row_id int64 0 1.02k | instruction_seed stringclasses 128
values | _source stringclasses 1
value | gpt41_mini_response stringclasses 128
values | __original_row_idx int64 1.5k 473k | length int64 3.38k 40k | ms_id int64 169k 214k | generated_text stringlengths 9.12k 160k ⌀ | final_answer stringlengths 1 134 | complete_responses_count int64 0 8 | qwen3_235b_thinking_generated_text stringlengths 15.5k 128k |
|---|---|---|---|---|---|---|---|---|---|---|
0 | A fair coin is flipped 10 times, and the number of consecutive heads that appear at any point during the 10 flips is recorded. What is the probability that the longest sequence of consecutive heads has a length of exactly 4? Express your answer as a common fraction. | ai2-adapt-dev/openmath-2-math | **Problem restatement:**
A fair coin is flipped 10 times. We look at all sequences of consecutive heads within those 10 flips and record the longest run of consecutive heads. We want the probability that the longest run is **exactly 4**.
---
### Step 1: Understand the problem
- Each flip is independent with probab... | 467,207 | 7,495 | 168,911 | <think>
Okay, so I need to find the probability that when flipping a fair coin 10 times, the longest run of consecutive heads is exactly 4. Hmm, let me think about how to approach this.
First, I know that the total number of possible outcomes is 2^10, which is 1024. So the denominator of my probability will be 1024. T... | \dfrac{139}{1024} | 8 | <think>
This is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.
Well, so the problem is: flip a fair coin 10 times, what's the probability the longest consecutive heads is exactly 4? Hmm, okay, so we need to count the number of 10-flip sequences w... |
1 | "A fair coin is flipped 10 times, and the number of consecutive heads that appear at any point durin(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem restatement:** \nA fair coin is flipped 10 times. We look at all sequences of consecutiv(...TRUNCATED) | 467,207 | 7,495 | 168,911 | "<think>\nOkay, so I need to find the probability that when flipping a fair coin 10 times, the longe(...TRUNCATED) | \dfrac{139}{1024} | 8 | "<think>\nThis is a complex or challenging question, and it is difficult to provide a direct and cor(...TRUNCATED) |
2 | "A fair coin is flipped 10 times, and the number of consecutive heads that appear at any point durin(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem restatement:** \nA fair coin is flipped 10 times. We look at all sequences of consecutiv(...TRUNCATED) | 467,207 | 7,495 | 168,911 | "<think>\nOkay, so I need to find the probability that when flipping a fair coin 10 times, the longe(...TRUNCATED) | \dfrac{139}{1024} | 8 | "<think>\nThis is a complex or challenging question, and it is difficult to provide a direct and cor(...TRUNCATED) |
3 | "A fair coin is flipped 10 times, and the number of consecutive heads that appear at any point durin(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem restatement:** \nA fair coin is flipped 10 times. We look at all sequences of consecutiv(...TRUNCATED) | 467,207 | 7,495 | 168,911 | "<think>\nOkay, so I need to find the probability that when flipping a fair coin 10 times, the longe(...TRUNCATED) | \dfrac{139}{1024} | 8 | "<think>\nThis is a complex or challenging question, and it is difficult to provide a direct and cor(...TRUNCATED) |
4 | "A fair coin is flipped 10 times, and the number of consecutive heads that appear at any point durin(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem restatement:** \nA fair coin is flipped 10 times. We look at all sequences of consecutiv(...TRUNCATED) | 467,207 | 7,495 | 168,911 | "<think>\nOkay, so I need to find the probability that when flipping a fair coin 10 times, the longe(...TRUNCATED) | \dfrac{139}{1024} | 8 | "<think>\nThis is a complex or challenging question, and it is difficult to provide a direct and cor(...TRUNCATED) |
5 | "A fair coin is flipped 10 times, and the number of consecutive heads that appear at any point durin(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem restatement:** \nA fair coin is flipped 10 times. We look at all sequences of consecutiv(...TRUNCATED) | 467,207 | 7,495 | 168,911 | "<think>\nOkay, so I need to find the probability that when flipping a fair coin 10 times, the longe(...TRUNCATED) | \dfrac{139}{1024} | 8 | "<think>\nThis is a complex or challenging question, and it is difficult to provide a direct and cor(...TRUNCATED) |
6 | "A fair coin is flipped 10 times, and the number of consecutive heads that appear at any point durin(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem restatement:** \nA fair coin is flipped 10 times. We look at all sequences of consecutiv(...TRUNCATED) | 467,207 | 7,495 | 168,911 | "<think>\nOkay, so I need to find the probability that when flipping a fair coin 10 times, the longe(...TRUNCATED) | \dfrac{139}{1024} | 8 | "<think>\nThis is a complex or challenging question, and it is difficult to provide a direct and cor(...TRUNCATED) |
7 | "A fair coin is flipped 10 times, and the number of consecutive heads that appear at any point durin(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem restatement:** \nA fair coin is flipped 10 times. We look at all sequences of consecutiv(...TRUNCATED) | 467,207 | 7,495 | 168,911 | "<think>\nOkay, so I need to find the probability that when flipping a fair coin 10 times, the longe(...TRUNCATED) | \dfrac{139}{1024} | 8 | "<think>\nThis is a complex or challenging question, and it is difficult to provide a direct and cor(...TRUNCATED) |
8 | "Find the number of positive integers less than 1000 that are not expressible as the sum of a perfec(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem:** \nFind the number of positive integers less than 1000 that **cannot** be expressed as(...TRUNCATED) | 418,349 | 5,370 | 168,912 | "<think>\nOkay, so I need to figure out how many positive integers less than 1000 cannot be written (...TRUNCATED) | 758 | 7 | "<think>\nThis is a complex or challenging question, and it is difficult to provide a direct and cor(...TRUNCATED) |
9 | "Find the number of positive integers less than 1000 that are not expressible as the sum of a perfec(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem:** \nFind the number of positive integers less than 1000 that **cannot** be expressed as(...TRUNCATED) | 418,349 | 5,370 | 168,912 | "<think>\nOkay, so I need to figure out how many positive integers less than 1000 cannot be written (...TRUNCATED) | 757 | 7 | "<think>\nThis is a complex or challenging question, and it is difficult to provide a direct and cor(...TRUNCATED) |
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open-thoughts-4-128-math-qwen3-235b-thinking-2507-annotated-32768-tokens
Math reasoning responses generated by Qwen3-235B-A22B-Thinking-2507 (Qwen/Qwen3-235B-A22B-Thinking-2507) via the Together AI serverless API.
Overview
- Total rows: 1,024
- Unique prompts: 128 (each with 8 response annotations)
- Source prompts: marin-community/open-thoughts-4-128-math-qwen3-32b-annotated-32768-tokens-n8-reformatted
- Generation model: Qwen/Qwen3-235B-A22B-Thinking-2507
- Max tokens: 32,768
- Temperature: 0.8
- Tokenizer used for stats: Qwen/Qwen3-235B-A22B-Thinking-2507
Statistics
| Metric | Value |
|---|---|
| Avg tokens per response | 24,292 |
| Median tokens per response | 26,740 |
Responses with <think> tag |
100.0% |
Complete responses (has </think> + \boxed{...}) |
626/1024 (61.1%) |
| Truncated responses | 398/1024 (38.9%) |
| Empty responses | 0 |
Columns
| Column | Description |
|---|---|
row_id |
Sequential identifier (0-1023) |
instruction_seed |
The math problem prompt |
qwen3_235b_thinking_generated_text |
Qwen3-235B-A22B-Thinking-2507 generated response (with <think>...</think> reasoning trace) |
ms_id |
Math seed ID -- groups all 8 responses for the same prompt |
_source |
Source dataset identifier |
gpt41_mini_response |
GPT-4.1 mini reference response |
length |
Response length |
Response Format
Each response in the qwen3_235b_thinking_generated_text column follows this format:
<think>
[model's reasoning trace]
</think>
[final answer, typically containing \boxed{...}]
Responses that are truncated (hit the 32,768 token limit) may be missing the closing </think> tag and/or the \boxed{...} answer.
Construction
Generated by sending each of the 128 math prompts to Qwen3-235B-A22B-Thinking-2507 8 times (n=8) via the Together AI serverless endpoint, with max_tokens=32768 and temperature=0.8. The model's reasoning trace (from the message.reasoning API field) is wrapped in <think>...</think> tags.
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