transfer-reasoning
Collection
29 items • Updated • 1
prompt stringlengths 169 1.24k | chosen stringlengths 5.13k 42.1k | rejected stringlengths 6.36k 56.5k | prompt_id stringlengths 64 64 | chosen_id stringlengths 77 77 | rejected_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 step by step.
First, let's recall that a four-digit number ranges from 1000 to 9999 inclusive. So, the thousand... | <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... | 0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43 | Qwen3-1.7B:0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43:6 | Qwen3-1.7B:0083f4d2a389c60674bff91f77a952059e6488ec730777e84f89602ae3b33a43:0 |
<|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 break this down step by step.
First, let's recall what a geometric sequence is. A geometric sequenc... | <think>
Okay, so I need to find the difference between the largest and smallest 3-digit geometric numbers. A geometric number has 3 distinct digits that form a geometric sequence when read from left to right. Let me break this down step by step.
First, let me recall what a geometric sequence is. In a geometric sequenc... | 00ac95ae0b335f87e7a84ba1f26781a39ca8a96a03ebc35d2ffefa76ce873ca7 | Qwen3-1.7B:00ac95ae0b335f87e7a84ba1f26781a39ca8a96a03ebc35d2ffefa76ce873ca7:2 | Qwen3-1.7B:00ac95ae0b335f87e7a84ba1f26781a39ca8a96a03ebc35d2ffefa76ce873ca7:6 |
<|im_start|>user
The expressions $A$ = $1 \times 2 + 3 \times 4 + 5 \times 6 + \cdots + 37 \times 38 + 39$ and $B$ = $1 + 2 \times 3 + 4 \times 5 + \cdots + 36 \times 37 + 38 \times 39$ are obtained by writing multiplication and addition operators in an alternating pattern between successive integers. Find the positiv... | <think>
Okay, so I need to find the positive difference between A and B, where A and B are these expressions that alternate between multiplication and addition. Let me try to understand the problem first.
First, let me parse the definitions of A and B.
For A: It's 1 × 2 + 3 × 4 + 5 × 6 + ... + 37 × 38 + 39. So starti... | <think>
Okay, let's try to figure out the positive difference between A and B. Both A and B are sums involving products of consecutive integers, but they're structured differently. Let me start by writing down what A and B are.
First, A is given as:
A = 1 × 2 + 3 × 4 + 5 × 6 + ... + 37 × 38 + 39
So, the pattern here... | 00b8579c76ca65d57bde0421653ab995cc7f3049455021c192dbc2fe9059252b | Qwen3-1.7B:00b8579c76ca65d57bde0421653ab995cc7f3049455021c192dbc2fe9059252b:7 | Qwen3-1.7B:00b8579c76ca65d57bde0421653ab995cc7f3049455021c192dbc2fe9059252b:3 |
<|im_start|>user
Let $z=a+bi$ be the complex number with $\vert z \vert = 5$ and $b > 0$ such that the distance between $(1+2i)z^3$ and $z^5$ is maximized, and let $z^4 = c+di$ . Find $c+d$ . 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 complex number z = a + bi with |z| = 5 and b > 0 such that the distance between (1 + 2i)z³ and z⁵ is maximized. Then, once I find z⁴ = c + di, I need to compute c + d. Alright, let's start breaking this down.
First, let me recall that for complex numbers, the modulus |z| = 5 means t... | <think>
Okay, so I need to find the complex number z = a + bi with |z| = 5 and b > 0 such that the distance between (1 + 2i)z³ and z⁵ is maximized. Then, once I find z⁴ = c + di, I need to find c + d. Alright, let me start breaking this down.
First, let me recall that for complex numbers, the modulus |z| is the distan... | 011d3c2d8f98c799bb23e2b4c6cab8c8a76ef136c78276bd32fde32152d822a8 | Qwen3-1.7B:011d3c2d8f98c799bb23e2b4c6cab8c8a76ef136c78276bd32fde32152d822a8:5 | Qwen3-1.7B:011d3c2d8f98c799bb23e2b4c6cab8c8a76ef136c78276bd32fde32152d822a8:6 |
"<|im_start|>user\nIn the Cartesian plane let $A = (1,0)$ and $B = \\left( 2, 2\\sqrt{3} \\right)$ .(...TRUNCATED) | "<think>\nOkay, so I need to find the coordinates of the center P of an equilateral triangle ABC whe(...TRUNCATED) | "<think>\nOkay, so I need to find the coordinates of the center P of an equilateral triangle ABC whe(...TRUNCATED) | 01392a38d0cb0a1ec79149121fc2ec7e3f1e4ce647665af0ceddd1de4b6dbf2a | Qwen3-1.7B:01392a38d0cb0a1ec79149121fc2ec7e3f1e4ce647665af0ceddd1de4b6dbf2a:6 | Qwen3-1.7B:01392a38d0cb0a1ec79149121fc2ec7e3f1e4ce647665af0ceddd1de4b6dbf2a:4 |
"<|im_start|>user\nIf the integer $k^{}_{}$ is added to each of the numbers $36^{}_{}$ , $300^{}_{}$(...TRUNCATED) | "<think>\nOkay, so I need to find the integer k such that when I add k to each of 36, 300, and 596, (...TRUNCATED) | "<think>\nOkay, so I need to find the integer k such that when you add k to each of 36, 300, and 596(...TRUNCATED) | 0146093f86c4a94ea00ac4239b962f0557071faf42d993008ecab88a21749177 | Qwen3-1.7B:0146093f86c4a94ea00ac4239b962f0557071faf42d993008ecab88a21749177:3 | Qwen3-1.7B:0146093f86c4a94ea00ac4239b962f0557071faf42d993008ecab88a21749177:2 |
"<|im_start|>user\nFind the sum of all positive integers $a=2^n3^m$ where $n$ and $m$ are non-negati(...TRUNCATED) | "<think>\nOkay, so I need to find the sum of all positive integers a = 2^n * 3^m where n and m are n(...TRUNCATED) | "<think>\nOkay, so I need to find the sum of all positive integers a = 2^n * 3^m where n and m are n(...TRUNCATED) | 019cb36ee47f82a65d5c297f217466524b70660a0dc31f7b8fc18b464c068d54 | Qwen3-1.7B:019cb36ee47f82a65d5c297f217466524b70660a0dc31f7b8fc18b464c068d54:1 | Qwen3-1.7B:019cb36ee47f82a65d5c297f217466524b70660a0dc31f7b8fc18b464c068d54:4 |
"<|im_start|>user\nLet $C$ be the graph of $xy = 1$ , and denote by $C^*$ the reflection of $C$ in t(...TRUNCATED) | "<think>\nOkay, so I need to find the equation of the reflection of the hyperbola $ xy = 1 $ over th(...TRUNCATED) | "<think>\nOkay, so I need to find the equation of the reflection of the hyperbola $ xy = 1 $ over th(...TRUNCATED) | 0225d56ac786106f6ada1a205b9d3856085c440267bacdba0a48745f2db680ea | Qwen3-1.7B:0225d56ac786106f6ada1a205b9d3856085c440267bacdba0a48745f2db680ea:4 | Qwen3-1.7B:0225d56ac786106f6ada1a205b9d3856085c440267bacdba0a48745f2db680ea:1 |
"<|im_start|>user\nThere are positive integers $x$ and $y$ that satisfy the system of equations \\[\(...TRUNCATED) | "<think>\nOkay, so I need to solve this system of logarithmic equations involving x and y. Let me st(...TRUNCATED) | "<think>\nOkay, so I need to solve this system of logarithmic equations involving x and y. The equat(...TRUNCATED) | 02b337a06c7cb8ff3a5b0c23aa467c19e800eac9aeaf693c6873bdb753585f42 | Qwen3-1.7B:02b337a06c7cb8ff3a5b0c23aa467c19e800eac9aeaf693c6873bdb753585f42:1 | Qwen3-1.7B:02b337a06c7cb8ff3a5b0c23aa467c19e800eac9aeaf693c6873bdb753585f42:2 |
"<|im_start|>user\nA fair die is rolled four times. The probability that each of the final three rol(...TRUNCATED) | "<think>\nOkay, so I need to find the probability that when rolling a fair die four times, each of t(...TRUNCATED) | "<think>\nOkay, so I need to find the probability that when rolling a fair die four times, each of t(...TRUNCATED) | 046433d2fb5556a6dc8cf6cf8756948ec448bcf2ddb301577a1e3977da68a6ee | Qwen3-1.7B:046433d2fb5556a6dc8cf6cf8756948ec448bcf2ddb301577a1e3977da68a6ee:7 | Qwen3-1.7B:046433d2fb5556a6dc8cf6cf8756948ec448bcf2ddb301577a1e3977da68a6ee:3 |
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dpo_sc
Historical AIME response data generated with Qwen3-1.7B for the UID comparison pipeline.
Train: 413 rows. Dev: 53 rows.
Both chosen and rejected responses are verifier-correct, complete, untruncated, and UID-eligible.
The response with the highest q_SC is chosen; the response with the lowest q_SC is rejected.
All four DPO variants use the same prompts. Each prompt must have at least two distinct responses and a score gap of at least 0.05 for all three scores (q_SC, q_UID, uid_product). Each qualifying prompt contributes one pair.
Columns: prompt, chosen, rejected, prompt_id, chosen_id, rejected_id.
The original local variant name is dpo_sc. manifest.json records the shared build settings and counts across all eight variants.
from datasets import load_dataset
data = load_dataset("talzoomanzoo/dpo_sc")
train = data["train"]
dev = data["dev"]
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