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Question: The first three terms of a geometric sequence form a geometric sequence with a common ratio of 2, while the common ratios of the three geometric sequences form an arithmetic sequence with a common difference of 1. The sum of the second terms of the three geometric sequences is 24, and the sum of the first thr... | {
"record_id": "f3905a46d917e8a228c36b976ec9e184a910caa0d1ea534d319a74f08e904822",
"dataset_name": "OpenR1-math",
"training_phase": "midtrain",
"sample_index": 0,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: The first three terms of a geometric sequence form a geometric sequence with a common ratio of 2, while the common ratios of the three geometric sequences form an arithmetic sequence with a common difference of 1. The sum of the second terms of the three geometric sequences is 24, and the sum of the first thr... | {
"record_id": "f3905a46d917e8a228c36b976ec9e184a910caa0d1ea534d319a74f08e904822",
"dataset_name": "OpenR1-math",
"training_phase": "midtrain",
"sample_index": 1,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: The first three terms of a geometric sequence form a geometric sequence with a common ratio of 2, while the common ratios of the three geometric sequences form an arithmetic sequence with a common difference of 1. The sum of the second terms of the three geometric sequences is 24, and the sum of the first thr... | {
"record_id": "f3905a46d917e8a228c36b976ec9e184a910caa0d1ea534d319a74f08e904822",
"dataset_name": "OpenR1-math",
"training_phase": "midtrain",
"sample_index": 2,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: The first three terms of a geometric sequence form a geometric sequence with a common ratio of 2, while the common ratios of the three geometric sequences form an arithmetic sequence with a common difference of 1. The sum of the second terms of the three geometric sequences is 24, and the sum of the first thr... | {
"record_id": "f3905a46d917e8a228c36b976ec9e184a910caa0d1ea534d319a74f08e904822",
"dataset_name": "OpenR1-math",
"training_phase": "midtrain",
"sample_index": 3,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: The first three terms of a geometric sequence form a geometric sequence with a common ratio of 2, while the common ratios of the three geometric sequences form an arithmetic sequence with a common difference of 1. The sum of the second terms of the three geometric sequences is 24, and the sum of the first thr... | {
"record_id": "f3905a46d917e8a228c36b976ec9e184a910caa0d1ea534d319a74f08e904822",
"dataset_name": "OpenR1-math",
"training_phase": "midtrain",
"sample_index": 4,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: The first three terms of a geometric sequence form a geometric sequence with a common ratio of 2, while the common ratios of the three geometric sequences form an arithmetic sequence with a common difference of 1. The sum of the second terms of the three geometric sequences is 24, and the sum of the first thr... | {
"record_id": "f3905a46d917e8a228c36b976ec9e184a910caa0d1ea534d319a74f08e904822",
"dataset_name": "OpenR1-math",
"training_phase": "midtrain",
"sample_index": 5,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: The first three terms of a geometric sequence form a geometric sequence with a common ratio of 2, while the common ratios of the three geometric sequences form an arithmetic sequence with a common difference of 1. The sum of the second terms of the three geometric sequences is 24, and the sum of the first thr... | {
"record_id": "f3905a46d917e8a228c36b976ec9e184a910caa0d1ea534d319a74f08e904822",
"dataset_name": "OpenR1-math",
"training_phase": "midtrain",
"sample_index": 6,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: The first three terms of a geometric sequence form a geometric sequence with a common ratio of 2, while the common ratios of the three geometric sequences form an arithmetic sequence with a common difference of 1. The sum of the second terms of the three geometric sequences is 24, and the sum of the first thr... | {
"record_id": "f3905a46d917e8a228c36b976ec9e184a910caa0d1ea534d319a74f08e904822",
"dataset_name": "OpenR1-math",
"training_phase": "midtrain",
"sample_index": 7,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: In the three-dimensional Euclidean space \(\mathbb{R}^3\), consider the hypersurface \( S = \{(x,y,z) \in \mathbb{R}^3 : z^2 = x^2 + y^2\} \). Given a function \( f \in C^{\infty}(S) \), does there exist a function \( u \in C^{\infty}(\mathbb{R}^3) \) such that \( u|_{S} = f \)?
Answer: We are asked: In β^3, ... | {
"record_id": "15eca0e662bf1f9a56b321eef3fe495b322b146d74682e088b4f10a1e568efae",
"dataset_name": "Nemotron-Math-v2",
"training_phase": "midtrain",
"sample_index": 0,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: In the three-dimensional Euclidean space \(\mathbb{R}^3\), consider the hypersurface \( S = \{(x,y,z) \in \mathbb{R}^3 : z^2 = x^2 + y^2\} \). Given a function \( f \in C^{\infty}(S) \), does there exist a function \( u \in C^{\infty}(\mathbb{R}^3) \) such that \( u|_{S} = f \)?
Answer: We are asked: In R^3, ... | {
"record_id": "15eca0e662bf1f9a56b321eef3fe495b322b146d74682e088b4f10a1e568efae",
"dataset_name": "Nemotron-Math-v2",
"training_phase": "midtrain",
"sample_index": 1,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: In the three-dimensional Euclidean space \(\mathbb{R}^3\), consider the hypersurface \( S = \{(x,y,z) \in \mathbb{R}^3 : z^2 = x^2 + y^2\} \). Given a function \( f \in C^{\infty}(S) \), does there exist a function \( u \in C^{\infty}(\mathbb{R}^3) \) such that \( u|_{S} = f \)?
Answer: We need to determine: ... | {
"record_id": "15eca0e662bf1f9a56b321eef3fe495b322b146d74682e088b4f10a1e568efae",
"dataset_name": "Nemotron-Math-v2",
"training_phase": "midtrain",
"sample_index": 2,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: In the three-dimensional Euclidean space \(\mathbb{R}^3\), consider the hypersurface \( S = \{(x,y,z) \in \mathbb{R}^3 : z^2 = x^2 + y^2\} \). Given a function \( f \in C^{\infty}(S) \), does there exist a function \( u \in C^{\infty}(\mathbb{R}^3) \) such that \( u|_{S} = f \)?
Answer: We need to determine w... | {
"record_id": "15eca0e662bf1f9a56b321eef3fe495b322b146d74682e088b4f10a1e568efae",
"dataset_name": "Nemotron-Math-v2",
"training_phase": "midtrain",
"sample_index": 3,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: In the three-dimensional Euclidean space \(\mathbb{R}^3\), consider the hypersurface \( S = \{(x,y,z) \in \mathbb{R}^3 : z^2 = x^2 + y^2\} \). Given a function \( f \in C^{\infty}(S) \), does there exist a function \( u \in C^{\infty}(\mathbb{R}^3) \) such that \( u|_{S} = f \)?
Answer: We are asked: In R^3, ... | {
"record_id": "15eca0e662bf1f9a56b321eef3fe495b322b146d74682e088b4f10a1e568efae",
"dataset_name": "Nemotron-Math-v2",
"training_phase": "midtrain",
"sample_index": 4,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: In the three-dimensional Euclidean space \(\mathbb{R}^3\), consider the hypersurface \( S = \{(x,y,z) \in \mathbb{R}^3 : z^2 = x^2 + y^2\} \). Given a function \( f \in C^{\infty}(S) \), does there exist a function \( u \in C^{\infty}(\mathbb{R}^3) \) such that \( u|_{S} = f \)?
Answer: We are asked: In three... | {
"record_id": "15eca0e662bf1f9a56b321eef3fe495b322b146d74682e088b4f10a1e568efae",
"dataset_name": "Nemotron-Math-v2",
"training_phase": "midtrain",
"sample_index": 5,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: In the three-dimensional Euclidean space \(\mathbb{R}^3\), consider the hypersurface \( S = \{(x,y,z) \in \mathbb{R}^3 : z^2 = x^2 + y^2\} \). Given a function \( f \in C^{\infty}(S) \), does there exist a function \( u \in C^{\infty}(\mathbb{R}^3) \) such that \( u|_{S} = f \)?
Answer: We are asked: In β^3, ... | {
"record_id": "15eca0e662bf1f9a56b321eef3fe495b322b146d74682e088b4f10a1e568efae",
"dataset_name": "Nemotron-Math-v2",
"training_phase": "midtrain",
"sample_index": 6,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: In the three-dimensional Euclidean space \(\mathbb{R}^3\), consider the hypersurface \( S = \{(x,y,z) \in \mathbb{R}^3 : z^2 = x^2 + y^2\} \). Given a function \( f \in C^{\infty}(S) \), does there exist a function \( u \in C^{\infty}(\mathbb{R}^3) \) such that \( u|_{S} = f \)?
Answer: We need to determine w... | {
"record_id": "15eca0e662bf1f9a56b321eef3fe495b322b146d74682e088b4f10a1e568efae",
"dataset_name": "Nemotron-Math-v2",
"training_phase": "midtrain",
"sample_index": 7,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: In a convex hexagon $ABCDEF$, the diagonals $AD$, $BE$, and $CF$ intersect at a common point $G$. If the areas of triangles $ABG$, $BCG$, $CDG$, $DEG$, $EFG$, and $FAG$ are all equal, prove that $ABCDEF$ is a regular hexagon and determine the area of the hexagon in terms of the area of one of the triangles.
A... | {
"record_id": "d4bd93393154e7ac0078563055ccb81dcc5b7703d2022326a8aef5b260f3d146",
"dataset_name": "Ring-lite-sft",
"training_phase": "midtrain",
"sample_index": 0,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: In a convex hexagon $ABCDEF$, the diagonals $AD$, $BE$, and $CF$ intersect at a common point $G$. If the areas of triangles $ABG$, $BCG$, $CDG$, $DEG$, $EFG$, and $FAG$ are all equal, prove that $ABCDEF$ is a regular hexagon and determine the area of the hexagon in terms of the area of one of the triangles.
A... | {
"record_id": "d4bd93393154e7ac0078563055ccb81dcc5b7703d2022326a8aef5b260f3d146",
"dataset_name": "Ring-lite-sft",
"training_phase": "midtrain",
"sample_index": 1,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: In a convex hexagon $ABCDEF$, the diagonals $AD$, $BE$, and $CF$ intersect at a common point $G$. If the areas of triangles $ABG$, $BCG$, $CDG$, $DEG$, $EFG$, and $FAG$ are all equal, prove that $ABCDEF$ is a regular hexagon and determine the area of the hexagon in terms of the area of one of the triangles.
A... | {
"record_id": "d4bd93393154e7ac0078563055ccb81dcc5b7703d2022326a8aef5b260f3d146",
"dataset_name": "Ring-lite-sft",
"training_phase": "midtrain",
"sample_index": 2,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: In a convex hexagon $ABCDEF$, the diagonals $AD$, $BE$, and $CF$ intersect at a common point $G$. If the areas of triangles $ABG$, $BCG$, $CDG$, $DEG$, $EFG$, and $FAG$ are all equal, prove that $ABCDEF$ is a regular hexagon and determine the area of the hexagon in terms of the area of one of the triangles.
A... | {
"record_id": "d4bd93393154e7ac0078563055ccb81dcc5b7703d2022326a8aef5b260f3d146",
"dataset_name": "Ring-lite-sft",
"training_phase": "midtrain",
"sample_index": 4,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: In a convex hexagon $ABCDEF$, the diagonals $AD$, $BE$, and $CF$ intersect at a common point $G$. If the areas of triangles $ABG$, $BCG$, $CDG$, $DEG$, $EFG$, and $FAG$ are all equal, prove that $ABCDEF$ is a regular hexagon and determine the area of the hexagon in terms of the area of one of the triangles.
A... | {
"record_id": "d4bd93393154e7ac0078563055ccb81dcc5b7703d2022326a8aef5b260f3d146",
"dataset_name": "Ring-lite-sft",
"training_phase": "midtrain",
"sample_index": 5,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: In a convex hexagon $ABCDEF$, the diagonals $AD$, $BE$, and $CF$ intersect at a common point $G$. If the areas of triangles $ABG$, $BCG$, $CDG$, $DEG$, $EFG$, and $FAG$ are all equal, prove that $ABCDEF$ is a regular hexagon and determine the area of the hexagon in terms of the area of one of the triangles.
A... | {
"record_id": "d4bd93393154e7ac0078563055ccb81dcc5b7703d2022326a8aef5b260f3d146",
"dataset_name": "Ring-lite-sft",
"training_phase": "midtrain",
"sample_index": 6,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: In a convex hexagon $ABCDEF$, the diagonals $AD$, $BE$, and $CF$ intersect at a common point $G$. If the areas of triangles $ABG$, $BCG$, $CDG$, $DEG$, $EFG$, and $FAG$ are all equal, prove that $ABCDEF$ is a regular hexagon and determine the area of the hexagon in terms of the area of one of the triangles.
A... | {
"record_id": "d4bd93393154e7ac0078563055ccb81dcc5b7703d2022326a8aef5b260f3d146",
"dataset_name": "Ring-lite-sft",
"training_phase": "midtrain",
"sample_index": 7,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: ystem of first-order linear differential equations:
\[
\begin{align*}
\frac{dx}{dt} & = x - y \\
\frac{dy}{dt} & = 2x + 4y
\end{align*}
\]
Answer: We are given a system of first-order linear differential equations:
dx/dt = x - y
dy/dt = 2x + 4y
We need to solve the system. Typically, we can solve by finding... | {
"record_id": "1da8b59c96fb7d7a223d380907f87942476f777f2851a1129c7d71f1e96dd986",
"dataset_name": "Nemotron-Cascade-2-SFT-Data",
"training_phase": "midtrain",
"sample_index": 0,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: ystem of first-order linear differential equations:
\[
\begin{align*}
\frac{dx}{dt} & = x - y \\
\frac{dy}{dt} & = 2x + 4y
\end{align*}
\]
Answer: We need to solve the system of first-order linear differential equations:
dx/dt = x - y
dy/dt = 2x + 4y
We need to find the general solution.
We can solve using... | {
"record_id": "1da8b59c96fb7d7a223d380907f87942476f777f2851a1129c7d71f1e96dd986",
"dataset_name": "Nemotron-Cascade-2-SFT-Data",
"training_phase": "midtrain",
"sample_index": 1,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: ystem of first-order linear differential equations:
\[
\begin{align*}
\frac{dx}{dt} & = x - y \\
\frac{dy}{dt} & = 2x + 4y
\end{align*}
\]
Answer: We are given a system of first-order linear differential equations:
dx/dt = x - y
dy/dt = 2x + 4y
We need to solve this system. Likely find the general solution.... | {
"record_id": "1da8b59c96fb7d7a223d380907f87942476f777f2851a1129c7d71f1e96dd986",
"dataset_name": "Nemotron-Cascade-2-SFT-Data",
"training_phase": "midtrain",
"sample_index": 2,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: ystem of first-order linear differential equations:
\[
\begin{align*}
\frac{dx}{dt} & = x - y \\
\frac{dy}{dt} & = 2x + 4y
\end{align*}
\]
Answer: We are given a system of first-order linear differential equations:
dx/dt = x - y
dy/dt = 2x + 4y
We need to solve this system. The standard method: write in mat... | {
"record_id": "1da8b59c96fb7d7a223d380907f87942476f777f2851a1129c7d71f1e96dd986",
"dataset_name": "Nemotron-Cascade-2-SFT-Data",
"training_phase": "midtrain",
"sample_index": 3,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: ystem of first-order linear differential equations:
\[
\begin{align*}
\frac{dx}{dt} & = x - y \\
\frac{dy}{dt} & = 2x + 4y
\end{align*}
\]
Answer: We are given a system of first-order linear differential equations:
dx/dt = x - y
dy/dt = 2x + 4y
We need to solve it. Possibly find general solution. Could be s... | {
"record_id": "1da8b59c96fb7d7a223d380907f87942476f777f2851a1129c7d71f1e96dd986",
"dataset_name": "Nemotron-Cascade-2-SFT-Data",
"training_phase": "midtrain",
"sample_index": 4,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: ystem of first-order linear differential equations:
\[
\begin{align*}
\frac{dx}{dt} & = x - y \\
\frac{dy}{dt} & = 2x + 4y
\end{align*}
\]
Answer: We need to solve a system of first-order linear differential equations:
dx/dt = x - y
dy/dt = 2x + 4y
We can solve this using eigenvalue method. Write in matrix ... | {
"record_id": "1da8b59c96fb7d7a223d380907f87942476f777f2851a1129c7d71f1e96dd986",
"dataset_name": "Nemotron-Cascade-2-SFT-Data",
"training_phase": "midtrain",
"sample_index": 5,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: ystem of first-order linear differential equations:
\[
\begin{align*}
\frac{dx}{dt} & = x - y \\
\frac{dy}{dt} & = 2x + 4y
\end{align*}
\]
Answer: We are given a system of first-order linear differential equations:
dx/dt = x - y
dy/dt = 2x + 4y
We need to find the general solution. This is a linear homogene... | {
"record_id": "1da8b59c96fb7d7a223d380907f87942476f777f2851a1129c7d71f1e96dd986",
"dataset_name": "Nemotron-Cascade-2-SFT-Data",
"training_phase": "midtrain",
"sample_index": 6,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: ystem of first-order linear differential equations:
\[
\begin{align*}
\frac{dx}{dt} & = x - y \\
\frac{dy}{dt} & = 2x + 4y
\end{align*}
\]
Answer: We are given a system of first-order linear differential equations:
dx/dt = x - y
dy/dt = 2x + 4y
We need to solve it? The instruction says: "" Usually in such c... | {
"record_id": "1da8b59c96fb7d7a223d380907f87942476f777f2851a1129c7d71f1e96dd986",
"dataset_name": "Nemotron-Cascade-2-SFT-Data",
"training_phase": "midtrain",
"sample_index": 7,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: What is the difference between the contrapositive and the converse of a conditional statement?
Answer: We need to explain the difference between contrapositive and converse of a conditional statement. We'll go step by step.
First, define a conditional statement: "If P, then Q" denoted P β Q.
Converse: Q β P... | {
"record_id": "8077cd4c56e9807574097272638c6037e347d8e790fcc17b3881a95fc3f59933",
"dataset_name": "dolphin-r1",
"training_phase": "midtrain",
"sample_index": 0,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: What is the difference between the contrapositive and the converse of a conditional statement?
Answer: We need to explain the difference between contrapositive and converse of a conditional statement. First, recall that a conditional statement is of the form "If P, then Q", often written P β Q.
- The convers... | {
"record_id": "8077cd4c56e9807574097272638c6037e347d8e790fcc17b3881a95fc3f59933",
"dataset_name": "dolphin-r1",
"training_phase": "midtrain",
"sample_index": 1,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: What is the difference between the contrapositive and the converse of a conditional statement?
Answer: We need to explain the difference between contrapositive and converse of a conditional statement. We'll reason step by step.
First, a conditional statement is of the form "If P, then Q", often denoted as P ... | {
"record_id": "8077cd4c56e9807574097272638c6037e347d8e790fcc17b3881a95fc3f59933",
"dataset_name": "dolphin-r1",
"training_phase": "midtrain",
"sample_index": 2,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: What is the difference between the contrapositive and the converse of a conditional statement?
Answer: We are asked: "What is the difference between the contrapositive and the converse of a conditional statement?" We need to reason step by step and put final answer within \boxed{}.
First, recall definitions:... | {
"record_id": "8077cd4c56e9807574097272638c6037e347d8e790fcc17b3881a95fc3f59933",
"dataset_name": "dolphin-r1",
"training_phase": "midtrain",
"sample_index": 3,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: What is the difference between the contrapositive and the converse of a conditional statement?
Answer: We are asked: "What is the difference between the contrapositive and the converse of a conditional statement?" We need to reason step by step and put the final answer within \boxed{}.
We need to explain the... | {
"record_id": "8077cd4c56e9807574097272638c6037e347d8e790fcc17b3881a95fc3f59933",
"dataset_name": "dolphin-r1",
"training_phase": "midtrain",
"sample_index": 4,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: What is the difference between the contrapositive and the converse of a conditional statement?
Answer: We are asked: "What is the difference between the contrapositive and the converse of a conditional statement?" This is a logical reasoning question. We need to explain the difference, step by step, and put t... | {
"record_id": "8077cd4c56e9807574097272638c6037e347d8e790fcc17b3881a95fc3f59933",
"dataset_name": "dolphin-r1",
"training_phase": "midtrain",
"sample_index": 5,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: What is the difference between the contrapositive and the converse of a conditional statement?
Answer: We need to explain the difference between contrapositive and converse of a conditional statement. A conditional statement has form "If P, then Q" (symbolically P β Q). The converse is "If Q, then P" (Q β P).... | {
"record_id": "8077cd4c56e9807574097272638c6037e347d8e790fcc17b3881a95fc3f59933",
"dataset_name": "dolphin-r1",
"training_phase": "midtrain",
"sample_index": 6,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: What is the difference between the contrapositive and the converse of a conditional statement?
Answer: We need to explain the difference between contrapositive and converse of a conditional statement. Let's recall:
Given a conditional statement: "If P then Q" (P β Q).
- The converse of P β Q is Q β P (swap ... | {
"record_id": "8077cd4c56e9807574097272638c6037e347d8e790fcc17b3881a95fc3f59933",
"dataset_name": "dolphin-r1",
"training_phase": "midtrain",
"sample_index": 7,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( b \) be a real number greater than 1. Consider the function \( T_b(x) \) defined recursively as follows:
\[ T_b(1) = b \]
\[ T_b(n) = b^{T_b(n-1)} \text{ for } n \geq 2 \]
Define \( T_b(0) \) as the unique real number \( a \) such that the sequence \( T_b(n) \) converges to \( a \). Determine the valu... | {
"record_id": "6757cd5f39db1922f9590ccedd36a7490e3cd506307a310cfdb0fa27b4a40efe",
"dataset_name": "Ring-lite-sft",
"training_phase": "midtrain",
"sample_index": 0,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( b \) be a real number greater than 1. Consider the function \( T_b(x) \) defined recursively as follows:
\[ T_b(1) = b \]
\[ T_b(n) = b^{T_b(n-1)} \text{ for } n \geq 2 \]
Define \( T_b(0) \) as the unique real number \( a \) such that the sequence \( T_b(n) \) converges to \( a \). Determine the valu... | {
"record_id": "6757cd5f39db1922f9590ccedd36a7490e3cd506307a310cfdb0fa27b4a40efe",
"dataset_name": "Ring-lite-sft",
"training_phase": "midtrain",
"sample_index": 1,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( b \) be a real number greater than 1. Consider the function \( T_b(x) \) defined recursively as follows:
\[ T_b(1) = b \]
\[ T_b(n) = b^{T_b(n-1)} \text{ for } n \geq 2 \]
Define \( T_b(0) \) as the unique real number \( a \) such that the sequence \( T_b(n) \) converges to \( a \). Determine the valu... | {
"record_id": "6757cd5f39db1922f9590ccedd36a7490e3cd506307a310cfdb0fa27b4a40efe",
"dataset_name": "Ring-lite-sft",
"training_phase": "midtrain",
"sample_index": 2,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( b \) be a real number greater than 1. Consider the function \( T_b(x) \) defined recursively as follows:
\[ T_b(1) = b \]
\[ T_b(n) = b^{T_b(n-1)} \text{ for } n \geq 2 \]
Define \( T_b(0) \) as the unique real number \( a \) such that the sequence \( T_b(n) \) converges to \( a \). Determine the valu... | {
"record_id": "6757cd5f39db1922f9590ccedd36a7490e3cd506307a310cfdb0fa27b4a40efe",
"dataset_name": "Ring-lite-sft",
"training_phase": "midtrain",
"sample_index": 3,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( b \) be a real number greater than 1. Consider the function \( T_b(x) \) defined recursively as follows:
\[ T_b(1) = b \]
\[ T_b(n) = b^{T_b(n-1)} \text{ for } n \geq 2 \]
Define \( T_b(0) \) as the unique real number \( a \) such that the sequence \( T_b(n) \) converges to \( a \). Determine the valu... | {
"record_id": "6757cd5f39db1922f9590ccedd36a7490e3cd506307a310cfdb0fa27b4a40efe",
"dataset_name": "Ring-lite-sft",
"training_phase": "midtrain",
"sample_index": 4,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( b \) be a real number greater than 1. Consider the function \( T_b(x) \) defined recursively as follows:
\[ T_b(1) = b \]
\[ T_b(n) = b^{T_b(n-1)} \text{ for } n \geq 2 \]
Define \( T_b(0) \) as the unique real number \( a \) such that the sequence \( T_b(n) \) converges to \( a \). Determine the valu... | {
"record_id": "6757cd5f39db1922f9590ccedd36a7490e3cd506307a310cfdb0fa27b4a40efe",
"dataset_name": "Ring-lite-sft",
"training_phase": "midtrain",
"sample_index": 5,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( b \) be a real number greater than 1. Consider the function \( T_b(x) \) defined recursively as follows:
\[ T_b(1) = b \]
\[ T_b(n) = b^{T_b(n-1)} \text{ for } n \geq 2 \]
Define \( T_b(0) \) as the unique real number \( a \) such that the sequence \( T_b(n) \) converges to \( a \). Determine the valu... | {
"record_id": "6757cd5f39db1922f9590ccedd36a7490e3cd506307a310cfdb0fa27b4a40efe",
"dataset_name": "Ring-lite-sft",
"training_phase": "midtrain",
"sample_index": 6,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( b \) be a real number greater than 1. Consider the function \( T_b(x) \) defined recursively as follows:
\[ T_b(1) = b \]
\[ T_b(n) = b^{T_b(n-1)} \text{ for } n \geq 2 \]
Define \( T_b(0) \) as the unique real number \( a \) such that the sequence \( T_b(n) \) converges to \( a \). Determine the valu... | {
"record_id": "6757cd5f39db1922f9590ccedd36a7490e3cd506307a310cfdb0fa27b4a40efe",
"dataset_name": "Ring-lite-sft",
"training_phase": "midtrain",
"sample_index": 7,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: If $S \subset A^{\times}$, what is $S^{-1}A$ isomorphic to?
Answer: We need to parse the question: "If $S \subset A^{\times}$, what is $S^{-1}A$ isomorphic to?" Where A is presumably a commutative ring with unity, and A^Γ denotes the multiplicative group of units. S is a subset of the units. Then S^{-1}A is t... | {
"record_id": "ad328f3a6c21dbfb3281eeeb75375e7c7ad4a31f2391220557565b1341e32a95",
"dataset_name": "DeepMath-103K",
"training_phase": "midtrain",
"sample_index": 0,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: If $S \subset A^{\times}$, what is $S^{-1}A$ isomorphic to?
Answer: We are asked: "If $S \subset A^{\times}$, what is $S^{-1}A$ isomorphic to?" Here A is presumably a commutative ring with 1? Typically in ring theory, given a multiplicative subset S of a ring A, we can form the localization S^{-1}A. If S is a... | {
"record_id": "ad328f3a6c21dbfb3281eeeb75375e7c7ad4a31f2391220557565b1341e32a95",
"dataset_name": "DeepMath-103K",
"training_phase": "midtrain",
"sample_index": 1,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: If $S \subset A^{\times}$, what is $S^{-1}A$ isomorphic to?
Answer: We need to parse the question: "If $S \subset A^{\times}$, what is $S^{-1}A$ isomorphic to?" Here A is presumably a commutative ring with 1 (usual context of localization). A^{\times} denotes the group of units (invertible elements) of A. S i... | {
"record_id": "ad328f3a6c21dbfb3281eeeb75375e7c7ad4a31f2391220557565b1341e32a95",
"dataset_name": "DeepMath-103K",
"training_phase": "midtrain",
"sample_index": 2,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: If $S \subset A^{\times}$, what is $S^{-1}A$ isomorphic to?
Answer: We are given: "If $S \subset A^{\times}$, what is $S^{-1}A$ isomorphic to?" This is a question about localization of a ring A at a multiplicative set S. The notation A^{\times} denotes the set of units of A. So S is a subset of the units. Usu... | {
"record_id": "ad328f3a6c21dbfb3281eeeb75375e7c7ad4a31f2391220557565b1341e32a95",
"dataset_name": "DeepMath-103K",
"training_phase": "midtrain",
"sample_index": 3,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: If $S \subset A^{\times}$, what is $S^{-1}A$ isomorphic to?
Answer: We need to parse the problem: "If $S \subset A^{\times}$, what is $S^{-1}A$ isomorphic to?" Here A is presumably a commutative ring (since we are talking about localization). A^{\times} denotes the multiplicative group of units (invertible el... | {
"record_id": "ad328f3a6c21dbfb3281eeeb75375e7c7ad4a31f2391220557565b1341e32a95",
"dataset_name": "DeepMath-103K",
"training_phase": "midtrain",
"sample_index": 4,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: If $S \subset A^{\times}$, what is $S^{-1}A$ isomorphic to?
Answer: We are asked: "If $S \subset A^{\times}$, what is $S^{-1}A$ isomorphic to?" Here A is presumably a commutative ring (likely with unity), and S is a subset of the group of units A^{\times}. Then we consider the localization of A at S, i.e., S^... | {
"record_id": "ad328f3a6c21dbfb3281eeeb75375e7c7ad4a31f2391220557565b1341e32a95",
"dataset_name": "DeepMath-103K",
"training_phase": "midtrain",
"sample_index": 5,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: If $S \subset A^{\times}$, what is $S^{-1}A$ isomorphic to?
Answer: We need to interpret the problem: "If $S \subset A^{\times}$, what is $S^{-1}A$ isomorphic to?" This is a question about localization. Here A is presumably a commutative ring with 1. A^{\times} denotes the group of units of A. S is a subset o... | {
"record_id": "ad328f3a6c21dbfb3281eeeb75375e7c7ad4a31f2391220557565b1341e32a95",
"dataset_name": "DeepMath-103K",
"training_phase": "midtrain",
"sample_index": 6,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: If $S \subset A^{\times}$, what is $S^{-1}A$ isomorphic to?
Answer: We are asked: "If $S \subset A^{\times}$, what is $S^{-1}A$ isomorphic to?" We need to reason step by step. The notation: $A$ is likely a commutative ring with unity (typical context of localization). $A^{\times}$ denotes the set of units of ... | {
"record_id": "ad328f3a6c21dbfb3281eeeb75375e7c7ad4a31f2391220557565b1341e32a95",
"dataset_name": "DeepMath-103K",
"training_phase": "midtrain",
"sample_index": 7,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Distribute five students, namely A, B, C, D, and E, to three universities: Peking University, Shanghai Jiao Tong University, and Zhejiang University, with the condition that each university must admit at least one student, and student A cannot be admitted to Peking University. The total number of different ad... | {
"record_id": "1be7a1d9036e2c572339cd0de453a1ae7d5a599886c7e32fbc2a6c8da28ba5ba",
"dataset_name": "numinamath",
"training_phase": "midtrain",
"sample_index": 0,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: Distribute five students, namely A, B, C, D, and E, to three universities: Peking University, Shanghai Jiao Tong University, and Zhejiang University, with the condition that each university must admit at least one student, and student A cannot be admitted to Peking University. The total number of different ad... | {
"record_id": "1be7a1d9036e2c572339cd0de453a1ae7d5a599886c7e32fbc2a6c8da28ba5ba",
"dataset_name": "numinamath",
"training_phase": "midtrain",
"sample_index": 1,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: Distribute five students, namely A, B, C, D, and E, to three universities: Peking University, Shanghai Jiao Tong University, and Zhejiang University, with the condition that each university must admit at least one student, and student A cannot be admitted to Peking University. The total number of different ad... | {
"record_id": "1be7a1d9036e2c572339cd0de453a1ae7d5a599886c7e32fbc2a6c8da28ba5ba",
"dataset_name": "numinamath",
"training_phase": "midtrain",
"sample_index": 2,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: Distribute five students, namely A, B, C, D, and E, to three universities: Peking University, Shanghai Jiao Tong University, and Zhejiang University, with the condition that each university must admit at least one student, and student A cannot be admitted to Peking University. The total number of different ad... | {
"record_id": "1be7a1d9036e2c572339cd0de453a1ae7d5a599886c7e32fbc2a6c8da28ba5ba",
"dataset_name": "numinamath",
"training_phase": "midtrain",
"sample_index": 3,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: Distribute five students, namely A, B, C, D, and E, to three universities: Peking University, Shanghai Jiao Tong University, and Zhejiang University, with the condition that each university must admit at least one student, and student A cannot be admitted to Peking University. The total number of different ad... | {
"record_id": "1be7a1d9036e2c572339cd0de453a1ae7d5a599886c7e32fbc2a6c8da28ba5ba",
"dataset_name": "numinamath",
"training_phase": "midtrain",
"sample_index": 4,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: Distribute five students, namely A, B, C, D, and E, to three universities: Peking University, Shanghai Jiao Tong University, and Zhejiang University, with the condition that each university must admit at least one student, and student A cannot be admitted to Peking University. The total number of different ad... | {
"record_id": "1be7a1d9036e2c572339cd0de453a1ae7d5a599886c7e32fbc2a6c8da28ba5ba",
"dataset_name": "numinamath",
"training_phase": "midtrain",
"sample_index": 5,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: Distribute five students, namely A, B, C, D, and E, to three universities: Peking University, Shanghai Jiao Tong University, and Zhejiang University, with the condition that each university must admit at least one student, and student A cannot be admitted to Peking University. The total number of different ad... | {
"record_id": "1be7a1d9036e2c572339cd0de453a1ae7d5a599886c7e32fbc2a6c8da28ba5ba",
"dataset_name": "numinamath",
"training_phase": "midtrain",
"sample_index": 6,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: Distribute five students, namely A, B, C, D, and E, to three universities: Peking University, Shanghai Jiao Tong University, and Zhejiang University, with the condition that each university must admit at least one student, and student A cannot be admitted to Peking University. The total number of different ad... | {
"record_id": "1be7a1d9036e2c572339cd0de453a1ae7d5a599886c7e32fbc2a6c8da28ba5ba",
"dataset_name": "numinamath",
"training_phase": "midtrain",
"sample_index": 7,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( H \) be a \( G_{\delta} \) subset of \( \mathbb{R} \) whose closure has a positive Lebesgue measure. Define \( S = H + H + H + H = \{ x + y + z + u : x, y, z, u \in H \} \). Suppose \( S \) contains an interval \([a, b]\). Calculate the length of the shortest such interval that can be contained in \( S... | {
"record_id": "f8a567e514e9deb4423f7824d146815dde1218bce8c957c0baf584028ca56d89",
"dataset_name": "OpenMathReasoning",
"training_phase": "midtrain",
"sample_index": 0,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( H \) be a \( G_{\delta} \) subset of \( \mathbb{R} \) whose closure has a positive Lebesgue measure. Define \( S = H + H + H + H = \{ x + y + z + u : x, y, z, u \in H \} \). Suppose \( S \) contains an interval \([a, b]\). Calculate the length of the shortest such interval that can be contained in \( S... | {
"record_id": "f8a567e514e9deb4423f7824d146815dde1218bce8c957c0baf584028ca56d89",
"dataset_name": "OpenMathReasoning",
"training_phase": "midtrain",
"sample_index": 1,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( H \) be a \( G_{\delta} \) subset of \( \mathbb{R} \) whose closure has a positive Lebesgue measure. Define \( S = H + H + H + H = \{ x + y + z + u : x, y, z, u \in H \} \). Suppose \( S \) contains an interval \([a, b]\). Calculate the length of the shortest such interval that can be contained in \( S... | {
"record_id": "f8a567e514e9deb4423f7824d146815dde1218bce8c957c0baf584028ca56d89",
"dataset_name": "OpenMathReasoning",
"training_phase": "midtrain",
"sample_index": 2,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( H \) be a \( G_{\delta} \) subset of \( \mathbb{R} \) whose closure has a positive Lebesgue measure. Define \( S = H + H + H + H = \{ x + y + z + u : x, y, z, u \in H \} \). Suppose \( S \) contains an interval \([a, b]\). Calculate the length of the shortest such interval that can be contained in \( S... | {
"record_id": "f8a567e514e9deb4423f7824d146815dde1218bce8c957c0baf584028ca56d89",
"dataset_name": "OpenMathReasoning",
"training_phase": "midtrain",
"sample_index": 3,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( H \) be a \( G_{\delta} \) subset of \( \mathbb{R} \) whose closure has a positive Lebesgue measure. Define \( S = H + H + H + H = \{ x + y + z + u : x, y, z, u \in H \} \). Suppose \( S \) contains an interval \([a, b]\). Calculate the length of the shortest such interval that can be contained in \( S... | {
"record_id": "f8a567e514e9deb4423f7824d146815dde1218bce8c957c0baf584028ca56d89",
"dataset_name": "OpenMathReasoning",
"training_phase": "midtrain",
"sample_index": 4,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( H \) be a \( G_{\delta} \) subset of \( \mathbb{R} \) whose closure has a positive Lebesgue measure. Define \( S = H + H + H + H = \{ x + y + z + u : x, y, z, u \in H \} \). Suppose \( S \) contains an interval \([a, b]\). Calculate the length of the shortest such interval that can be contained in \( S... | {
"record_id": "f8a567e514e9deb4423f7824d146815dde1218bce8c957c0baf584028ca56d89",
"dataset_name": "OpenMathReasoning",
"training_phase": "midtrain",
"sample_index": 5,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( H \) be a \( G_{\delta} \) subset of \( \mathbb{R} \) whose closure has a positive Lebesgue measure. Define \( S = H + H + H + H = \{ x + y + z + u : x, y, z, u \in H \} \). Suppose \( S \) contains an interval \([a, b]\). Calculate the length of the shortest such interval that can be contained in \( S... | {
"record_id": "f8a567e514e9deb4423f7824d146815dde1218bce8c957c0baf584028ca56d89",
"dataset_name": "OpenMathReasoning",
"training_phase": "midtrain",
"sample_index": 6,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( H \) be a \( G_{\delta} \) subset of \( \mathbb{R} \) whose closure has a positive Lebesgue measure. Define \( S = H + H + H + H = \{ x + y + z + u : x, y, z, u \in H \} \). Suppose \( S \) contains an interval \([a, b]\). Calculate the length of the shortest such interval that can be contained in \( S... | {
"record_id": "f8a567e514e9deb4423f7824d146815dde1218bce8c957c0baf584028ca56d89",
"dataset_name": "OpenMathReasoning",
"training_phase": "midtrain",
"sample_index": 7,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: What is the concept of a quotient space, and how does it arise in various areas of mathematics. In what way is it related to the idea of an equivalence relation.
Answer: We need to explain the concept of a quotient space and its relation to equivalence relations. Also, how it arises in various areas of mathem... | {
"record_id": "36af34b5c3121281a28fe851a5bc77781ab949d95ce218638c91ebbc751c2eef",
"dataset_name": "dolphin-r1",
"training_phase": "midtrain",
"sample_index": 0,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: What is the concept of a quotient space, and how does it arise in various areas of mathematics. In what way is it related to the idea of an equivalence relation.
Answer: We need to explain the concept of a quotient space and its relation to equivalence relations, and show how it arises in various areas of mat... | {
"record_id": "36af34b5c3121281a28fe851a5bc77781ab949d95ce218638c91ebbc751c2eef",
"dataset_name": "dolphin-r1",
"training_phase": "midtrain",
"sample_index": 1,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: What is the concept of a quotient space, and how does it arise in various areas of mathematics. In what way is it related to the idea of an equivalence relation.
Answer: We need to explain the concept of a quotient space, how it arises in various areas of mathematics, and its relation to equivalence relations... | {
"record_id": "36af34b5c3121281a28fe851a5bc77781ab949d95ce218638c91ebbc751c2eef",
"dataset_name": "dolphin-r1",
"training_phase": "midtrain",
"sample_index": 2,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: What is the concept of a quotient space, and how does it arise in various areas of mathematics. In what way is it related to the idea of an equivalence relation.
Answer: We need to explain the concept of a quotient space, and how it arises in various areas of mathematics. Also relate it to equivalence relatio... | {
"record_id": "36af34b5c3121281a28fe851a5bc77781ab949d95ce218638c91ebbc751c2eef",
"dataset_name": "dolphin-r1",
"training_phase": "midtrain",
"sample_index": 3,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: What is the concept of a quotient space, and how does it arise in various areas of mathematics. In what way is it related to the idea of an equivalence relation.
Answer: We need to explain the concept of a quotient space, how it arises in various areas of mathematics, and its relation to equivalence relations... | {
"record_id": "36af34b5c3121281a28fe851a5bc77781ab949d95ce218638c91ebbc751c2eef",
"dataset_name": "dolphin-r1",
"training_phase": "midtrain",
"sample_index": 4,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: What is the concept of a quotient space, and how does it arise in various areas of mathematics. In what way is it related to the idea of an equivalence relation.
Answer: We need to answer: "What is the concept of a quotient space, and how does it arise in various areas of mathematics. In what way is it relate... | {
"record_id": "36af34b5c3121281a28fe851a5bc77781ab949d95ce218638c91ebbc751c2eef",
"dataset_name": "dolphin-r1",
"training_phase": "midtrain",
"sample_index": 5,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: What is the concept of a quotient space, and how does it arise in various areas of mathematics. In what way is it related to the idea of an equivalence relation.
Answer: We need to explain the concept of a quotient space, how it arises in various areas of mathematics, and its relation to equivalence relations... | {
"record_id": "36af34b5c3121281a28fe851a5bc77781ab949d95ce218638c91ebbc751c2eef",
"dataset_name": "dolphin-r1",
"training_phase": "midtrain",
"sample_index": 6,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: What is the concept of a quotient space, and how does it arise in various areas of mathematics. In what way is it related to the idea of an equivalence relation.
Answer: We need to explain quotient space concept, its relation to equivalence relations, and how it appears in various math areas. We should give a... | {
"record_id": "36af34b5c3121281a28fe851a5bc77781ab949d95ce218638c91ebbc751c2eef",
"dataset_name": "dolphin-r1",
"training_phase": "midtrain",
"sample_index": 7,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: Let $\Omega$ be a circle with center $O$ and let $A, B$ be points inside $\Omega$ (not collinear with $O$). Consider a diameter $CD$ of $\Omega$ such that the quadrilateral $ABCD$ is cyclic. If the distance from $O$ to $AB$ is $d$, and the radius of $\Omega$ is $r$, find the length of $CD$ in terms of $d$ and... | {
"record_id": "0850f8418506750167882b652b4ad44c81aec3b56c5c5e36ca434de3061d3f9e",
"dataset_name": "OpenMathReasoning",
"training_phase": "midtrain",
"sample_index": 0,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let $\Omega$ be a circle with center $O$ and let $A, B$ be points inside $\Omega$ (not collinear with $O$). Consider a diameter $CD$ of $\Omega$ such that the quadrilateral $ABCD$ is cyclic. If the distance from $O$ to $AB$ is $d$, and the radius of $\Omega$ is $r$, find the length of $CD$ in terms of $d$ and... | {
"record_id": "0850f8418506750167882b652b4ad44c81aec3b56c5c5e36ca434de3061d3f9e",
"dataset_name": "OpenMathReasoning",
"training_phase": "midtrain",
"sample_index": 1,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let $\Omega$ be a circle with center $O$ and let $A, B$ be points inside $\Omega$ (not collinear with $O$). Consider a diameter $CD$ of $\Omega$ such that the quadrilateral $ABCD$ is cyclic. If the distance from $O$ to $AB$ is $d$, and the radius of $\Omega$ is $r$, find the length of $CD$ in terms of $d$ and... | {
"record_id": "0850f8418506750167882b652b4ad44c81aec3b56c5c5e36ca434de3061d3f9e",
"dataset_name": "OpenMathReasoning",
"training_phase": "midtrain",
"sample_index": 2,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let $\Omega$ be a circle with center $O$ and let $A, B$ be points inside $\Omega$ (not collinear with $O$). Consider a diameter $CD$ of $\Omega$ such that the quadrilateral $ABCD$ is cyclic. If the distance from $O$ to $AB$ is $d$, and the radius of $\Omega$ is $r$, find the length of $CD$ in terms of $d$ and... | {
"record_id": "0850f8418506750167882b652b4ad44c81aec3b56c5c5e36ca434de3061d3f9e",
"dataset_name": "OpenMathReasoning",
"training_phase": "midtrain",
"sample_index": 3,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let $\Omega$ be a circle with center $O$ and let $A, B$ be points inside $\Omega$ (not collinear with $O$). Consider a diameter $CD$ of $\Omega$ such that the quadrilateral $ABCD$ is cyclic. If the distance from $O$ to $AB$ is $d$, and the radius of $\Omega$ is $r$, find the length of $CD$ in terms of $d$ and... | {
"record_id": "0850f8418506750167882b652b4ad44c81aec3b56c5c5e36ca434de3061d3f9e",
"dataset_name": "OpenMathReasoning",
"training_phase": "midtrain",
"sample_index": 4,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let $\Omega$ be a circle with center $O$ and let $A, B$ be points inside $\Omega$ (not collinear with $O$). Consider a diameter $CD$ of $\Omega$ such that the quadrilateral $ABCD$ is cyclic. If the distance from $O$ to $AB$ is $d$, and the radius of $\Omega$ is $r$, find the length of $CD$ in terms of $d$ and... | {
"record_id": "0850f8418506750167882b652b4ad44c81aec3b56c5c5e36ca434de3061d3f9e",
"dataset_name": "OpenMathReasoning",
"training_phase": "midtrain",
"sample_index": 5,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let $\Omega$ be a circle with center $O$ and let $A, B$ be points inside $\Omega$ (not collinear with $O$). Consider a diameter $CD$ of $\Omega$ such that the quadrilateral $ABCD$ is cyclic. If the distance from $O$ to $AB$ is $d$, and the radius of $\Omega$ is $r$, find the length of $CD$ in terms of $d$ and... | {
"record_id": "0850f8418506750167882b652b4ad44c81aec3b56c5c5e36ca434de3061d3f9e",
"dataset_name": "OpenMathReasoning",
"training_phase": "midtrain",
"sample_index": 6,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: Let $\Omega$ be a circle with center $O$ and let $A, B$ be points inside $\Omega$ (not collinear with $O$). Consider a diameter $CD$ of $\Omega$ such that the quadrilateral $ABCD$ is cyclic. If the distance from $O$ to $AB$ is $d$, and the radius of $\Omega$ is $r$, find the length of $CD$ in terms of $d$ and... | {
"record_id": "0850f8418506750167882b652b4ad44c81aec3b56c5c5e36ca434de3061d3f9e",
"dataset_name": "OpenMathReasoning",
"training_phase": "midtrain",
"sample_index": 7,
"judge_correct": true,
"model": "DeepSeek-V4-Flash"
} |
Question: In the finite element method (FEM), how are homogeneous natural boundary conditions (e.g., zero heat flux) implicitly accounted for in the formulation of the problem?
Answer: We need to explain how homogeneous natural boundary conditions (like zero heat flux) are implicitly accounted for in FEM formulation. T... | {
"record_id": "bf7ecbb4a0d072e8d8976e5e41fcd21553ef4aa3035776d736658ddbad85e130",
"dataset_name": "stepfun_sft",
"training_phase": "midtrain",
"sample_index": 0,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: In the finite element method (FEM), how are homogeneous natural boundary conditions (e.g., zero heat flux) implicitly accounted for in the formulation of the problem?
Answer: We need to answer: In the finite element method (FEM), how are homogeneous natural boundary conditions (e.g., zero heat flux) implicitl... | {
"record_id": "bf7ecbb4a0d072e8d8976e5e41fcd21553ef4aa3035776d736658ddbad85e130",
"dataset_name": "stepfun_sft",
"training_phase": "midtrain",
"sample_index": 1,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: In the finite element method (FEM), how are homogeneous natural boundary conditions (e.g., zero heat flux) implicitly accounted for in the formulation of the problem?
Answer: We need to answer: "In the finite element method (FEM), how are homogeneous natural boundary conditions (e.g., zero heat flux) implicit... | {
"record_id": "bf7ecbb4a0d072e8d8976e5e41fcd21553ef4aa3035776d736658ddbad85e130",
"dataset_name": "stepfun_sft",
"training_phase": "midtrain",
"sample_index": 2,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: In the finite element method (FEM), how are homogeneous natural boundary conditions (e.g., zero heat flux) implicitly accounted for in the formulation of the problem?
Answer: We are asked: "In the finite element method (FEM), how are homogeneous natural boundary conditions (e.g., zero heat flux) implicitly ac... | {
"record_id": "bf7ecbb4a0d072e8d8976e5e41fcd21553ef4aa3035776d736658ddbad85e130",
"dataset_name": "stepfun_sft",
"training_phase": "midtrain",
"sample_index": 3,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: In the finite element method (FEM), how are homogeneous natural boundary conditions (e.g., zero heat flux) implicitly accounted for in the formulation of the problem?
Answer: We need to explain how homogeneous natural boundary conditions (e.g., zero heat flux) are implicitly accounted for in finite element fo... | {
"record_id": "bf7ecbb4a0d072e8d8976e5e41fcd21553ef4aa3035776d736658ddbad85e130",
"dataset_name": "stepfun_sft",
"training_phase": "midtrain",
"sample_index": 4,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: In the finite element method (FEM), how are homogeneous natural boundary conditions (e.g., zero heat flux) implicitly accounted for in the formulation of the problem?
Answer: We need to answer: In FEM, how are homogeneous natural boundary conditions (e.g., zero heat flux) implicitly accounted for in the formu... | {
"record_id": "bf7ecbb4a0d072e8d8976e5e41fcd21553ef4aa3035776d736658ddbad85e130",
"dataset_name": "stepfun_sft",
"training_phase": "midtrain",
"sample_index": 5,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: In the finite element method (FEM), how are homogeneous natural boundary conditions (e.g., zero heat flux) implicitly accounted for in the formulation of the problem?
Answer: We need to answer: In FEM, how are homogeneous natural boundary conditions (e.g., zero heat flux) implicitly accounted for in the formu... | {
"record_id": "bf7ecbb4a0d072e8d8976e5e41fcd21553ef4aa3035776d736658ddbad85e130",
"dataset_name": "stepfun_sft",
"training_phase": "midtrain",
"sample_index": 6,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: In the finite element method (FEM), how are homogeneous natural boundary conditions (e.g., zero heat flux) implicitly accounted for in the formulation of the problem?
Answer: We are asked: "In the finite element method (FEM), how are homogeneous natural boundary conditions (e.g., zero heat flux) implicitly ac... | {
"record_id": "bf7ecbb4a0d072e8d8976e5e41fcd21553ef4aa3035776d736658ddbad85e130",
"dataset_name": "stepfun_sft",
"training_phase": "midtrain",
"sample_index": 7,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( k \) be a given positive integer, and let \( a_{1}, a_{2}, \cdots, a_{k} \) be pairwise coprime positive integers. Prove that there exists a sequence of \( k \) consecutive integers such that the \( j \)-th number in this sequence is divisible by \( a_{j} \) for \( 1 \leq j \leq k \).
Answer: We need t... | {
"record_id": "df283c7ed96818d6d78b61404eae331a526af63fbec84b44e48023c40e889f67",
"dataset_name": "numinamath",
"training_phase": "midtrain",
"sample_index": 0,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( k \) be a given positive integer, and let \( a_{1}, a_{2}, \cdots, a_{k} \) be pairwise coprime positive integers. Prove that there exists a sequence of \( k \) consecutive integers such that the \( j \)-th number in this sequence is divisible by \( a_{j} \) for \( 1 \leq j \leq k \).
Answer: We are as... | {
"record_id": "df283c7ed96818d6d78b61404eae331a526af63fbec84b44e48023c40e889f67",
"dataset_name": "numinamath",
"training_phase": "midtrain",
"sample_index": 1,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( k \) be a given positive integer, and let \( a_{1}, a_{2}, \cdots, a_{k} \) be pairwise coprime positive integers. Prove that there exists a sequence of \( k \) consecutive integers such that the \( j \)-th number in this sequence is divisible by \( a_{j} \) for \( 1 \leq j \leq k \).
Answer: We need t... | {
"record_id": "df283c7ed96818d6d78b61404eae331a526af63fbec84b44e48023c40e889f67",
"dataset_name": "numinamath",
"training_phase": "midtrain",
"sample_index": 2,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( k \) be a given positive integer, and let \( a_{1}, a_{2}, \cdots, a_{k} \) be pairwise coprime positive integers. Prove that there exists a sequence of \( k \) consecutive integers such that the \( j \)-th number in this sequence is divisible by \( a_{j} \) for \( 1 \leq j \leq k \).
Answer: We are gi... | {
"record_id": "df283c7ed96818d6d78b61404eae331a526af63fbec84b44e48023c40e889f67",
"dataset_name": "numinamath",
"training_phase": "midtrain",
"sample_index": 3,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
Question: Let \( k \) be a given positive integer, and let \( a_{1}, a_{2}, \cdots, a_{k} \) be pairwise coprime positive integers. Prove that there exists a sequence of \( k \) consecutive integers such that the \( j \)-th number in this sequence is divisible by \( a_{j} \) for \( 1 \leq j \leq k \).
Answer: We are gi... | {
"record_id": "df283c7ed96818d6d78b61404eae331a526af63fbec84b44e48023c40e889f67",
"dataset_name": "numinamath",
"training_phase": "midtrain",
"sample_index": 4,
"judge_correct": null,
"model": "DeepSeek-V4-Flash"
} |
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