = 2 $, in **terms of $ i $ and $ j $**.
---
### Step 1: Let the populat... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 0 | train | <|im_start|>user
Problem: Find the fraction of the form \(\frac{n}{23}\) that is the closest to the fraction \(\frac{37}{57}\) (where \(n\) is an integer).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|endoftext|><|... | We are given the task to find the fraction of the form $\frac{n}{23}$ that is **closest** to $\frac{37}{57}$, where $n$ is an integer.
---
### Step 1: Convert $\frac{37}{57}$ to a decimal for comparison
$$
\frac{37}{57} \approx 0.649122807
$$
We want to find an integer $n$ such that $\frac{n}{23}$ is **closest to**... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 1 | train | <|im_start|>user
Problem: How many odd integers are there between $\frac{17}{4}$ and $\frac{35}{2}?$
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|end... | We are asked to find how many **odd integers** lie **strictly between** the two numbers:
$$
\frac{17}{4} \quad \text{and} \quad \frac{35}{2}
$$
---
### Step 1: Convert the fractions to decimals (for easier comparison)
$$
\frac{17}{4} = 4.25, \quad \frac{35}{2} = 17.5
$$
So, we are looking for **odd integers** **st... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 2 | train | <|im_start|>user
Problem: Solve for $x$: $2(3^x) = 162$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftex... | We are given the equation:
$$
2(3^x) = 162
$$
---
### Step 1: Divide both sides by 2
$$
3^x = \frac{162}{2} = 81
$$
So now we have:
$$
3^x = 81
$$
---
### Step 2: Express 81 as a power of 3
We know that:
$$
81 = 3^4
$$
So:
$$
3^x = 3^4
$$
---
### Step 3: Equate the exponents
Since the bases are the same,... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 3 | train | <|im_start|>user
Problem: The function $g\left(x\right)$ is defined as $\sqrt{\dfrac{x}{2}}$ for all positive $x$ . $ $ $$ g\left(g\left(g\left(g\left(g\left(\frac{1}{2}\right)+1\right)+1\right)+1\right)+1\right) $$ $ $ can be expressed as $\cos(b)$ using degrees, where $0^\circ < b < 90^\circ$ and $b =... | We are given a nested function definition and asked to compute:
$$
g\left(g\left(g\left(g\left(g\left(\frac{1}{2}\right)+1\right)+1\right)+1\right)+1\right)
$$
where:
$$
g(x) = \sqrt{\frac{x}{2}}
$$
and this is supposed to simplify to:
$$
\cos(b)
$$
where $ 0^\circ < b < 90^\circ $, and $ b = \frac{p}{q} $ with $... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 4 | train | <|im_start|>user
Problem: On the planet Lemniscate, the people use an advanced version of the periodic table. They know that $\mathrm{Kr}$ deteriorates into $\mathrm{Pl}$ and then into a stable element As. Starting with a block of $\mathrm{Kr}$ of size 10, at time $t$, let:
- $x(t)$ be the amount of $\mathrm{Kr}$,
- $y... | We are given a system of three variables that describe the decay of a radioactive element on the planet Lemniscate:
- $ x(t) $: amount of **Kr** at time $ t $
- $ y(t) $: amount of **Pl** at time $ t $
- $ z(t) $: amount of **As** at time $ t $
We are told:
1. $ x'(t) = -x(t) $: The rate of decay of Kr is prop... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 5 | train | <|im_start|>user
Problem: A thin diverging lens, with an optical power \( D_p = -6 \) diopters, is illuminated by a light beam with a diameter of \( d_1 = 5 \) cm. On a screen parallel to the lens, a bright spot with a diameter of \( d_2 = 20 \) cm is observed. After replacing the thin diverging lens with a thin conver... | We are given:
- A **diverging lens** with optical power $ D_p = -6 $ diopters.
- A light beam with **diameter $ d_1 = 5 $ cm**.
- On a screen **parallel to the lens**, a bright spot is formed with diameter $ d_2 = 20 $ cm.
- The **same spot size (20 cm diameter)** is achieved by a **converging lens**.
- We are to **de... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 6 | train | <|im_start|>user
Problem: Show that the line
$$
\left(m^{2}+6m+3\right)x - \left(2m^{2}+18m+2\right)y - 3m + 2 = 0
$$
passes through a fixed point, regardless of the value assigned to \( m \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|en... | We are given a line in the form:
$$
\left(m^{2}+6m+3\right)x - \left(2m^{2}+18m+2\right)y - 3m + 2 = 0
$$
We are to **show that this line passes through a fixed point, regardless of the value of $ m $**.
---
### Step 1: Understand the structure
The equation is of the form:
$$
A(m)x + B(m)y + C(m) = 0
$$
Where:
-... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 7 | train | <|im_start|>user
Problem: On every kilometer marker along the highway between the villages of Yolkino and Palkino, there is a post with a sign. On one side of the sign, it states the number of kilometers to Yolkino, and on the other side, the number of kilometers to Palkino. An observant individual noticed that the sum... | We are told that:
- Along every kilometer marker (post) on the highway between Yolkino and Palkino, there is a sign.
- On one side of the sign, the distance to **Yolkino** is written.
- On the other side, the distance to **Palkino** is written.
- The **sum** of these two numbers on **every** post is **13**.
- The task... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 8 | train | <|im_start|>user
Problem: Formulate the Taylor series expansion for \( n=2 \) of the function \( f(x, y) = x^y \) near the point \( M_0(1,1) \) and approximately calculate \( 1.1^{1.02} \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
| We are asked to **formulate the Taylor series expansion of $ f(x, y) = x^y $** around the point $ M_0(1,1) $, up to the second-order terms, and then use that to **approximate the value of** $ 1.1^{1.02} $.
---
### Step 1: Understand the function
We are dealing with the function:
$$
f(x, y) = x^y
$$
Our goal is to ... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 9 | train | <|im_start|>user
Problem:
Compose the equation of the tangent line to the given curve at the point with abscissa \(x_{0}\).
$$
y = \frac{x^{2}}{10} + 3, \quad x_{0} = 2
$$
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftex... | We are given the curve:
$$
y = \frac{x^2}{10} + 3
$$
and the point where the **tangent line** is to be found has **abscissa** $ x_0 = 2 $. That is, we want the **tangent line to the curve at the point where $ x = 2 $**.
---
### Step 1: Find the point on the curve at $ x = 2 $
We substitute $ x = 2 $ into the equat... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 10 | train | <|im_start|>user
Problem: Evaluate $|\omega^2+6\omega+58|$ if $\omega=9+2i$.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|e... | We are given a complex number:
$$
\omega = 9 + 2i
$$
And we need to compute the modulus of the complex expression:
$$
\omega^2 + 6\omega + 58
$$
### Step 1: Compute $\omega^2$
Given:
$$
\omega = 9 + 2i
$$
Now compute $\omega^2 = (9 + 2i)^2$
Use the formula $(a + b)^2 = a^2 + 2ab + b^2$
$$
\omega^2 = (9 + 2i)^2... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 11 | train | <|im_start|>user
Problem: Given \( n \in \mathbb{N} \), compute: \((-1)^{n} \cdot(-1)^{2n+1} \cdot(-1)^{n+1} \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endo... | We are given the expression:
$$
(-1)^{n} \cdot (-1)^{2n+1} \cdot (-1)^{n+1}
$$
and are asked to simplify it for $ n \in \mathbb{N} $.
---
### Step 1: Use the Law of Exponents for Powers of -1
Recall that:
$$
(-1)^a \cdot (-1)^b = (-1)^{a+b}
$$
So we can combine all the terms into a single exponent:
$$
(-1)^n \cd... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 12 | train | <|im_start|>user
Problem:
A workshop plans to process a batch of parts, with a goal of processing 50 parts each day. To improve quality, the workshop slowed down the processing speed and processed 6 fewer parts each day, resulting in taking 2 extra days according to the plan, with 32 parts still unfinished. How many p... | We are given the following information:
- The workshop originally planned to process **50 parts per day**.
- Due to a slowdown, they processed **6 fewer parts per day**, i.e., **44 parts per day**.
- This caused them to take **2 more days** than planned.
- At the end, **32 parts** were still **unfinished**.
We are to... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 13 | train | <|im_start|>user
Problem: Given that $f(x) = x^{2}-2x+5$ and $g(x) =x+3$, what is the value of $f(g(5)) -g(f(5))$?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|en... | We are given two functions:
$$
f(x) = x^2 - 2x + 5
$$
$$
g(x) = x + 3
$$
We need to find the value of:
$$
f(g(5)) - g(f(5))
$$
---
### Step 1: Compute $ g(5) $
$$
g(5) = 5 + 3 = 8
$$
---
### Step 2: Compute $ f(g(5)) = f(8) $
$$
f(8) = 8^2 - 2(8) + 5 = 64 - 16 + 5 = 53
$$
So, $ f(g(5)) = 53 $
---
### Step 3... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 14 | train | <|im_start|>user
Problem: \(\frac{\sin 22^{\circ} \cos 8^{\circ}+\cos 158^{\circ} \cos 98^{\circ}}{\sin 23^{\circ} \cos 7^{\circ}+\cos 157^{\circ} \cos 97^{\circ}}\).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
| We are given the expression:
$$
\frac{\sin 22^{\circ} \cos 8^{\circ} + \cos 158^{\circ} \cos 98^{\circ}}{\sin 23^{\circ} \cos 7^{\circ} + \cos 157^{\circ} \cos 97^{\circ}}
$$
---
### Step 1: Simplify Trigonometric Expressions
Let’s simplify the **numerator** and **denominator** by converting some angle values using... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 15 | train | <|im_start|>user
Problem: Let \( f: \mathbb{R} \rightarrow \mathbb{R} \) be such that \( x + f(x) = f(f(x)) \). Determine the solutions of \( f(f(x)) = 0 \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|endoftext|>... | We are given the functional equation:
$$
x + f(x) = f(f(x))
$$
We are to **determine the solutions** of the equation:
$$
f(f(x)) = 0
$$
---
### Step 1: Understand the functional equation
Given:
$$
f(f(x)) = x + f(x)
$$
We are trying to solve:
$$
f(f(x)) = 0
$$
Using the functional equation, we can **replace**... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 16 | train | <|im_start|>user
Problem: Find \(\lim _{x \rightarrow 0}[(x-\sin x) \ln x]\).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|... | We are asked to find the limit:
$$
\lim_{x \to 0} [(x - \sin x) \ln x]
$$
---
### Step 1: Analyze the expression
Let’s first examine the behavior of each component as $ x \to 0 $:
- $ x \to 0 $
- $ \ln x \to -\infty $ as $ x \to 0^+ $
- $ \sin x \to 0 $ as $ x \to 0 $
So, the term $ x - \sin x $ goes to 0, and $ ... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 17 | train | <|im_start|>user
Problem: Given that $O$ is a regular octahedron, that $C$ is the cube whose vertices are the centers of the faces of $O,$ and that the ratio of the volume of $O$ to that of $C$ is $\frac mn,$ where $m$ and $n$ are relatively prime integers, find $m+n.$
Please reason step by step, and put your final a... | We are given a **regular octahedron** $ O $, and a **cube** $ C $ whose **vertices** are the **centers of the faces** of $ O $. We are to find the ratio of the **volumes** of $ O $ to $ C $, and express it as $ \frac{m}{n} $, where $ m $ and $ n $ are **relatively prime**, then compute $ m + n $.
---
### Step 1: Unde... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 18 | train | <|im_start|>user
Problem: Each time Kim pours water from a jug into a glass, exactly 10% of the water remaining in the jug is used. What is the minimum number of times that she must pour water into a glass so that less than half the water remains in the jug?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Please reason step by ste... | We are given that **each time Kim pours water from a jug into a glass**, **exactly 10% of the water remaining in the jug is used**. So after each pour, **90% of the water remains** in the jug.
We are to find the **minimum number of times** she must do this so that **less than half** of the water remains in the jug.
-... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_15.json | 15 | 19 | train | <|im_start|>user
Problem: The sequence \( \left(x_{n}\right) \) is defined recursively by \( x_{0} = 1 \), \( x_{1} = 1 \), and:
\[ x_{n+2} = \frac{1 + x_{n+1}}{x_{n}} \]
for all \( n \geq 0 \). Calculate \( x_{2007} \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>ass... | We are given a recursive sequence defined as:
$$
x_0 = 1, \quad x_1 = 1,
$$
$$
x_{n+2} = \frac{1 + x_{n+1}}{x_n}, \quad \text{for } n \geq 0.
$$
We are asked to **compute $ x_{2007} $**.
---
### Step 1: Compute first few terms manually
Let’s compute the first few terms to look for a **pattern**.
We already have:
... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_20.json | 20 | 0 | train | <|im_start|>user
Problem: The sequence \( \left(x_{n}\right) \) is defined by the conditions:
\[ x_{1} = \frac{1}{2}, \quad x_{n+1} = \sqrt{\frac{1 - \sqrt{1 - x_{n}^{2}}}{2}} \]
Find the formula for \( x_{n} \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<... | We are given a recursive sequence defined by:
$$
x_1 = \frac{1}{2}, \quad x_{n+1} = \sqrt{\frac{1 - \sqrt{1 - x_n^2}}{2}}
$$
We are to find an explicit formula for $ x_n $.
---
### Step 1: Understand the recursive definition
We begin by calculating the first few terms to see if we can detect a pattern.
#### Compu... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_20.json | 20 | 1 | train | <|im_start|>user
Problem: A bug (considered to have negligible size) starts from the origin of the coordinate plane and first moves one unit to the right to \((1,0)\). Then, it rotates \(90^{\circ}\) counterclockwise and moves \(\frac{1}{2}\) unit to \(\left(1, \frac{1}{2}\right)\). If it continues this pattern, rotati... | We are given a bug that:
1. Starts at the origin: $ (0, 0) $.
2. First moves 1 unit **to the right** to point $ (1, 0) $.
3. Then **rotates $ 90^\circ $ counterclockwise** and moves **half the previous distance** — so now it moves $ \frac{1}{2} $ unit.
4. Repeats this pattern: rotates $ 90^\circ $ counterclockwise, th... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_20.json | 20 | 2 | train | <|im_start|>user
Problem: Find the probability that heads will appear an even number of times in an experiment where:
a) a fair coin is tossed $n$ times;
b) a coin with the probability of heads being $p$ ($0 < p < 1$) is tossed $n$ times.
Please reason step by step, and put your final answer within \boxed{}.<|im_end... | We are asked to find the **probability that heads appear an even number of times** in a series of coin tosses.
Let’s go through the problem **step by step**, and then provide the answer in both parts **a)** and **b)**.
---
### **Part a) A fair coin is tossed $ n $ times**
Let’s denote the probability that we get an... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_20.json | 20 | 3 | train | <|im_start|>user
Problem: Prove the following variant of Binet's formula:
\[2^{n-1} F_{n}=\sum_{k=0}^{\left\lfloor\frac{n-1}{2}\right\rfloor} \binom{n}{2k+1} 5^{k}.\]
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|e... | We are asked to prove the identity:
$$
2^{n-1} F_n = \sum_{k=0}^{\left\lfloor \frac{n-1}{2} \right\rfloor} \binom{n}{2k+1} 5^k
$$
where $ F_n $ is the $ n $-th **Fibonacci number** defined by:
$$
F_0 = 0,\quad F_1 = 1,\quad F_n = F_{n-1} + F_{n-2} \text{ for } n \geq 2
$$
---
### **Step 1: Use of Binet’s Formula**... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_20.json | 20 | 4 | train | <|im_start|>user
Problem: On the Cartesian plane, the midpoint between two points $A(a,b)$ and $B(c,d)$ is $M(m,n)$. If $A$ is moved vertically upwards 8 units and horizontally to the right 2 units, and $B$ is moved vertically downwards 2 units and horizontally to the left 10 units, then the new midpoint between $A$ an... | We are given two points:
- $ A(a, b) $
- $ B(c, d) $
The **midpoint** $ M(m, n) $ of $ A $ and $ B $ is given by the midpoint formula:
$$
M = \left( \frac{a + c}{2}, \frac{b + d}{2} \right)
$$
Now, the points are **moved as follows**:
- Point $ A $ is **moved vertically upwards 8 units and horizontally to the righ... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_20.json | 20 | 5 | train | <|im_start|>user
Problem: How many 4-digit numbers exist where the thousands digit is greater than the hundreds digit?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|>... | We are asked to find how many **4-digit numbers** exist where the **thousands digit is greater than the hundreds digit**.
---
### Step 1: Understand the Range of 4-digit Numbers
A **4-digit number** ranges from **1000** to **9999**, inclusive.
That gives us a total of:
$$
9999 - 1000 + 1 = 9000 \text{ total 4-digit... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_20.json | 20 | 6 | train | <|im_start|>user
Problem: Jose, Thuy, and Kareem each start with the number 10. Jose subtracts 1 from the number 10, doubles his answer, and then adds 2. Thuy doubles the number 10, subtracts 1 from her answer, and then adds 2. Kareem subtracts 1 from the number 10, adds 2 to his number, and then doubles the result.... | We are given three people — **Jose**, **Thuy**, and **Kareem** — who each start with the number **10**. They perform a series of arithmetic operations in a different order, and we need to find out who ends up with the **largest final result**.
---
### Step 1: Understand the operations
Let's break down each person’s ... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_20.json | 20 | 7 | train | <|im_start|>user
Problem: When \( 0 < x \leqslant 1 \), which of the following inequalities is correct?
A. \(\frac{\sin x}{x} < \left(\frac{\sin x}{x}\right)^{2} \leqslant \frac{\sin x^{2}}{x^{2}}\)
B. \(\left(\frac{\sin x}{x}\right)^{2} < \frac{\sin x}{x} \leqslant \frac{\sin x^{2}}{x^{2}}\)
C. \(\left(\frac{\sin... | We are given the domain $ 0 < x \leq 1 $, and we are to determine which inequality among the options A, B, C, D is correct, involving expressions of the form:
$$
\frac{\sin x}{x}, \quad \left( \frac{\sin x}{x} \right)^2, \quad \frac{\sin x^2}{x^2}
$$
---
### Step 1: Analyze $\frac{\sin x}{x}$
We start with a well-k... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_20.json | 20 | 8 | train | <|im_start|>user
Problem: The function \( f(x) \) is defined on \(\mathbf{R}\). For any real number \( x \), it holds that \( f(1+x) = f(3-x) \) and \( f(2+x) = -f(4-x) \). Find the value of \( f(1) + f(2) + \cdots + f(100) \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start... | We are given the function $ f(x) $ is defined on $ \mathbb{R} $ and satisfies the following two conditions:
1. $ f(1 + x) = f(3 - x) $ for all real $ x $
2. $ f(2 + x) = -f(4 - x) $ for all real $ x $
We are asked to compute:
$$
f(1) + f(2) + \cdots + f(100)
$$
---
### Step 1: Use the first condition to find a sym... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_20.json | 20 | 9 | train | <|im_start|>user
Problem: A certain natural number \( A \) is divided with remainder by all natural numbers less than \( A \). The sum of all the distinct remainders turns out to be equal to \( A \). Find \( A \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<t... | We are given a **natural number $ A $** with a unique property:
> When $ A $ is divided by **every natural number less than $ A $**, the **sum of the distinct remainders** from these divisions is equal to $ A $.
Our goal is to find this value of $ A $.
---
## Step 1: Understand what it means to divide $ A $ by a nu... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_20.json | 20 | 10 | train | <|im_start|>user
Problem: A finite set $M$ of real numbers has the following properties: $M$ has at least $4$ elements, and there exists a bijective function $f:M\to M$ , different from the identity, such that $ab\leq f(a)f(b)$ for all $a\neq b\in M.$ Prove that the sum of the elements of $M$ is $0.$
Pl... | We are given a finite set $ M \subseteq \mathbb{R} $ with at least 4 elements, and there exists a **non-identity bijective function** $ f: M \to M $ such that:
$$
ab \leq f(a)f(b) \quad \text{for all } a \neq b \in M
$$
Our goal is to **prove that the sum of the elements of $ M $ is 0**.
---
### Step 1: Understand ... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_20.json | 20 | 11 | train | <|im_start|>user
Problem: \(PP^{\prime}\) is any chord of the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) that is parallel to the \(y\)-axis. \(A\) and \(A^{\prime}\) are the two vertices on the \(x\)-axis. The lines \(A^{\prime} P\) and \(A P^{\prime}\) intersect at \(Q\). Find the locus of \(Q\).
Please re... | We are given an ellipse:
$$
\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1
$$
And a chord $ PP' $ of this ellipse that is **parallel to the $ y $-axis**, i.e., **vertical**.
The vertices on the $ x $-axis are:
$$
A = (a, 0), \quad A' = (-a, 0)
$$
We are told that lines $ A'P $ and $ AP' $ intersect at a point $ Q $. We are... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_20.json | 20 | 12 | train | <|im_start|>user
Problem: A bag contains 7 labeled white balls and 3 black balls. Event \( A \): Drawing two balls from the bag, first a black ball and then a white ball. Find \( P(A) \).
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endofte... | We are given a bag with:
- 7 **white** balls
- 3 **black** balls
So, total number of balls in the bag is:
$$
7 + 3 = 10 \text{ balls}
$$
We are to find the **probability of Event A**:
> **Event A**: Drawing **first a black ball**, then a **white ball** from the bag (without replacement).
We are to find:
$$
P... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_20.json | 20 | 13 | train | <|im_start|>user
Problem: Let $P(x)$ be a polynomial such that when $P(x)$ is divided by $x-17$, the remainder is $14$, and when $P(x)$ is divided by $x-13$, the remainder is $6$. What is the remainder when $P(x)$ is divided by $(x-13)(x-17)$?
Please reason step by step, and put your final answer within \boxed{}.<|im_... | We are given:
- When $ P(x) $ is divided by $ x - 17 $, the **remainder is 14**.
- When $ P(x) $ is divided by $ x - 13 $, the **remainder is 6**.
- We are to find the **remainder** when $ P(x) $ is divided by $ (x - 13)(x - 17) $.
---
### Step 1: Use the **Remainder Theorem**
The **Remainder Theorem** says that if... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_20.json | 20 | 14 | train | <|im_start|>user
Problem:
How many positive integers \( n \), where \( 10 \leq n \leq 100 \), are there such that \(\frac{n^2 - 9}{n^2 - 7}\) is a fraction in its lowest terms?
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endo... | We are given the expression:
$$
\frac{n^2 - 9}{n^2 - 7}
$$
and we are to find how many integers $ n $ between 10 and 100 (inclusive) make this fraction **in its lowest terms**.
### Step 1: Understand when a fraction is in lowest terms
A fraction $ \frac{a}{b} $ is in its lowest terms when **the greatest common divi... |
opsd-plain-4b-rollouts | opsd-plain | 4b | /home/irteam/outputs/opsd_plain_4b | generations_step_20.json | 20 | 15 | train | <|im_start|>user
Problem: Prove that for integers $a, b, c, d$, the product $A=(b-a)(c-a)(d-a)(b-c)(d-c)(d-b)$ is divisible by 12.
Please reason step by step, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
<think>
</think>
<|endoftext|><|endoftext|><|endoftext|><|endoftext|><|endoftext|><... | We are given that $ A = (b-a)(c-a)(d-a)(b-c)(d-c)(d-b) $, where $ a, b, c, d $ are integers, and we are to prove that **12 divides** this product $ A $, i.e., $ 12 \mid A $.
### Step 1: Understand the structure of $ A $
This is the product of 6 terms:
$$
A = (b-a)(c-a)(d-a)(b-c)(d-c)(d-b)
$$
Each term is a difference... |
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opsd-plain-4b-rollouts
This dataset contains rollout generations collected during training.
Source experiment
- method:
opsd-plain - model_size:
4b - experiment_dir:
/home/irteam/outputs/opsd_plain_4b
Format
Each row contains:
stepsample_indexpromptcompletionmethodmodel_sizesource_file
Viewer structure
all: all rollout rows togetherstep_<N>: only one rollout step, easier to inspect in the dataset viewer
Notes
- This dataset was prepared from
generations/generations_step_*.jsonfiles. - Step-specific configs are generated automatically for easier browsing.
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