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The dataset generation failed
Error code: DatasetGenerationError
Exception: CastError
Message: Couldn't cast
id: string
prompt: string
response: string
question: string
ground_truth: string
source: string
data_source: string
source_index: int64
sample_index: int64
teacher_model: string
temperature: double
top_p: double
max_tokens: int64
raw_response: string
endpoint: string
finish_reason: string
usage: struct<prompt_tokens: int64, total_tokens: int64, completion_tokens: int64, prompt_tokens_details: n (... 4 chars omitted)
child 0, prompt_tokens: int64
child 1, total_tokens: int64
child 2, completion_tokens: int64
child 3, prompt_tokens_details: null
rough_exact: bool
boxed_answer: string
to
{'id': Value('string'), 'prompt': Value('string'), 'response': Value('string'), 'question': Value('string'), 'ground_truth': Value('string'), 'source': Value('string'), 'data_source': Value('string'), 'source_index': Value('int64'), 'sample_index': Value('int64'), 'teacher_model': Value('string'), 'temperature': Value('float64'), 'top_p': Value('float64'), 'max_tokens': Value('int64'), 'boxed_answer': Value('string'), 'rough_exact': Value('bool')}
because column names don't match
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1816, in _prepare_split_single
for key, table in generator:
^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/packaged_modules/json/json.py", line 310, in _generate_tables
self._cast_table(pa_table, json_field_paths=json_field_paths),
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/packaged_modules/json/json.py", line 130, in _cast_table
pa_table = table_cast(pa_table, self.info.features.arrow_schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2369, in table_cast
return cast_table_to_schema(table, schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2297, in cast_table_to_schema
raise CastError(
datasets.table.CastError: Couldn't cast
id: string
prompt: string
response: string
question: string
ground_truth: string
source: string
data_source: string
source_index: int64
sample_index: int64
teacher_model: string
temperature: double
top_p: double
max_tokens: int64
raw_response: string
endpoint: string
finish_reason: string
usage: struct<prompt_tokens: int64, total_tokens: int64, completion_tokens: int64, prompt_tokens_details: n (... 4 chars omitted)
child 0, prompt_tokens: int64
child 1, total_tokens: int64
child 2, completion_tokens: int64
child 3, prompt_tokens_details: null
rough_exact: bool
boxed_answer: string
to
{'id': Value('string'), 'prompt': Value('string'), 'response': Value('string'), 'question': Value('string'), 'ground_truth': Value('string'), 'source': Value('string'), 'data_source': Value('string'), 'source_index': Value('int64'), 'sample_index': Value('int64'), 'teacher_model': Value('string'), 'temperature': Value('float64'), 'top_p': Value('float64'), 'max_tokens': Value('int64'), 'boxed_answer': Value('string'), 'rough_exact': Value('bool')}
because column names don't match
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1348, in compute_config_parquet_and_info_response
parquet_operations = convert_to_parquet(builder)
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 980, in convert_to_parquet
builder.download_and_prepare(
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 890, in download_and_prepare
self._download_and_prepare(
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 951, in _download_and_prepare
self._prepare_split(split_generator, **prepare_split_kwargs)
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1683, in _prepare_split
for job_id, done, content in self._prepare_split_single(
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1869, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
id string | prompt string | response string | question string | ground_truth string | source string | data_source string | source_index int64 | sample_index int64 | teacher_model string | temperature float64 | top_p float64 | max_tokens int64 | boxed_answer string | rough_exact bool |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000000_s0 | <|im_start|>user
In triangle $ABC$, $\sin \angle A = \frac{4}{5}$ and $\angle A < 90^\circ$. Let $D$ be a point outside triangle $ABC$ such that $\angle BAD = \angle DAC$ and $\angle BDC = 90^\circ$. Suppose that $AD = 1$ and that $\frac{BD}{CD} = \frac{3}{2}$. If $AB + AC$ can be expressed in the form $\frac{a\sqrt{b}... | We are given a triangle $ ABC $ with:
- $ \sin \angle A = \frac{4}{5} $
- $ \angle A < 90^\circ $
- $ D $ is a point outside triangle $ ABC $ such that $ \angle BAD = \angle DAC $, i.e., $ AD $ is the angle bisector of $ \angle BAC $
- $ \angle BDC = 90^\circ $
- $ AD = 1 $
- $ \frac{BD}{CD} = \frac{3}{2} $
- We are t... | In triangle $ABC$, $\sin \angle A = \frac{4}{5}$ and $\angle A < 90^\circ$. Let $D$ be a point outside triangle $ABC$ such that $\angle BAD = \angle DAC$ and $\angle BDC = 90^\circ$. Suppose that $AD = 1$ and that $\frac{BD}{CD} = \frac{3}{2}$. If $AB + AC$ can be expressed in the form $\frac{a\sqrt{b}}{c}$ where $a, b... | 34 | open-r1/DAPO-Math-17k-Processed | math_dapo | 0 | 0 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 1057 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000000_s1 | <|im_start|>user
In triangle $ABC$, $\sin \angle A = \frac{4}{5}$ and $\angle A < 90^\circ$. Let $D$ be a point outside triangle $ABC$ such that $\angle BAD = \angle DAC$ and $\angle BDC = 90^\circ$. Suppose that $AD = 1$ and that $\frac{BD}{CD} = \frac{3}{2}$. If $AB + AC$ can be expressed in the form $\frac{a\sqrt{b}... | We are given:
- In triangle $ ABC $, $ \sin \angle A = \frac{4}{5} $, and $ \angle A < 90^\circ $.
- Point $ D $ is outside triangle $ ABC $, such that $ \angle BAD = \angle DAC $, and $ \angle BDC = 90^\circ $.
- $ AD = 1 $, and $ \frac{BD}{CD} = \frac{3}{2} $.
- We are to find $ AB + AC $ in the form $ \frac{a\sqrt{... | In triangle $ABC$, $\sin \angle A = \frac{4}{5}$ and $\angle A < 90^\circ$. Let $D$ be a point outside triangle $ABC$ such that $\angle BAD = \angle DAC$ and $\angle BDC = 90^\circ$. Suppose that $AD = 1$ and that $\frac{BD}{CD} = \frac{3}{2}$. If $AB + AC$ can be expressed in the form $\frac{a\sqrt{b}}{c}$ where $a, b... | 34 | open-r1/DAPO-Math-17k-Processed | math_dapo | 0 | 1 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 700 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000000_s2 | <|im_start|>user
In triangle $ABC$, $\sin \angle A = \frac{4}{5}$ and $\angle A < 90^\circ$. Let $D$ be a point outside triangle $ABC$ such that $\angle BAD = \angle DAC$ and $\angle BDC = 90^\circ$. Suppose that $AD = 1$ and that $\frac{BD}{CD} = \frac{3}{2}$. If $AB + AC$ can be expressed in the form $\frac{a\sqrt{b}... | We are given a triangle $ ABC $ with:
- $ \sin \angle A = \frac{4}{5} $ and $ \angle A < 90^\circ $
- Point $ D $ lies outside triangle $ ABC $ such that $ \angle BAD = \angle DAC $ and $ \angle BDC = 90^\circ $
- $ AD = 1 $
- $ \frac{BD}{CD} = \frac{3}{2} $
- We are to find $ AB + AC $ in the form $ \frac{a\sqrt{b}}{... | In triangle $ABC$, $\sin \angle A = \frac{4}{5}$ and $\angle A < 90^\circ$. Let $D$ be a point outside triangle $ABC$ such that $\angle BAD = \angle DAC$ and $\angle BDC = 90^\circ$. Suppose that $AD = 1$ and that $\frac{BD}{CD} = \frac{3}{2}$. If $AB + AC$ can be expressed in the form $\frac{a\sqrt{b}}{c}$ where $a, b... | 34 | open-r1/DAPO-Math-17k-Processed | math_dapo | 0 | 2 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 10 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000000_s3 | <|im_start|>user
In triangle $ABC$, $\sin \angle A = \frac{4}{5}$ and $\angle A < 90^\circ$. Let $D$ be a point outside triangle $ABC$ such that $\angle BAD = \angle DAC$ and $\angle BDC = 90^\circ$. Suppose that $AD = 1$ and that $\frac{BD}{CD} = \frac{3}{2}$. If $AB + AC$ can be expressed in the form $\frac{a\sqrt{b}... | We are given a triangle $ ABC $ with:
- $ \sin \angle A = \frac{4}{5} $
- $ \angle A < 90^\circ $
- $ D $ is a point outside triangle $ ABC $ such that:
- $ \angle BAD = \angle DAC $, so $ AD $ is the angle bisector of $ \angle A $
- $ \angle BDC = 90^\circ $
- $ AD = 1 $
- $ \frac{BD}{CD} = \frac{3}{2} $
- We... | In triangle $ABC$, $\sin \angle A = \frac{4}{5}$ and $\angle A < 90^\circ$. Let $D$ be a point outside triangle $ABC$ such that $\angle BAD = \angle DAC$ and $\angle BDC = 90^\circ$. Suppose that $AD = 1$ and that $\frac{BD}{CD} = \frac{3}{2}$. If $AB + AC$ can be expressed in the form $\frac{a\sqrt{b}}{c}$ where $a, b... | 34 | open-r1/DAPO-Math-17k-Processed | math_dapo | 0 | 3 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 54 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000001_s0 | <|im_start|>user
Let $ABCD$ be a unit square in the plane. Points $X$ and $Y$ are chosen independently and uniformly at random on the perimeter of $ABCD$. If the expected value of the area of triangle $\triangle AXY$ can be expressed as $\frac{m}{n}$ for relatively prime positive integers $m$ and $n$, compute $m+n$.
Pl... | We are given a unit square $ABCD$, with side length 1, and points $X$ and $Y$ chosen independently and uniformly at random on the perimeter of the square. We are to compute the **expected value of the area of triangle $AXY$**.
---
### Step 1: Understand the setup
Let’s consider the square $ABCD$ with vertices:
- $A... | Let $ABCD$ be a unit square in the plane. Points $X$ and $Y$ are chosen independently and uniformly at random on the perimeter of $ABCD$. If the expected value of the area of triangle $\triangle AXY$ can be expressed as $\frac{m}{n}$ for relatively prime positive integers $m$ and $n$, compute $m+n$. | 113 | open-r1/DAPO-Math-17k-Processed | math_dapo | 1 | 0 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 1 + 4 = 5 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000001_s1 | <|im_start|>user
Let $ABCD$ be a unit square in the plane. Points $X$ and $Y$ are chosen independently and uniformly at random on the perimeter of $ABCD$. If the expected value of the area of triangle $\triangle AXY$ can be expressed as $\frac{m}{n}$ for relatively prime positive integers $m$ and $n$, compute $m+n$.
Pl... | We are given a unit square $ABCD$ with side length 1. Points $X$ and $Y$ are chosen **independently and uniformly at random** on the perimeter of the square. We are to find the **expected value of the area of triangle $AXY$** and express it as $\frac{m}{n}$ with $m$ and $n$ coprime, then compute $m+n$.
---
### Step 1... | Let $ABCD$ be a unit square in the plane. Points $X$ and $Y$ are chosen independently and uniformly at random on the perimeter of $ABCD$. If the expected value of the area of triangle $\triangle AXY$ can be expressed as $\frac{m}{n}$ for relatively prime positive integers $m$ and $n$, compute $m+n$. | 113 | open-r1/DAPO-Math-17k-Processed | math_dapo | 1 | 1 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 7 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000001_s2 | <|im_start|>user
Let $ABCD$ be a unit square in the plane. Points $X$ and $Y$ are chosen independently and uniformly at random on the perimeter of $ABCD$. If the expected value of the area of triangle $\triangle AXY$ can be expressed as $\frac{m}{n}$ for relatively prime positive integers $m$ and $n$, compute $m+n$.
Pl... | We are given a unit square $ABCD$, with side length 1. Points $X$ and $Y$ are chosen independently and uniformly at random on the perimeter of the square. We are to find the **expected value** of the area of triangle $\triangle AXY$.
---
### Step 1: Understand the setup
Let the square $ABCD$ have vertices:
- $A = (0... | Let $ABCD$ be a unit square in the plane. Points $X$ and $Y$ are chosen independently and uniformly at random on the perimeter of $ABCD$. If the expected value of the area of triangle $\triangle AXY$ can be expressed as $\frac{m}{n}$ for relatively prime positive integers $m$ and $n$, compute $m+n$. | 113 | open-r1/DAPO-Math-17k-Processed | math_dapo | 1 | 2 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 13 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000001_s3 | <|im_start|>user
Let $ABCD$ be a unit square in the plane. Points $X$ and $Y$ are chosen independently and uniformly at random on the perimeter of $ABCD$. If the expected value of the area of triangle $\triangle AXY$ can be expressed as $\frac{m}{n}$ for relatively prime positive integers $m$ and $n$, compute $m+n$.
Pl... | We are given a unit square $ABCD$ with side length 1, and points $X$ and $Y$ are chosen **independently and uniformly** at random on the **perimeter** of the square.
We are to find the **expected area** of triangle $ \triangle AXY $, and express it as a reduced fraction $\frac{m}{n}$, then compute $m+n$.
---
### Ste... | Let $ABCD$ be a unit square in the plane. Points $X$ and $Y$ are chosen independently and uniformly at random on the perimeter of $ABCD$. If the expected value of the area of triangle $\triangle AXY$ can be expressed as $\frac{m}{n}$ for relatively prime positive integers $m$ and $n$, compute $m+n$. | 113 | open-r1/DAPO-Math-17k-Processed | math_dapo | 1 | 3 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 3 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000002_s0 | <|im_start|>user
Let $a, b, c$ be distinct numbers such that the equations $x^2 + ax + 1 = 0$ and $x^2 + bx + c = 0$ have a common real root, and the equations $x^2 + x + a = 0$ and $x^2 + cx + b = 0$ also have a common real root. Compute the sum $a + b + c$.
Please solve the problem concisely. Show the key steps, and ... | We are given three distinct real numbers $ a, b, c $, and two pairs of quadratic equations with a common real root each:
1. $ x^2 + ax + 1 = 0 $ and $ x^2 + bx + c = 0 $ have a common real root.
2. $ x^2 + x + a = 0 $ and $ x^2 + cx + b = 0 $ have a common real root.
We are to find $ a + b + c $.
---
### Step 1: Le... | Let $a, b, c$ be distinct numbers such that the equations $x^2 + ax + 1 = 0$ and $x^2 + bx + c = 0$ have a common real root, and the equations $x^2 + x + a = 0$ and $x^2 + cx + b = 0$ also have a common real root. Compute the sum $a + b + c$. | -3 | open-r1/DAPO-Math-17k-Processed | math_dapo | 2 | 0 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 0 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000002_s1 | <|im_start|>user
Let $a, b, c$ be distinct numbers such that the equations $x^2 + ax + 1 = 0$ and $x^2 + bx + c = 0$ have a common real root, and the equations $x^2 + x + a = 0$ and $x^2 + cx + b = 0$ also have a common real root. Compute the sum $a + b + c$.
Please solve the problem concisely. Show the key steps, and ... | We are given that:
- $ a, b, c $ are **distinct** real numbers.
- The equations $ x^2 + ax + 1 = 0 $ and $ x^2 + bx + c = 0 $ have a **common real root**.
- The equations $ x^2 + x + a = 0 $ and $ x^2 + cx + b = 0 $ also have a **common real root**.
We are to find the **sum** $ a + b + c $.
---
### Step 1: Let the ... | Let $a, b, c$ be distinct numbers such that the equations $x^2 + ax + 1 = 0$ and $x^2 + bx + c = 0$ have a common real root, and the equations $x^2 + x + a = 0$ and $x^2 + cx + b = 0$ also have a common real root. Compute the sum $a + b + c$. | -3 | open-r1/DAPO-Math-17k-Processed | math_dapo | 2 | 1 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | a + b + c = 0 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000002_s2 | <|im_start|>user
Let $a, b, c$ be distinct numbers such that the equations $x^2 + ax + 1 = 0$ and $x^2 + bx + c = 0$ have a common real root, and the equations $x^2 + x + a = 0$ and $x^2 + cx + b = 0$ also have a common real root. Compute the sum $a + b + c$.
Please solve the problem concisely. Show the key steps, and ... | We are given that:
- $ a, b, c $ are **distinct** real numbers.
- The equations:
$$
x^2 + ax + 1 = 0 \quad \text{(1)}
$$
$$
x^2 + bx + c = 0 \quad \text{(2)}
$$
have a **common real root**.
- The equations:
$$
x^2 + x + a = 0 \quad \text{(3)}
$$
$$
x^2 + cx + b = 0 \quad \text{(4)}
$$
also ... | Let $a, b, c$ be distinct numbers such that the equations $x^2 + ax + 1 = 0$ and $x^2 + bx + c = 0$ have a common real root, and the equations $x^2 + x + a = 0$ and $x^2 + cx + b = 0$ also have a common real root. Compute the sum $a + b + c$. | -3 | open-r1/DAPO-Math-17k-Processed | math_dapo | 2 | 2 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | -3 | true |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000002_s3 | <|im_start|>user
Let $a, b, c$ be distinct numbers such that the equations $x^2 + ax + 1 = 0$ and $x^2 + bx + c = 0$ have a common real root, and the equations $x^2 + x + a = 0$ and $x^2 + cx + b = 0$ also have a common real root. Compute the sum $a + b + c$.
Please solve the problem concisely. Show the key steps, and ... | We are given three distinct numbers $ a, b, c $ such that:
1. The equations $ x^2 + ax + 1 = 0 $ and $ x^2 + bx + c = 0 $ have a **common real root**.
2. The equations $ x^2 + x + a = 0 $ and $ x^2 + cx + b = 0 $ also have a **common real root**.
We are to find the **sum** $ a + b + c $.
---
### Step 1: Use the con... | Let $a, b, c$ be distinct numbers such that the equations $x^2 + ax + 1 = 0$ and $x^2 + bx + c = 0$ have a common real root, and the equations $x^2 + x + a = 0$ and $x^2 + cx + b = 0$ also have a common real root. Compute the sum $a + b + c$. | -3 | open-r1/DAPO-Math-17k-Processed | math_dapo | 2 | 3 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 3 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000003_s0 | <|im_start|>user
There are $7$ boxes arranged in a row and numbered $1$ through $7$. You have a stack of $2015$ cards, which you place one by one in the boxes. The first card is placed in box $1$, the second in box $2$, and so forth up to the seventh card which is placed in box $7$. You then start working back in the o... | We are given a sequence of placing 2015 cards into 7 boxes arranged in a row, in a specific pattern.
---
### Step 1: Understand the pattern
- Start with box 1 → box 2 → box 3 → box 4 → box 5 → box 6 → box 7 (7 cards).
- Then go back: box 6 → box 5 → box 4 → box 3 → box 2 → box 1 (6 cards).
- Then go forward again: b... | There are $7$ boxes arranged in a row and numbered $1$ through $7$. You have a stack of $2015$ cards, which you place one by one in the boxes. The first card is placed in box $1$, the second in box $2$, and so forth up to the seventh card which is placed in box $7$. You then start working back in the other direction, p... | 3 | open-r1/DAPO-Math-17k-Processed | math_dapo | 3 | 0 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 3 | true |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000003_s1 | <|im_start|>user
There are $7$ boxes arranged in a row and numbered $1$ through $7$. You have a stack of $2015$ cards, which you place one by one in the boxes. The first card is placed in box $1$, the second in box $2$, and so forth up to the seventh card which is placed in box $7$. You then start working back in the o... | We are given a sequence of placing cards into 7 boxes arranged in a row. The cards are placed in a **back-and-forth** pattern:
- First, cards are placed **left to right** from box 1 to box 7.
- Then, cards are placed **right to left** from box 7 to box 1.
- This pattern repeats: left to right, right to left, left to r... | There are $7$ boxes arranged in a row and numbered $1$ through $7$. You have a stack of $2015$ cards, which you place one by one in the boxes. The first card is placed in box $1$, the second in box $2$, and so forth up to the seventh card which is placed in box $7$. You then start working back in the other direction, p... | 3 | open-r1/DAPO-Math-17k-Processed | math_dapo | 3 | 1 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 1 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000003_s2 | <|im_start|>user
There are $7$ boxes arranged in a row and numbered $1$ through $7$. You have a stack of $2015$ cards, which you place one by one in the boxes. The first card is placed in box $1$, the second in box $2$, and so forth up to the seventh card which is placed in box $7$. You then start working back in the o... | We are given a problem involving 7 boxes arranged in a row, numbered 1 through 7, and a stack of 2015 cards to be placed in them in a specific pattern.
---
### Step 1: Understand the Pattern
We are told that the cards are placed in the boxes in the following order:
- **Forward direction**: 1 → 2 → 3 → 4 → 5 → 6 → 7... | There are $7$ boxes arranged in a row and numbered $1$ through $7$. You have a stack of $2015$ cards, which you place one by one in the boxes. The first card is placed in box $1$, the second in box $2$, and so forth up to the seventh card which is placed in box $7$. You then start working back in the other direction, p... | 3 | open-r1/DAPO-Math-17k-Processed | math_dapo | 3 | 2 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 1 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000003_s3 | <|im_start|>user
There are $7$ boxes arranged in a row and numbered $1$ through $7$. You have a stack of $2015$ cards, which you place one by one in the boxes. The first card is placed in box $1$, the second in box $2$, and so forth up to the seventh card which is placed in box $7$. You then start working back in the o... | We are given a problem involving 7 boxes arranged in a row, and a stack of 2015 cards being placed in them in a specific pattern.
---
### Step 1: Understand the Pattern
- The cards are placed **in order** from box 1 to box 7.
- Then, they are placed **backwards** from box 6 to box 1.
- Then forward again from box 2 ... | There are $7$ boxes arranged in a row and numbered $1$ through $7$. You have a stack of $2015$ cards, which you place one by one in the boxes. The first card is placed in box $1$, the second in box $2$, and so forth up to the seventh card which is placed in box $7$. You then start working back in the other direction, p... | 3 | open-r1/DAPO-Math-17k-Processed | math_dapo | 3 | 3 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 7 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000004_s0 | <|im_start|>user
Let $S$ be the set of triples $(a,b,c)$ of non-negative integers such that $a+b+c$ is even. The value of the sum
\[ \sum_{(a,b,c) \in S} \frac{1}{2^a 3^b 5^c} \]
can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Compute $m+n$.
Please solve the problem concisel... | We are given the set $ S $ of triples $ (a, b, c) $ of non-negative integers such that $ a + b + c $ is even, and we are to compute the sum:
$$
\sum_{(a,b,c) \in S} \frac{1}{2^a 3^b 5^c}
$$
---
### Step 1: Understand the Sum
We are summing over all non-negative integer triples $ (a, b, c) $ such that $ a + b + c $ ... | Let $S$ be the set of triples $(a,b,c)$ of non-negative integers such that $a+b+c$ is even. The value of the sum
\[ \sum_{(a,b,c) \in S} \frac{1}{2^a 3^b 5^c} \]
can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Compute $m+n$. | 37 | open-r1/DAPO-Math-17k-Processed | math_dapo | 4 | 0 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 65 + 24 = 89 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000004_s1 | <|im_start|>user
Let $S$ be the set of triples $(a,b,c)$ of non-negative integers such that $a+b+c$ is even. The value of the sum
\[ \sum_{(a,b,c) \in S} \frac{1}{2^a 3^b 5^c} \]
can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Compute $m+n$.
Please solve the problem concisel... | We are given the set $ S $ of triples $ (a, b, c) $ of non-negative integers such that $ a + b + c $ is even, and the sum:
$$
\sum_{(a,b,c) \in S} \frac{1}{2^a 3^b 5^c}
$$
We are to compute this sum and express it as $ \frac{m}{n} $, where $ m $ and $ n $ are coprime, and then find $ m + n $.
---
### Step 1: Unders... | Let $S$ be the set of triples $(a,b,c)$ of non-negative integers such that $a+b+c$ is even. The value of the sum
\[ \sum_{(a,b,c) \in S} \frac{1}{2^a 3^b 5^c} \]
can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Compute $m+n$. | 37 | open-r1/DAPO-Math-17k-Processed | math_dapo | 4 | 1 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 23 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000004_s2 | <|im_start|>user
Let $S$ be the set of triples $(a,b,c)$ of non-negative integers such that $a+b+c$ is even. The value of the sum
\[ \sum_{(a,b,c) \in S} \frac{1}{2^a 3^b 5^c} \]
can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Compute $m+n$.
Please solve the problem concisel... | We are given the set $ S $ of triples $ (a, b, c) $ of non-negative integers such that $ a + b + c $ is even. We are to compute the sum:
$$
\sum_{(a,b,c) \in S} \frac{1}{2^a 3^b 5^c}
$$
---
### Step 1: Understand the Set $ S $
We are summing over all non-negative integer triples $ (a, b, c) $ such that $ a + b + c ... | Let $S$ be the set of triples $(a,b,c)$ of non-negative integers such that $a+b+c$ is even. The value of the sum
\[ \sum_{(a,b,c) \in S} \frac{1}{2^a 3^b 5^c} \]
can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Compute $m+n$. | 37 | open-r1/DAPO-Math-17k-Processed | math_dapo | 4 | 2 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 15 + 8 = 23 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000004_s3 | <|im_start|>user
Let $S$ be the set of triples $(a,b,c)$ of non-negative integers such that $a+b+c$ is even. The value of the sum
\[ \sum_{(a,b,c) \in S} \frac{1}{2^a 3^b 5^c} \]
can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Compute $m+n$.
Please solve the problem concisel... | We are given the set $ S $ of triples $ (a, b, c) $ of **non-negative integers** such that $ a + b + c $ is **even**, and we are to compute the sum:
$$
\sum_{(a,b,c) \in S} \frac{1}{2^a 3^b 5^c}
$$
---
### Step 1: Understand the Sum
The sum is over all non-negative integer triples $ (a, b, c) $ such that $ a + b + ... | Let $S$ be the set of triples $(a,b,c)$ of non-negative integers such that $a+b+c$ is even. The value of the sum
\[ \sum_{(a,b,c) \in S} \frac{1}{2^a 3^b 5^c} \]
can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Compute $m+n$. | 37 | open-r1/DAPO-Math-17k-Processed | math_dapo | 4 | 3 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 47 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000005_s0 | <|im_start|>user
For which $n$ is $n^4 + 6n^3 + 11n^2 + 3n + 31$ a perfect square?
Please solve the problem concisely. Show the key steps, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| We are given the polynomial:
$$
f(n) = n^4 + 6n^3 + 11n^2 + 3n + 31
$$
We are to determine for which values of $ n $, this expression is a **perfect square**.
---
### Step 1: Try small integer values for $ n $
Let's test small integer values of $ n $ to see if the expression becomes a perfect square.
#### Try $ n... | For which $n$ is $n^4 + 6n^3 + 11n^2 + 3n + 31$ a perfect square? | 10 | open-r1/DAPO-Math-17k-Processed | math_dapo | 5 | 0 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | n = 10 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000005_s1 | <|im_start|>user
For which $n$ is $n^4 + 6n^3 + 11n^2 + 3n + 31$ a perfect square?
Please solve the problem concisely. Show the key steps, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| We are given the expression:
$$
n^4 + 6n^3 + 11n^2 + 3n + 31
$$
and asked to find for which values of $ n $ it is a **perfect square**.
---
### Step 1: Try small integer values of $ n $
We'll test small integer values of $ n $ to see if the expression becomes a perfect square.
#### Try $ n = 0 $:
$$
0^4 + 6 \cdot... | For which $n$ is $n^4 + 6n^3 + 11n^2 + 3n + 31$ a perfect square? | 10 | open-r1/DAPO-Math-17k-Processed | math_dapo | 5 | 1 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 1 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000005_s2 | <|im_start|>user
For which $n$ is $n^4 + 6n^3 + 11n^2 + 3n + 31$ a perfect square?
Please solve the problem concisely. Show the key steps, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| We are given the expression:
$$
n^4 + 6n^3 + 11n^2 + 3n + 31
$$
We are to find for which integer values of $ n $ this expression is a **perfect square**.
---
### Step 1: Try small integer values of $ n $
We will evaluate the expression for small integer values of $ n $ and see when it is a perfect square.
#### Tr... | For which $n$ is $n^4 + 6n^3 + 11n^2 + 3n + 31$ a perfect square? | 10 | open-r1/DAPO-Math-17k-Processed | math_dapo | 5 | 2 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | \text{No such integer } n | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000005_s3 | <|im_start|>user
For which $n$ is $n^4 + 6n^3 + 11n^2 + 3n + 31$ a perfect square?
Please solve the problem concisely. Show the key steps, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| We are given the expression:
$$
n^4 + 6n^3 + 11n^2 + 3n + 31
$$
and asked to determine for which values of $ n $ it is a **perfect square**.
---
### Step 1: Try small integer values of $ n $
Let’s test small integer values for $ n $ and see if the expression is a perfect square.
#### Try $ n = 0 $:
$$
0^4 + 6 \c... | For which $n$ is $n^4 + 6n^3 + 11n^2 + 3n + 31$ a perfect square? | 10 | open-r1/DAPO-Math-17k-Processed | math_dapo | 5 | 3 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | -2 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000006_s3 | <|im_start|>user
Four positive integers $a, b, c, d$ satisfy the condition $a < b < c < d$. Determine the smallest possible value of $d$ such that the arithmetic mean of the numbers $a, b, c$ is half of the arithmetic mean of the numbers $a, b, c, d$.
Please solve the problem concisely. Show the key steps, and put your... | We are given four positive integers $ a < b < c < d $, and the condition:
$$
\text{Arithmetic mean of } a, b, c = \frac{1}{2} \text{ of the arithmetic mean of } a, b, c, d
$$
Let’s write this condition mathematically.
---
### Step 1: Use the arithmetic mean formula
$$
\frac{a + b + c}{3} = \frac{1}{2} \cdot \frac{... | Four positive integers $a, b, c, d$ satisfy the condition $a < b < c < d$. Determine the smallest possible value of $d$ such that the arithmetic mean of the numbers $a, b, c$ is half of the arithmetic mean of the numbers $a, b, c, d$. | 10 | open-r1/DAPO-Math-17k-Processed | math_dapo | 6 | 3 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 6 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000007_s0 | <|im_start|>user
$n$ coins are arranged in a circle. If two neighboring coins both show heads or both show tails, you can flip both coins. How many distinct arrangements of the coins are there such that no arrangement can be transformed into another by performing these operations?
Please solve the problem concisely. Sh... | We are given $ n $ coins arranged in a **circle**, and the allowed operation is:
> **Flip both neighboring coins** (i.e., flip two adjacent coins).
We are to find the number of **distinct arrangements** of the coins such that **no arrangement can be transformed into another** by performing this operation.
---
### S... | $n$ coins are arranged in a circle. If two neighboring coins both show heads or both show tails, you can flip both coins. How many distinct arrangements of the coins are there such that no arrangement can be transformed into another by performing these operations? | 2 | open-r1/DAPO-Math-17k-Processed | math_dapo | 7 | 0 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 2 | true |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000007_s1 | <|im_start|>user
$n$ coins are arranged in a circle. If two neighboring coins both show heads or both show tails, you can flip both coins. How many distinct arrangements of the coins are there such that no arrangement can be transformed into another by performing these operations?
Please solve the problem concisely. Sh... | We are given $ n $ coins arranged in a **circle**, and we can perform the following operation: **flip two neighboring coins** (i.e., if two coins are both heads or both tails, we flip both).
We are to find the number of **distinct arrangements** of the coins such that **no arrangement can be transformed into another**... | $n$ coins are arranged in a circle. If two neighboring coins both show heads or both show tails, you can flip both coins. How many distinct arrangements of the coins are there such that no arrangement can be transformed into another by performing these operations? | 2 | open-r1/DAPO-Math-17k-Processed | math_dapo | 7 | 1 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 1 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000007_s2 | <|im_start|>user
$n$ coins are arranged in a circle. If two neighboring coins both show heads or both show tails, you can flip both coins. How many distinct arrangements of the coins are there such that no arrangement can be transformed into another by performing these operations?
Please solve the problem concisely. Sh... | We are given $ n $ coins arranged in a **circle**, and we can perform the following operation:
- **Flip two neighboring coins** (i.e., flip both coins if they are both heads or both tails).
We are to find the number of **distinct arrangements** of the coins such that **no arrangement can be transformed into another**... | $n$ coins are arranged in a circle. If two neighboring coins both show heads or both show tails, you can flip both coins. How many distinct arrangements of the coins are there such that no arrangement can be transformed into another by performing these operations? | 2 | open-r1/DAPO-Math-17k-Processed | math_dapo | 7 | 2 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 2 | true |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000007_s3 | <|im_start|>user
$n$ coins are arranged in a circle. If two neighboring coins both show heads or both show tails, you can flip both coins. How many distinct arrangements of the coins are there such that no arrangement can be transformed into another by performing these operations?
Please solve the problem concisely. Sh... | We are given $ n $ coins arranged in a **circle**, and the allowed operation is to **flip two neighboring coins** (i.e., flip both if they are both heads or both tails).
We are to find the **number of distinct arrangements** of the coins such that **no arrangement can be transformed into another** by performing these ... | $n$ coins are arranged in a circle. If two neighboring coins both show heads or both show tails, you can flip both coins. How many distinct arrangements of the coins are there such that no arrangement can be transformed into another by performing these operations? | 2 | open-r1/DAPO-Math-17k-Processed | math_dapo | 7 | 3 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 2^{n-1} | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000008_s0 | <|im_start|>user
Determine the smallest prime $p$ such that $2018!$ is divisible by $p^3$, but not divisible by $p^4$.
Please solve the problem concisely. Show the key steps, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| We are given the task to find the **smallest prime $ p $** such that:
$$
2018! \text{ is divisible by } p^3 \text{ but not by } p^4.
$$
---
### Step 1: Understanding the Problem
We are to find the **smallest prime** $ p $ such that:
- $ p^3 \mid 2018! $
- $ p^4 \nmid 2018! $
This means that **the exponent of $ p ... | Determine the smallest prime $p$ such that $2018!$ is divisible by $p^3$, but not divisible by $p^4$. | 509 | open-r1/DAPO-Math-17k-Processed | math_dapo | 8 | 0 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 47 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000008_s2 | <|im_start|>user
Determine the smallest prime $p$ such that $2018!$ is divisible by $p^3$, but not divisible by $p^4$.
Please solve the problem concisely. Show the key steps, and put your final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| We are asked to find the **smallest prime $ p $** such that:
$$
2018! \text{ is divisible by } p^3 \text{ but not by } p^4.
$$
---
### Step 1: Understand the divisibility condition
A number $ N $ is divisible by $ p^3 $ if the **exponent of $ p $ in the prime factorization of $ N $** is at least 3.
So, we need to ... | Determine the smallest prime $p$ such that $2018!$ is divisible by $p^3$, but not divisible by $p^4$. | 509 | open-r1/DAPO-Math-17k-Processed | math_dapo | 8 | 2 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 3 | false |
dapo_qwen3_1p7b_full17260x4_nothink_8192_batched_000009_s0 | <|im_start|>user
Suppose you have a sphere tangent to the $xy$-plane with its center having a positive $z$-coordinate. If it is projected from a point $P=(0,b,a)$ to the $xy$-plane, it gives the conic section $y=x^2$. If we write $a=\frac{p}{q}$ where $p$ and $q$ are integers, find $p+q$.
Please solve the problem conci... | We are given a sphere tangent to the $ xy $-plane with center at $ (0, c, d) $, where $ d > 0 $, and it is projected from the point $ P = (0, b, a) $ to the $ xy $-plane, resulting in the conic section $ y = x^2 $.
---
### Step 1: Understand the projection
The sphere is tangent to the $ xy $-plane, so its center is ... | Suppose you have a sphere tangent to the $xy$-plane with its center having a positive $z$-coordinate. If it is projected from a point $P=(0,b,a)$ to the $xy$-plane, it gives the conic section $y=x^2$. If we write $a=\frac{p}{q}$ where $p$ and $q$ are integers, find $p+q$. | 3 | open-r1/DAPO-Math-17k-Processed | math_dapo | 9 | 0 | qwen3-1.7b | 0.7 | 0.95 | 8,192 | 2 | false |
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