input stringlengths 11 2.08k | chosen stringlengths 19.4k 68.5k | rejected stringlengths 19.1k 326k | source stringclasses 2
values |
|---|---|---|---|
If $128^3 = 16^x$, what is the value of $2^{-x}$? Express your answer as a common fraction. | <|start_header_id|>system<|end_header_id|>
Cutting Knowledge Date: December 2023
Today Date: 26 Jul 2024
<|eot_id|><|start_header_id|>user<|end_header_id|>
<|im_start|>system
You are a helpful assistant.
MASness (How much Multi-Agent System-ness): Minimal
Valid Channels: thinking, agent, answer
Model: gpt-oss-1... | <|start_header_id|>system<|end_header_id|>
Cutting Knowledge Date: December 2023
Today Date: 26 Jul 2024
<|eot_id|><|start_header_id|>user<|end_header_id|>
<|im_start|>system
You are a helpful assistant.
MASness (How much Multi-Agent System-ness): Minimal
Valid Channels: thinking, agent, answer
Model: gpt-oss-1... | correct-over-incorrect |
1. Given non-negative real numbers \( x, y, z \) satisfying \( x^{2} + y^{2} + z^{2} + x + 2y + 3z = \frac{13}{4} \), determine the maximum value of \( x + y + z \).
2. Given \( f(x) \) is an odd function defined on \( \mathbb{R} \) with a period of 3, and when \( x \in \left(0, \frac{3}{2} \right) \), \( f(x) = \ln \... | <|start_header_id|>system<|end_header_id|>
Cutting Knowledge Date: December 2023
Today Date: 26 Jul 2024
<|eot_id|><|start_header_id|>user<|end_header_id|>
<|im_start|>system
You are a helpful assistant.
MASness (How much Multi-Agent System-ness): Minimal
Valid Channels: thinking, agent, answer
Model: gpt-oss-1... | <|start_header_id|>system<|end_header_id|>
Cutting Knowledge Date: December 2023
Today Date: 26 Jul 2024
<|eot_id|><|start_header_id|>user<|end_header_id|>
<|im_start|>system
You are a helpful assistant.
MASness (How much Multi-Agent System-ness): Minimal
Valid Channels: thinking, agent, answer
Model: gpt-oss-1... | correct-over-incorrect |
Simplify: $$\sqrt[3]{5488000}$$ | <|start_header_id|>system<|end_header_id|>
Cutting Knowledge Date: December 2023
Today Date: 26 Jul 2024
<|eot_id|><|start_header_id|>user<|end_header_id|>
<|im_start|>system
You are a helpful assistant.
MASness (How much Multi-Agent System-ness): Minimal
Valid Channels: thinking, agent, answer
Model: gpt-oss-1... | <|start_header_id|>system<|end_header_id|>
Cutting Knowledge Date: December 2023
Today Date: 26 Jul 2024
<|eot_id|><|start_header_id|>user<|end_header_id|>
<|im_start|>system
You are a helpful assistant.
MASness (How much Multi-Agent System-ness): Minimal
Valid Channels: thinking, agent, answer
Model: gpt-oss-1... | correct-over-incorrect |
Let $A B C$ be a triangle with $A B=23, B C=24$, and $C A=27$. Let $D$ be the point on segment $A C$ such that the incircles of triangles $B A D$ and $B C D$ are tangent. Determine the ratio $C D / D A$. | <|start_header_id|>system<|end_header_id|>
Cutting Knowledge Date: December 2023
Today Date: 26 Jul 2024
<|eot_id|><|start_header_id|>user<|end_header_id|>
<|im_start|>system
You are a helpful assistant.
MASness (How much Multi-Agent System-ness): Minimal
Valid Channels: thinking, agent, answer
Model: gpt-oss-1... | <|start_header_id|>system<|end_header_id|>
Cutting Knowledge Date: December 2023
Today Date: 26 Jul 2024
<|eot_id|><|start_header_id|>user<|end_header_id|>
<|im_start|>system
You are a helpful assistant.
MASness (How much Multi-Agent System-ness): Minimal
Valid Channels: thinking, agent, answer
Model: gpt-oss-1... | correct-over-incorrect |
"The volume of the solid formed by rotating an isosceles right triangle with legs of length 1 around(...TRUNCATED) | "<|start_header_id|>system<|end_header_id|>\n\nCutting Knowledge Date: December 2023\nToday Date: 26(...TRUNCATED) | "<|start_header_id|>system<|end_header_id|>\n\nCutting Knowledge Date: December 2023\nToday Date: 26(...TRUNCATED) | correct-over-incorrect |
"Knights, who always tell the truth, and liars, who always lie, live on an island. One day, 30 inhab(...TRUNCATED) | "<|start_header_id|>system<|end_header_id|>\n\nCutting Knowledge Date: December 2023\nToday Date: 26(...TRUNCATED) | "<|start_header_id|>system<|end_header_id|>\n\nCutting Knowledge Date: December 2023\nToday Date: 26(...TRUNCATED) | specialized-over-base |
Let $f(x) = \frac{x^6 - 2}{4}$. Find $f^{-1}\left(-\frac{1}{8}\right)$. | "<|start_header_id|>system<|end_header_id|>\n\nCutting Knowledge Date: December 2023\nToday Date: 26(...TRUNCATED) | "<|start_header_id|>system<|end_header_id|>\n\nCutting Knowledge Date: December 2023\nToday Date: 26(...TRUNCATED) | correct-over-incorrect |
"If\n\\[(1 + \\tan 1^\\circ)(1 + \\tan 2^\\circ)(1 + \\tan 3^\\circ) \\dotsm (1 + \\tan 45^\\circ) =(...TRUNCATED) | "<|start_header_id|>system<|end_header_id|>\n\nCutting Knowledge Date: December 2023\nToday Date: 26(...TRUNCATED) | "<|start_header_id|>system<|end_header_id|>\n\nCutting Knowledge Date: December 2023\nToday Date: 26(...TRUNCATED) | correct-over-incorrect |
"In a tournament each player played exactly one game against each of the other players. In each game(...TRUNCATED) | "<|start_header_id|>system<|end_header_id|>\n\nCutting Knowledge Date: December 2023\nToday Date: 26(...TRUNCATED) | "<|start_header_id|>system<|end_header_id|>\n\nCutting Knowledge Date: December 2023\nToday Date: 26(...TRUNCATED) | correct-over-incorrect |
"Given that $a,b$ are constants, and $a \\neq 0$, $f\\left( x \\right)=ax^{2}+bx$, $f\\left( 2 \\rig(...TRUNCATED) | "<|start_header_id|>system<|end_header_id|>\n\nCutting Knowledge Date: December 2023\nToday Date: 26(...TRUNCATED) | "<|start_header_id|>system<|end_header_id|>\n\nCutting Knowledge Date: December 2023\nToday Date: 26(...TRUNCATED) | correct-over-incorrect |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 8