transfer-reasoning
Collection
29 items • Updated • 1
prompt stringclasses 514
values | response stringlengths 4.39k 60.4k | weight float64 0.53 1.81 | prompt_id stringclasses 514
values | trace_id stringlengths 77 77 |
|---|---|---|---|---|
<|im_start|>user
An integer between $1000$ and $9999,$ inclusive, is called balanced if the sum of its two leftmost digits equals the sum of its two rightmost digits. How many balanced integers are there? Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| <think>
Okay, so I need to figure out how many four-digit numbers are "balanced." A balanced integer is one where the sum of the first two digits equals the sum of the last two digits. Let me break this down.
First, let me clarify the problem. A four-digit number ranges from 1000 to 9999, inclusive. So the thousands d... | 1.034692 | 0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43 | Qwen3-1.7B:0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43:0 |
<|im_start|>user
An integer between $1000$ and $9999,$ inclusive, is called balanced if the sum of its two leftmost digits equals the sum of its two rightmost digits. How many balanced integers are there? Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| <think>
Okay, so I need to figure out how many four-digit numbers are "balanced." A balanced integer is one where the sum of the first two digits equals the sum of the last two digits. Let me break this down step by step.
First, let's clarify the problem. A four-digit number ranges from 1000 to 9999, inclusive. So the... | 1.032395 | 0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43 | Qwen3-1.7B:0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43:1 |
<|im_start|>user
An integer between $1000$ and $9999,$ inclusive, is called balanced if the sum of its two leftmost digits equals the sum of its two rightmost digits. How many balanced integers are there? Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| <think>
Okay, so I need to figure out how many four-digit numbers are "balanced." A balanced integer is one where the sum of the first two digits equals the sum of the last two digits. Let me break this down step by step.
First, let's clarify the problem. A four-digit number ranges from 1000 to 9999, inclusive. So, th... | 0.7925 | 0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43 | Qwen3-1.7B:0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43:2 |
<|im_start|>user
An integer between $1000$ and $9999,$ inclusive, is called balanced if the sum of its two leftmost digits equals the sum of its two rightmost digits. How many balanced integers are there? Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| <think>
Okay, so I need to figure out how many four-digit numbers are "balanced." A balanced integer is one where the sum of the first two digits equals the sum of the last two digits. Let me break this down step by step.
First, let's clarify the problem. A four-digit number ranges from 1000 to 9999, inclusive. So the... | 1.025535 | 0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43 | Qwen3-1.7B:0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43:3 |
<|im_start|>user
An integer between $1000$ and $9999,$ inclusive, is called balanced if the sum of its two leftmost digits equals the sum of its two rightmost digits. How many balanced integers are there? Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| <think>
Okay, so I need to figure out how many four-digit numbers are "balanced." A balanced integer is one where the sum of the first two digits equals the sum of the last two digits. Let me break this down.
First, let's clarify the structure of a four-digit number. A four-digit number can be represented as ABCD, whe... | 1.244269 | 0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43 | Qwen3-1.7B:0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43:4 |
<|im_start|>user
An integer between $1000$ and $9999,$ inclusive, is called balanced if the sum of its two leftmost digits equals the sum of its two rightmost digits. How many balanced integers are there? Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| <think>
Okay, so I need to figure out how many four-digit numbers are "balanced." A balanced integer is one where the sum of the first two digits equals the sum of the last two digits. Let me break this down.
First, let's clarify the problem. A four-digit number ranges from 1000 to 9999, inclusive. So the first digit ... | 1.039301 | 0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43 | Qwen3-1.7B:0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43:5 |
<|im_start|>user
An integer between $1000$ and $9999,$ inclusive, is called balanced if the sum of its two leftmost digits equals the sum of its two rightmost digits. How many balanced integers are there? Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| <think>
Okay, so I need to figure out how many four-digit numbers are "balanced." A balanced integer is one where the sum of the first two digits equals the sum of the last two digits. Let me break this down step by step.
First, let's recall that a four-digit number ranges from 1000 to 9999 inclusive. So, the thousand... | 0.917689 | 0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43 | Qwen3-1.7B:0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43:6 |
<|im_start|>user
An integer between $1000$ and $9999,$ inclusive, is called balanced if the sum of its two leftmost digits equals the sum of its two rightmost digits. How many balanced integers are there? Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant
| <think>
Okay, so I need to figure out how many four-digit numbers are "balanced." A balanced integer is one where the sum of the two leftmost digits equals the sum of the two rightmost digits. Let me break this down.
First, let's clarify the structure of a four-digit number. A four-digit number can be represented as A... | 0.91362 | 0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43 | Qwen3-1.7B:0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43:7 |
<|im_start|>user
Call a $3$ -digit number geometric if it has $3$ distinct digits which, when read from left to right, form a geometric sequence. Find the difference between the largest and smallest geometric numbers. Let's think step by step and output the final answer within \boxed{}.<|im_end|>
<|im_start|>assistant... | <think>
Okay, so I need to find the difference between the largest and smallest 3-digit geometric numbers. A geometric number has three distinct digits that form a geometric sequence when read from left to right. Let me try to break this down step by step.
First, let me recall what a geometric sequence is. A geometric... | 0.829886 | 00ac95ae0b335f87e7a84ba1f26781a39ca8a96a03ebc35d2ffefa76ce873ca7 | Qwen3-1.7B:00ac95ae0b335f87e7a84ba1f26781a39ca8a96a03ebc35d2ffefa76ce873ca7:0 |
"<|im_start|>user\nCall a $3$ -digit number geometric if it has $3$ distinct digits which, when read(...TRUNCATED) | "<think>\nOkay, so I need to find the difference between the largest and smallest 3-digit geometric (...TRUNCATED) | 0.978218 | 00ac95ae0b335f87e7a84ba1f26781a39ca8a96a03ebc35d2ffefa76ce873ca7 | Qwen3-1.7B:00ac95ae0b335f87e7a84ba1f26781a39ca8a96a03ebc35d2ffefa76ce873ca7:1 |
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sft_uid_mix
Historical AIME response data generated with Qwen3-1.7B for the UID comparison pipeline.
Train: 2967 rows. Dev: 355 rows.
Responses are verifier-correct, complete, untruncated, and UID-eligible. Duplicate response strings are removed within each prompt. All four SFT variants contain the same responses, with different weights.
Weights use q_UID: weight_i = n * exp(alpha * score_i) / sum_j exp(alpha * score_j), with alpha=2.0. Weights have mean 1 within each prompt. Training must use the weight column to apply the intended weighted SFT objective.
Columns: prompt, response, weight, prompt_id, trace_id.
The original local variant name is sft_uid_mix. manifest.json records the shared build settings and counts across all eight variants.
from datasets import load_dataset
data = load_dataset("talzoomanzoo/sft_uid_mix")
train = data["train"]
dev = data["dev"]
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