id stringlengths 5 36 | conversations listlengths 2 2 |
|---|---|
d60e2d1580a1f682364fee1ef6968383 | [
{
"content": "์๋์ ์ฆ์ํผ๋ ๋ฒ๊ฐ์ ๊ฐ๋ฉฐ ์ฃผ์ฌ์๋ฅผ ๊ตด๋ฆฌ๊ณ , ๊ตด๋ฆฐ ์ซ์๋ ์ง๊ธ๊น์ง ๊ตด๋ฆฐ ์ซ์๋ค์ ํฉ์ ํญ์ ๋ํด์ง๋๋ค. ๋จผ์ 4๋ก ๋๋์ด์ง๋ ํฉ์ ๋ง๋๋ ์ฌ๋์ด ์น๋ฆฌํฉ๋๋ค. ์๋๊ฐ ๋จผ์ ์์ํ๋ค๋ฉด, ๊ทธ๋
๊ฐ ์น๋ฆฌํ ํ๋ฅ ์ ์ผ๋ง์ผ๊น์? ์ฐจ๊ทผ์ฐจ๊ทผ ์๊ฐํด ๋ณด๊ณ , ์ต์ข
๋ต์ \\boxed{} ์์ ๋ฃ์ด ์ถ๋ ฅํด ์ฃผ์ธ์.",
"from": "human"
},
{
"content": "<think>\nHere's a thinking process to solve the problem:\n\n1. **Understand the Goal... |
5c6390265c069f64f6b9c9bdbb48a2c7 | [
{
"content": "$\\Gamma$๋ ์ค์ฌ์ด $O$์ธ ์์ด๊ณ , $P$๋ ์ ๋ฐ์ ์ ์ด๋ค. $PA$๊ฐ $\\Gamma$์ ์ ํ๋ ์ ๋ถ $A$๊ฐ ์๊ณ , $B$๋ $A$์ ๋์นญ์ธ ์ ์ด๋ค. $P$๋ฅผ ์ง๋๋ ์ $\\Delta$๊ฐ $\\Gamma$์ $C$์ $D$์์ ๋ง๋๋ค. $C$๋ฅผ ์ง๋๋ $PO$์ ํํํ ์ ์ด $AB$๋ฅผ $M$์์, $BD$๋ฅผ $E$์์ ๊ต์ฐจํ๋ค. $M$์ด $CE$์ ์ค์ ์์ ์ฆ๋ช
ํ์์ค. ์ฐจ๊ทผ์ฐจ๊ทผ ์๊ฐํ๊ณ , ์ต์ข
๋ต์ \\boxed{} ์์ ์ ์ํ์์ค.",
"from": "human"
},
{
"content"... |
9d2a7243d51f1260870b365729debc39 | [
{
"content": "๋ง์ฝ $\\varepsilon_k, k=1, 2, ..., 2013$์ด ๋ชจ๋ 2013๋ฒ์งธ ๋จ์๊ทผ์ด๋ผ๋ฉด, ๋ค์ ๊ณฑ์ ๊ณ์ฐํ์์ค: \\[ \\prod_{k=1}^{2013}(2-\\varepsilon_k^2). \\] ๋จ๊ณ๋ณ๋ก ์๊ฐํด ๋ณด๊ณ , ์ต์ข
๋ต์ \\boxed{ ์์ ์ ์ํ์์ค.",
"from": "human"
},
{
"content": "<think>\nHere's a thinking process to solve the problem:\n\n1. **Understand the Goal:** The ... |
aabeda49a325025d0e4d86d51c25d3b2 | [
{
"content": "$\\frac{1}{8} \\ldots \\frac{1}{9} \\ldots \\frac{1}{28}$๋ฅผ ํฌํจํ๋ ํํ์ ์ฐ์ ์ฐ์ฐ ๊ธฐํธ์ ๊ดํธ๋ฅผ ๋ฐฐ์ดํ์ฌ ๊ณ์ฐ ๊ฒฐ๊ณผ๊ฐ $\\frac{1}{2016}$๊ณผ ๊ฐ๊ฒ ๋ง๋์ธ์. ๋จ๊ณ๋ณ๋ก ์๊ฐํ๊ณ ์ต์ข
๋ต์ \\boxed{ ์์ ์ถ๋ ฅํ์ธ์.",
"from": "human"
},
{
"content": "<think>\nHere's a thinking process to solve the problem:\n\n1. **Understand the Goal:** The o... |
ef316dee16e03eb10e9962bc478a03bf | [
{
"content": "\\( p \\in \\mathbb{N}\\) ์ด๊ณ \\( f \\in \\mathbb{Z}[X]\\) ์ด๋ฉด์ \\( f(p) = 6 \\), \\( f(p+1) = 18 \\), ๊ทธ๋ฆฌ๊ณ \\( f(p+2) = 54\\) ์
๋๋ค. \\( f(x) = 2 \\) ๋ผ๋ ๋ฐฉ์ ์์ด \\( \\mathbb{Z} \\) ์์์ ๋ช ๊ฐ์ ํด๋ฅผ ๊ฐ์ง๊น์? ์ฐจ๊ทผ์ฐจ๊ทผ ์๊ฐํ๊ณ , ์ต์ข
๋ต์ \\boxed{ ์์ ๋ฃ์ด ์ถ๋ ฅํ์ธ์.",
"from": "human"
},
{
"content": "<think>\nHere's a th... |
421f9aa267588a535c7e8ff4c000d350 | [{"content":"ํจ์ \\( f: \\mathbb{N} \\setminus \\{0,1\\} \\to \\mathbb{R} \\)๋ฅผ ๋ค์๊ณผ ๊ฐ์ด(...TRUNCATED) |
c5f9e6630de19966bf4539c81559bd65 | [{"content":"10 ์ด์์ธ ๋ชจ๋ $n$ ๊ฐ์ ์ฐพ๋, $\\binom{n}{10} \\binom{n+1}{10}$์ด ์์ ์ (...TRUNCATED) |
aa2a24ef2d9d2f54722436ede2092450 | [{"content":"\\[ \\int \\frac{dx}{(x+a)^{m}(x+b)^{n}} \\] ์ ์ ๋ถ์ ๊ณ์ฐํ๊ณ , ์ฌ๊ธฐ์ $m, (...TRUNCATED) |
1e6529709f1c75ce6bdb02e31dd33e0a | [{"content":"$a_0=0$, $a_1=b$์ด๊ณ , ์ฌ๊ท ๊ด๊ณ์ $a_{n+1}=a_n\\sqrt{1+a_{n-1}^2}+a_{n-1}\\sqrt{(...TRUNCATED) |
82595070d45b1a9d9d886d165d0189b3 | [{"content":"๋ชจ๋ x, y์ ๋ํด ํจ์ \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\)๋ฅผ ์ฐพ์(...TRUNCATED) |
End of preview. Expand in Data Studio
Translating Jackrong/Qwen3.5-27B-Claude-4.6-Opus-Reasoning-Distilled's training dataset via TranslateGemma.
The dataset consists of high-quality, filtered reasoning distillation data:
| Dataset Name | Description / Purpose |
|---|---|
| nohurry/Opus-4.6-Reasoning-3000x-filtered | Provides comprehensive Claude 4.6 Opus reasoning trajectories. |
| Jackrong/Qwen3.5-reasoning-700x | Additional curated reasoning samples designed to strengthen structured step-by-step problem solving and improve reasoning diversity. |
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