Dataset Viewer
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[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
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{
"content": "下列關於「學術自由」之敘述，何者錯誤？ \n(A)憲法上之講學自由規定為對於學術自由之制度性保障 \n(B)為保障學術自由應承認大學自治之制度 \n(C)大學自治制度包含學習自由之保障 \n(D)大學欠缺法律之授權而制定學則限制學生之學習自由，違反法律保留原則",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "12. (10 分) 當 $N$ 取所有的數字 $1,2,3, \\cdots, 2015$ 時，形如 $3^{n}+n^{3}$ 的數字有多少個能被 7 整除？",
"role": "user"
}
]
| $288.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "5. 依據航空產品與其各項裝備及零組件適航檢定管理規則，航空器分類為(A)通用類、特技類、特種作業類、\n通勤類及運輸類(B)渦輪類、渦輪螺旋槳類、螺旋槳類、直昇機類(C)重型航空器、中型航空器、輕型航空器\n(D)短路航空器、中程航空器、長程航空器。",
"role": "user"
}
]
| $A$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "37 熱聚性丙烯酸樹脂於全口義齒濕式煮聚（processing）時之方式，下列何者最正確？\n(A)一階段法：74℃ 3 小時；二階段法：74℃ 20 分鐘，而後 100℃ 20 分鐘\n(B)一階段法：74℃ 3 小時；二階段法：74℃ 60-90 分鐘，而後 100℃ 30-60 分鐘\n(C)一階段法：74℃ 8 小時；二階段法：74℃ 20 分鐘，而後 100℃ 20 分鐘\n(D)一階段法：74℃ 8 小時；二階段法：74℃ 60-90 分鐘，而後 100℃ 30-60 分鐘",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "11 那一項聽覺誘發電位檢查最常使用於診斷聽神經瘤？\n(A)耳蝸電位圖（electrocochleography） (B)聽性腦幹反應（ABR）\n(C)聽性穩定狀態反應（ASSR） (D)前庭誘發肌性電位（VEMP）",
"role": "user"
}
]
| $B$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "4. (3 分) 在三角形 $A B C$ 的邊 $B C$ 上作為直徑，構造一個半徑為 20 公分的圓。這個圓分別在邊 $A B$ 和 $A C$ 上與點 $X$ 和 $Y$ 相交。求 $B X \\cdot A B + C Y \\cdot A C$ 的值。",
"role": "user"
}
]
| $1600.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "一位技術專家正在設計一個互動式教育工具，專注於模擬森林砍伐對當地生態系統隨時間的影響。模擬將森林建模為一個 \\( n \\times n \\) 的網格，每個單元格可以包含一棵樹或是空的。任何單元格中樹的概率隨著時間的推移因森林砍伐而減少，這一過程由指數衰減函數 \\( P(t) = P_0 e^{-\\lambda t} \\) 模型化，其中 \\( P_0 \\) 是單元格中樹的初始概率，\\( \\lambda \\) 是森林砍伐的常數速率，\\( t \\) 是以年為單位的時間。\n\n1. 給定初始概率 \\( P_0 = 0.8 \\)，砍伐速率 \\( \\lambda = 0.05 \\)，以及網格大小為 \\( 10 \\times 10 \\)，計算在 20 年後網格上剩餘的樹的預期數量。\n\n2. 專家希望添加一個功能，允許用戶以固定速率「重新種植」樹木，這一過程由線性函數 \\( R(t) = kt \\) 模型化，其中 \\( k \\) 是每年重新種植的速率。如果目標是在 20 年後保持至少 50% 的網格覆蓋樹木，確定實現此目標所需的最低速率 \\( k \\)。",
"role": "user"
}
]
| $29.43$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "6. Miller和Modigliani的股利不相關理論必須依靠下列那一個投資決策和股利決策的關係？ (A)投資方案的價值取決於股利發放的情況 (B)只要制定了股利政策，則投資決策便可以依照希望而訂 (C)投資政策會比股利決策優先制定完成，而且不因股利政策而有所變動 (D)既然股利政策不具相關性，因此投資政策和股利政策之間也沒有任何關係",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "Define poverty.\nOptions:\nA: Poverty is the lack of resources to secure basic life necessities.\nB: Poverty is the condition where a person has excessive wealth and resources.\nC: Poverty is the inability to afford a good standard of living.\nD: Poverty is the condition of having too little money to fulfill basic needs as society currently defines those needs.\nE: Poverty is the inability to purchase luxury items and services.\nF: Poverty is the state of living in a rural area without urban amenities.\nG: Poverty is the temporary lack of employment.\nH: Poverty is the state of being inferior in quality or insufficient in amount.\nI: Poverty is the condition of having an income that is less than the median income of a country.\nJ: Poverty is exclusively the state of not having access to education.",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "50. 使用安全索，以手拉信號通訊，連拉七下表示(A)放鬆(B)收緊(C)上升(D)搜索信號。",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "有一組票號從 1 到 30（號碼可能重複）。每位學生抽了一張票。老師可以執行以下操作：讀取一個包含幾個（可能只有一個）號碼的列表，並要求持有這些號碼的學生舉手。老師需要執行這個操作多少次才能找出每位學生的票號？（不一定有 30 位學生。）",
"role": "user"
}
]
| $5.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "下列何者不屬於民事訴訟程序第二審上訴之合法要件？\n(A)上訴遵守法定不變期間 \n(B)上訴繳納裁判費 \n(C)提出上訴理由書\n(D)上訴利益",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "任務 3. (15 分) 在研究所，一名科學員工伊凡·伊萬諾維奇收到了一個包含約 300 個油樣的物體（設計用於 300 個樣本的容器，幾乎完全填滿）。每個樣本在硫含量方面有特定的特徵 - 要麼是低硫，要麼是高硫，並且在密度方面 - 要麼是輕的，要麼是重的。隨機選取一個樣本為重油樣本的相對頻率（統計概率）是 $\\frac{1}{8}$。隨機選取一個樣本為輕的低硫油樣本的相對頻率是 $\\frac{22}{37}$。如果重油樣本中沒有低硫樣本，這個物體包含多少個高硫油樣本？",
"role": "user"
}
]
| $120.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "2.依土地登記規則規定，土地所有權第一次登記之申請書及附件，應保存多久？\n(A)1年(B) 3 年 (C) 15 年 (D)永久保存",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "8. 我們考慮所有可能的集合，這些集合由 2017 個不同的自然數組成，其中在每個集合中，沒有任何數字可以表示為集合中兩個其他數字的和。這樣的集合中最大數字的最小值是多少？\n\n答案：4032。",
"role": "user"
}
]
| $4032.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "7. 病人的理學檢查，發現叩診時左胸呈現鈍音（dullness），聽診時左胸的呼吸音減弱，則\n 下列那一項診斷最有可能? (A) 左肺動脈栓塞 (B) 左側肋膜積液 (C) 左側自發性氣胸 (D) 左肺肺炎",
"role": "user"
}
]
| $B$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "13 下列關於類比轉數位訊號處理過程，位元數（number of bits）的敘述何者正確？\n(A)位元數愈高產生的量化噪音（quantization noise）愈大\n(B)位元數愈高產生的量化噪音愈低\n(C)相同位元數，輸入的訊號音量愈高，量化噪音愈大\n(D)相同位元數，輸入的訊號音量愈低，量化噪音愈小",
"role": "user"
}
]
| $B$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "137. 遺體化妝以刀片修飾眉毛時，刀片的拿法，其傾斜度以何者最為適當？ (A)15°(B)30°(C)45°(D)60°。",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "28. 如圖所示，刀尖位於機械原點上，若執行程式 G92 X250.0 Y200.0 Z150.0；G91 G43 Z5.0 H01；之後，刀尖距離工\n件表面高度為 5 ㎜，則 H01 應為 (A)-150.00(B)150.00(C)5.00(D)-5.00。",
"role": "user"
}
]
| $A$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "問題 11.6。在立方體 $A B C D A_{1} B_{1} C_{1} D_{1}$ 內部，有一個半徑為 10 的球的中心 $O$。該球在面 $A A_{1} D_{1} D$ 上與半徑為 1 的圓相交，在面 $A_{1} B_{1} C_{1} D_{1}$ 上與半徑為 1 的圓相交，在面 $C D D_{1} C_{1}$ 上與半徑為 3 的圓相交。求線段 $O D_{1}$ 的長度。",
"role": "user"
}
]
| $17.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "2. 利用楔型夾片與抗張材之咬合作用使抗張材與錨頭連接之裝置稱為(A)承壓鈑(B)鎖定器(C)錨頭(D)封\n漿器。",
"role": "user"
}
]
| $B$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "【題組】46.倘借款屆期，A 公司未清償借款本息，經 B 銀行發函請求 A 公司履行，A 公司隨即向 B 銀行請求延期清償，並獲 B 銀行\n允許。下列何者錯誤？\n(A) B 銀行向 A 公司請求履行，及為其他中斷時效之行為，對於連帶保證人乙不生效力\n(B)乙除對於其延期已為同意外，不負保證責任\n(C)乙得以 A 公司對於 B 銀行之債權，主張抵銷\n(D)保證債務，除契約另有訂定外，包含主債務之利息、違約金、損害賠償及其他從屬於主債務之負擔",
"role": "user"
}
]
| $A$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "36.下列有關符合文件、安全管理證書、臨時符合文件及臨時安全管理證書所使用之語文之\n敘述，何者最妥當？\n(A)只用船籍國語文即可\n(B)只用英文或法文之一即可\n(C)只用英文、法文或西班牙文之一即可\n(D)如船籍國語文非英文或法文之一，除船籍國語文之外，應有英文或法文之一譯本",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "64.甲簽發面額新臺幣壹仟萬元之本票交付乙，發票日為 103 年 2 月 1 日，到期日為 103 年 2 月 1 日，A 為擔當付款人。乙\n背書交付丙，丙背書交付丁。丁於 103 年 2 月 3 日向發票人甲請求支付票款遭拒，丁遂於 103 年 2 月 5 日向擔當付款人 A 提\n示請求付款亦遭拒，於翌日作成拒絕付款證書對甲、乙兩人追索。甲、乙對丁得否抗辯？\n(A)甲對丁無抗辯事由，乙對丁有抗辯事由 (B)甲、乙對丁均有限定之抗辯事由\n(C)甲對丁有限定抗辯事由，乙對丁無抗辯事由 (D)甲、乙對丁均無抗辯事由",
"role": "user"
}
]
| $A$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "28.申請特定寵物業許可證並獲核准後，若發生停業、歇業情事\n時，應向哪個機關辦理註銷或備查?(A)農委會(B)防檢處(C)新北市經發局(D)新北市動保處。",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "20\t有關Phenylethylamine類交感神經作用藥物之敘述，下列何者正確？\n(A)\t三級或四級胺（Tertiary or quaternary amine）呈現較強之直接促進作用\n(B)\t胺基（Amino）上之取代基增大，對α受體之促進作用增強\n(C)\tN-tert-Butyl group可增加α作用之選擇性\n(D)\t胺基上有較大的取代基可防止其受MAO之作用",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "讓 \\( O \\) 是正三角錐 \\( P-ABC \\) 的底面 \\( \\triangle ABC \\) 的中心。一個通過 \\( O \\) 的移動平面與三條側邊或其延長線相交於點 \\( Q, R, S \\)。確定表達式 \\(\\frac{1}{PQ}+\\frac{1}{PR}+\\frac{1}{PS}\\) 的性質。\n\n(A) 有最大值但沒有最小值\n\n(B) 有最小值但沒有最大值\n\n(C) 同時有最大值和最小值，且最大值不等於最小值\n\n(D) 是一個與平面 \\( QRS \\) 無關的常數",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "49. 內層線路與孔銅連接的可靠度如：多層印刷電路板內層銅與通孔鍍\n層的連結、增層電路板盲孔底部線路的連結等。若其可靠度不良時\n很難判定，若已在使用中則問題更將複雜化。可靠度的項目必須個\n別檢討才能掌控問題之所在。下列何者為相關影響品質可靠度的項目？\n(A)內層銅在化學銅的前處理；(B)化學銅的物性；(C)電鍍銅的物\n性；(D)以上皆對",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "20.刑法第 15 條第 1 項規定：「對於犯罪結果之發生，法律上有防止之義務，能防止而不防止者，與因積極行為發生結果者同。」此項所謂之「對於犯罪結果之發生，法律上有防止之義務」，學說上如何稱呼？\n \n(A)客觀注意義務\n \n(B)主觀注意義務\n \n(C)客觀歸責\n \n(D)保證人地位",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "3 在心理治療中，若案主診斷資料不足的時候，諮商師下列那一個動作較適宜？\n(A)諮商師可以根據案主當下描述的問題，提出他個人的看法\n(B)諮商師可以根據過去相關的治療經驗，試著與案主溝通\n(C)諮商師可以要求案主對目前的困境，提出一個暫時性的假設\n(D)諮商師可以依據目前的狀況給予一個暫時性的假設，一方面與案主討論，另方面繼續蒐集資料",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "尋找當數字 $10^{10}+10^{10^{2}}+10^{10^{3}}+\\ldots+10^{10^{10}}$ 被 7 除時的餘數。",
"role": "user"
}
]
| $5.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "Knop K.A.\n\n智者會議的重新認證過程如下：國王將他們排成一列，並給每個人戴上一頂帽子，顏色為白色、藍色或紅色。所有智者都能看到他們面前所有智者帽子的顏色，但他們無法看到自己帽子的顏色或在他們身後智者的帽子顏色。每分鐘，智者中的一位必須喊出三種顏色中的一種（每位智者僅喊出一次顏色）。\n\n在這個過程完成後，國王將處決每位喊出顏色與其帽子顏色不同的智者。\n\n在重新認證的前夕，所有一百名智者達成一致，制定了一個計劃以最小化處決人數。那麼，保證有多少人能避免處決？",
"role": "user"
}
]
| $99.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "範例 5 給定實數 $x, y$ 滿足 $x+y=3, \\frac{1}{x+y^{2}}+\\frac{1}{x^{2}+y}=\\frac{1}{2}$。 \n找出 $x^{5}+y^{5}$ 的值。[3] \n(2017，國中數學聯賽)",
"role": "user"
}
]
| $123.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "7. 四個人去書店買書。每個人買了 4 本不同的書，並且每兩個人恰好有 2 本書是共同的。因此，這 4 個人至少買了 $\\qquad$ 種書。",
"role": "user"
}
]
| $7.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "64. 起重機在額定荷重下使其上升、直行、迴轉或橫行時，各該最高速率稱為(A)運行速率(B)容許下降速率(C)吊升速率(D)額定速率。",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "證券投資信託基金保管機構辦理基金資產交割作業，如有交易內容不符法令規定時，保管機構應如何辦理？\n(A)依交割指示照常辦理交割 (B)先依交割指示辦理交割，並儘速通知投信公司補正\n(C)通知交易對象補正 (D)拒絕依交割指示辦理交割，並儘速通知投信公司補正",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "18 有關男性化不完全之敘述，下列何者錯誤？\n (A)可能是因為胎兒睪丸製造的睪固酮（testosterone）不足 (B)生殖始基（genital anlagen）對於數量正常的雄性素反應減少是原因之一 (C)細胞核型為 46, XX (D)雄性素反應性組織內無法合成 5α 雙羥基睪固酮（5α-dihydrotestosterone）為原因之一",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "73 身心障礙者的擴大溝通系統與替代性溝通（AAC）動作方式表達之發展層次，學者（Rowland 與\nStremel-Campbell）認為該動作表達的溝通行為發展有其次序，請問「動作是反射性的，或非自主性\n的對刺激物做出反應」，應屬於下列何期？ \n(A)前意圖期（preintentional） (B)意圖期（intentional behaviors） \n(C)前符號期（presymbolic behaviors） (D)符號期（symbolic behaviors）",
"role": "user"
}
]
| $A$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "55.民事訴訟程序中，抗告法院認為當事人之抗告為有理由者，應如何裁定？\n(A)應發交或變更原裁定 (B)應移送或變更原裁定 (C)應廢棄或變更原裁定 (D)應撤銷或變更原裁定",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "Petya 找到了某個偶數自然數 \\( n \\) 的所有奇數因數的總和，而 Vasya 找到了所有偶數因數的總和。他們的結果的乘積能否等於 2016？如果可以，找出所有這樣的數字 \\( n \\)。",
"role": "user"
}
]
| $88.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "在加法和減法的例子中，學生根據以下規則將數字替換為字母：相同的字母被相同的數字替換，不同的字母被不同的數字替換。從多少個不同的例子中可以得到記錄 $0<\\overline{\\overline{Б A}}+\\overline{\\text { БА }}-\\overline{\\text { ЯГА }}<10$？",
"role": "user"
}
]
| $31.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "在一個小屋裡，有幾位島上的居民聚集在一起，其中一些屬於 Ah 部落，另一些屬於 Uh 部落。Ah 部落的居民總是說實話，而 Uh 部落的居民總是說謊。一位居民說：“我們在小屋裡的人數不超過 16 個。”然後補充道：“我們都是 Uh 部落的人。”另一位居民說：“我們在小屋裡的人數不超過 17 個。”然後指出：“我們中有一些來自 Ah 部落。”第三位居民說：“我們在小屋裡有五個人。”並環顧四周，觀察到：“我們中至少有三位居民來自 Uh 部落。”小屋裡有多少位居民屬於 Ah 部落？",
"role": "user"
}
]
| $15.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "15.下列敘述何者正確？ A.再生資源未依規定回收再利用者，視為廢棄物，應依廢棄物清理法規定回收、\n清除、處理 B.依廢棄物清理法公告之應回收廢棄物，且屬資源回收再利用法公告之再生資源者，其回\n收、貯存及回收清除處理費用之收支、保管及運用，依廢棄物清理法之規定\n(A)僅 A \n(B)僅 B \n(C)AB 均正確 \n (D)AB 均錯誤",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "100. 弦跳傳播(chordal hop propagation)的主要特徵是什麼？\n(A) 遠離電臺之間的大圓方位傳播\n(B) 沒有來自地面的中間反射的連續電離層反射\n(C) 橫過地磁赤道的傳播\n(D) 信號反射回發射臺",
"role": "user"
}
]
| $B$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "29. 下列有關汽缸壓縮壓力錶使用之敘述，何者錯誤？ (A)發動引擎使達到正常工作溫度(B)將每一缸之火星塞拆下並\n裝上壓力錶(C)將點火線圈（＋）端接線搭鐵(D)搖轉引擎直至壓力錶指針不再升高為止。",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "(3) $f(x)$ 是定義在 $(0,1)$ 的一個函數，對於任何 $1<x<y<+\\infty$，都有 $f\\left(\\frac{1}{x}\\right)-f\\left(\\frac{1}{y}\\right)=f\\left(\\frac{x-y}{1-x y}\\right)$。設 $a_{n}=f\\left(\\frac{1}{n^{2}+5 n+5}\\right)\\left(n \\in \\mathbf{N}^{*}\\right)$，則 $a_{1}+a_{2}+\\cdots+a_{8}=(\\quad)$。\n(A) $f\\left(\\frac{1}{2}\\right)$\n(B) $f\\left(\\frac{1}{3}\\right)$\n(C) $f\\left(\\frac{1}{4}\\right)$\n(D) $f\\left(\\frac{1}{5}\\right)$",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "71. 55 歲病人因右側下肺葉巨大惡性腫瘤來進行開胸術 ( open thoracotomy ) ，術前咳嗽且痰多，\n 麻醉採 double lumen ETT 插管全身麻醉，手術採左側躺。麻醉誘導過程有設置左手 A - line\n 與右側鎖骨下 CVC。手術進入胸腔後十分鐘，發現血氧降低、呼吸器顯示氣道壓力過大、\n 通氣量不足 ( tidal volume = 50 mL ) 。下列鑑別診斷何者最不可能？\n (A) 手術器械操作或腫瘤壓迫病患氣管造成呼吸道堵塞\n (B) CVC 打針刺傷右側肺部，進而逐漸造成張力性氣胸\n (C) double lumen 氣管內管置放位置不正確或不慎移位\n (D) 呼吸器管路彎折 ( kinking ) 或有痰塊塞住呼吸管路",
"role": "user"
}
]
| $B$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "50下列敘述何者為正確？ (A)機關採最有利標之決標，決定最有利標後，應再洽該廠商辦理議價。 (B)機關辦理統包工程採購，可依採購法第22條第1項第9款之規定評選優勝廠商。 (C)評定最有利標涉及評分，評選項目子項有配分者，其配分應載明於招標文件。個別子項不合格即不得作為最有利標者，亦應於招標文件載明其情形。 (D)採最有利標決標原則得通案報上級機關核准。",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "定義一個運算 $H\\left(x_{1}, x_{2}, \\cdots x_{n} \\mid y_{1}, y_{2}, \\cdots y_{n}\\right)=\\frac{x_{1}+x_{2}+\\cdots+x_{n}}{y_{1}+y_{2}+\\cdots+y_{n}}\\left(y_{1}+y_{2}+\\cdots+y_{n} \\neq 0\\right)$, 下列說法正確的有（）個\n\n(1) $H(1,2 \\mid 3)=1$;\n\n(2) 若 $H\\left(4 \\mid x^{2},-4\\right)-H(1 \\mid x,-2)=-1$, 則 $x=-1$ 或 2 ;\n\n(3) $H(1 \\mid 1,2)+H\\left(1 \\mid 2^{2}, 4\\right)+H\\left(1 \\mid 3^{2}, 6\\right)+\\cdots+H\\left(1 \\mid 10^{2}, 20\\right)=\\frac{175}{264}$;\n\n(4) 若 $H(a \\mid b, c, d)=H(b \\mid a, c, d)=H(c \\mid a, b, d)=H(d \\mid a, b, c)$, 則 $\\frac{c+d}{a+b}=1$.\n\nA. 1\nB. 2\nC. 3\nD. 4\n\n",
"role": "user"
}
]
| $B$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "一個正六邊形被分成6個全等的等邊三角形區域，分別標記為 \\(A, B, C, D, E, F\\)。每個區域將種植觀賞植物，條件是同一區域使用相同的植物，而相鄰區域使用不同的植物。考慮到有4種不同類型的植物可用，可能的種植方案有多少種？",
"role": "user"
}
]
| $732.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "17.甲簽發金額新臺幣10萬元之記名本票於乙，乙於票據背書並附記：「6萬元轉讓書商丙，4萬元轉讓水果商丁。」\n則下列敘述何者正確？ \n(A)乙之背書無效 (B)丙得請求甲給付新臺幣6萬元 \n(C)本票無效 (D)乙負擔保付款責任",
"role": "user"
}
]
| $A$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "$5$ 家航空公司在一個由 $36$ 個城市組成的國家運營。在任何一對城市之間，恰好有一家公司運營雙向航班。如果某家航空公司在城市 $A, B$ 和 $B, C$ 之間運營，我們稱三元組 $A, B, C$ 為 [i]適當連接[/i]。確定最大的可能值 $k$，使得無論這些航班如何安排，至少有 $k$ 個適當連接的三元組。",
"role": "user"
}
]
| $3780.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "29.\t\t測總溶解固體及總懸浮固體時，水樣之貯存(A)應貯存在室內(B)應貯存室內暗處(C)應在 4℃保存玻璃櫃內(D) 應在 4℃暗處。",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "12、 以 SWIFT MT700 開發信用狀時，倘 71B 欄位留空未填，則有關之費用其負擔為何？ \n (A) 所有費用由受益人負擔 (B) 所有費用由申請人負擔 (C) 除讓購及轉讓費用外，其他費用由申請人負擔 (D) 除開狀費用外，其他費用由受益人負擔",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "讓序列 $\\{a_{n}\\}$ 和 $\\{b_{n}\\}$ 的項數為 $m$。序列 $\\{a_{n}\\}$ 和 $\\{b_{n}\\}$ 之間的距離定義為 $\\sum_{i=1}^{m}|a_{i}-b_{i}|$。 \n$(Ⅰ)$ 計算序列 $1$, $4$, $6$, $7$ 和 $3$, $4$, $11$, $8$ 之間的距離。 \n$(Ⅱ)$ 設 $A$ 為滿足遞迴關係 $a_{n+1}=\\frac{1+a_{n}}{1-a_{n}}$ 的所有序列 $\\{a_{n}\\}$ 的集合。設 $\\{b_{n}\\}$ 和 $\\{c_{n}\\}$ 為 $A$ 中的兩個元素，均有 $m$ 項。如果 $b_{1}=2$, $c_{1}=3$，且 $\\{b_{n}\\}$ 和 $\\{c_{n}\\}$ 之間的距離小於 $2016$，求 $m$ 的最大值。 \n$(Ⅲ)$ 設 $S$ 為所有 $7$ 項序列 $\\{a_{n}|1\\leqslant n\\leqslant 7, a_{n}=0$ 或 $1\\}$ 的集合。設 $T\\subseteq S$，使得 $T$ 中任兩個元素之間的距離大於或等於 $3$。證明 $T$ 中的元素數量小於或等於 $16$。",
"role": "user"
}
]
| $8.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "一所學校安排5個班級參觀4個工廠進行社會實踐，每個班級參觀一個工廠。每個工廠必須至少接待一個班級。不同安排的總數是______。（用數字回答）",
"role": "user"
}
]
| $240.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "可以選擇的不同自然數的最大數量是多少，以使得它們中任何三個的和都是質數？",
"role": "user"
}
]
| $4.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "某個四位數是完全平方數。如果將最左邊的數字去掉，它變成完全立方數；如果去掉前兩個數字，它變成某個整數的四次方。找出這個數字。",
"role": "user"
}
]
| $9216.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "4. 在進行職務規劃時，下列何種情境宜優先考量是否有職務區隔\n（Segregation Of Duties, SOD）之設計？\n(A)執行資安內部稽核時，業務人員負責查核資訊單位的資安事故通報\n作業流程\n(B) 程式設計人員於程式上架更新時，應在負責更新系統程式的資訊部\n門待命\n(C) 採購人員於向廠商下單訂購前，應在庫存系統確認庫存數量\n(D)人力資源部門主管，負責人資資訊系統之更新與維護",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "17 一土層之地下水位在地表，飽和單位重 20 kN/m ，地下 2 m 深，過壓密比為 16。何者可能是 2 m 深處的\n 水平有效應力？ (A)5 kN/m2 (B)10 kN/m2 (C)20 kN/m2 (D)40 kN/m2",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "12 在下列何種審計服務，會計師所提供的確信程度，為高度，但非絕對：\n(A)財務報表之核閱 (B)財務資訊之代編 (C)專案審查 (D)管理顧問",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "76 VEMP 測試時，刺激形式、直接刺激的標靶器官與傳入的神經為何？\n (A) 聲音，耳蝸（cochlea），耳蝸神經 (B)聲音，球囊（saccule），下前庭神經 (C)動能，橢圓囊（utricle），上前庭神經 (D)溫差，水平半規管（HSCC），上前庭神經",
"role": "user"
}
]
| $B$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "甲有土地一筆，設定地上權於乙，存續期間為 20 年，乙在該地上建築倉庫 10 棟使用。存續期間屆\n滿時，上開倉庫之市價為新臺幣 1000 萬元，甲乃向乙表示願以該時價購買倉庫，以為補償。下列敘\n述，何者正確？\n(A)甲縱不欲延長地上權之期間，亦無請求購買倉庫之權\n(B)甲、乙間之倉庫買賣契約，於甲向乙表示願以時價購買時，即已成立\n(C)甲提出時價補償，乙無正當理由拒絕時，甲得訴請乙訂立倉庫買賣契約\n(D)甲、乙間之地上權設定契約須有甲得購買建築物之約定，甲始得請求購買倉庫",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "4 依司法院大法官解釋，人身自由限制程序是否符合憲法正當法律程序，應考量的因素不包括下列何者？\n(A)國家財政負擔 (B)有無替代程序 (C)案件涉及之事物領域 (D)所涉及基本權之種類",
"role": "user"
}
]
| $A$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "6.依司法院大法官釋字第 499 號解釋之意旨，憲法之修改若變更憲法中具有本質重要性規定，其效力如何？ \n(A)仍有效力 (B)失其效力 (C)由人民公決之 (D)由修憲機關檢討改進",
"role": "user"
}
]
| $B$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "7 海巡人員發現有娛樂船舶超載旅客且有即將翻覆之危險，不聽勸告，強行要出海，應優先如何處置？\n (A)請航政主管機關派員，儘速阻止其出港 (B)逕行實施強制性處分，阻止該船舶出港 (C)蒐集相關事證，函請航政主管機關裁罰 (D)速派巡防艇在旁實施戒護，並持續勸告 （請接背面） 101年 公 務 人 員 特 種 考 試 警 察 人 員 考 試 、 全一張 101年公務人員特種考試一般警察人員考試及 代號：51330 （背面） 101年 特 種 考 試 交 通 事 業 鐵 路 人 員 考 試 試 題 等 別： 三等警察人員考試 類 科： 水上警察人員 科 目： 水上警察情境實務（包括海巡法規、實務操作標準作業程序、人 權保障與正當法律程序）",
"role": "user"
}
]
| $B$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "61. 當強制排氣式瓦斯熱水器排氣管頂罩受到 15m/s 風速，廢氣未能順利排出時，可利用下列何種裝置來關閉燃氣\n通路？ (A)熄火安全裝置(B)防止超壓安全裝置(C)防止不完全燃燒安全裝置(D)防止過大風壓安全裝置。",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "45 被告一行為觸犯數罪名，成立同種罪名之想像競合犯，犯罪之直接被害人有數人，若其中一被害人已先委任律師代理提起自訴，其他被害人未委任律師代理，逕行對被告提起自訴，法院對後提起之自訴應如何處理？\n(A)法院應定期間以裁定命自訴人委任代理人，逾期仍不委任者，依刑事訴訟法第329 條第2 項規定，諭知不受理判決\n(B)法院毋庸命補正，逕以後提起之自訴違反自訴的限制規定，依刑事訴訟法第334 條規定，諭知自訴不受理判決\n(C)法院毋庸命補正，逕以同一案件在同一法院重行起訴，依刑事訴訟法第343 條準用第303 條第2 款規定，諭知不受理判決\n(D)法院毋庸命補正，逕依刑事訴訟法第326 條第3 項規定，以裁定駁回自訴",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "33.本國銀行辦理信用衍生性金融商品交易，如為信用風險承擔者，且合約信用實體為銀行之利害關係人，其應經之\n特殊決議程序為：\n(A)董事會二分之一以上董事出席及出席董事二分之一以上決議\n(B)董事會二分之一以上董事出席及出席董事三分之二以上決議\n(C)董事會三分之二以上董事出席及出席董事二分之一以上決議\n(D)董事會三分之二以上董事出席及出席董事四分之三以上決議",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "21 在屏遮擋塊(beam block)下的劑量計算，受到下列那些因素的影響： ①射束能量 ②遮擋擋塊的厚度 ③照野未被屏遮的範圍 ④照野大小\n(A)①②④\n(B)①③④ (C)③④ (D)①②③④",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "下列何者不屬於民事訴訟程序第二審上訴之合法要件？\n(A)上訴遵守法定不變期間 \n(B)上訴繳納裁判費 \n(C)提出上訴理由書\n(D)上訴利益",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "假設 \\( p \\) 是一個質數，證明存在一個質數 \\( q \\)，使得對於任何正整數 \\( n \\)，都有 \\( q \\nmid n^{p} - p \\)。",
"role": "user"
}
]
| $q$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "(12 分) 在班級活動中, 4 名男生和 3 名女生站成一排表演節目: (寫出必要的數學式, 結果用數字作答)\n\n(1) 三名女生不能相鄰, 有多少種不同的站法?\n\n（2）女生甲不能站在左端, 女生乙不能站在右端, 有多少種不同的排法?\n\n（3）甲乙丙三人按高低從左到右有多少種不同的排法?（甲乙丙三位同學身高互不相等)\n\n(4) 從中選出 2 名男生和 2 名女生表演分四個不同角色朗誦, 有多少種選派方法?\n",
"role": "user"
}
]
| $1440.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "給定 \\(x, y, z \\in \\mathbf{R}^{+}\\)，且 \\(\\frac{1}{x}+\\frac{2}{y}+\\frac{3}{z}=1\\)，找出 \\(x+\\frac{y}{2}+\\frac{z}{3}\\) 的最小值。 \nA. 5\nB. 6\nC. 8\nD. 9",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "正方形獨立基腳尺寸為 400 cm × 400 cm × 60 cm，有效深度為 d = 50 cm，使用之混凝土抗壓\n強度為 280 kgf/cm2\n，且未配有剪力鋼筋，基腳支撐 45 cm × 45 cm 之方形內柱。【題組】9 請問該基腳抵抗雙向作用之剪力強度 Vc？\n(A)248 tf (B) 337tf (C) 425tf (D) 514tf",
"role": "user"
}
]
| $B$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "28. 如圖所示，刀尖位於機械原點上，若執行程式 G92 X250.0 Y200.0 Z150.0；G91 G43 Z5.0 H01；之後，刀尖距離工\n件表面高度為 5 ㎜，則 H01 應為 (A)-150.00(B)150.00(C)5.00(D)-5.00。",
"role": "user"
}
]
| $A$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "Find 1 over 6 + 1 over 8.\nOptions:\nA: 7 over 24\nB: 2 over 14\nC: 1 over 7\nD: 1 over 4",
"role": "user"
}
]
| $A$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "4. 有16名學生參加考試，所有問題都是多選題，每題有4個選項。考試結束後發現：任何兩名學生最多只有一題的答案相同。最多有多少題？（第33屆國際數學奧林匹克）",
"role": "user"
}
]
| $5.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "12. 有關 Factoring 與輸出保險之敘述，下列何者錯誤？\n(A)Factoring 需逐筆審核，輸出保險則在授信額\n度內循環使用(B)Factoring 限 O/A 與 D/A 付款條件，輸出保險則包含 O/A、D/P、D/A、L/C 及分期\n付款等付款條件(C)Factoring 在無追索權下承擔 100%之應收帳款債權，輸出保險則只承擔約 70-90\n%之應收帳款債權(D)Factoring 應收帳款管理商有義務向進口商催款，輸出保險則由出口商自行負責催款。",
"role": "user"
}
]
| $A$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "48 原住民學生報考高級中等以上學校新生入學考試，依法享有優待。其優待方式自九十六學年度招生考試，取得原住民文化及語言能力證明者，以加總分多少計算之？ \n(A)百分之二十五 (B)百分之三十 (C)百分之三十五 (D)百分之四十",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "2、 指定銀行辦理出口信用狀通知及保兌業務，憑辦文件為何？ \n (A) 應憑進口商提供之交易文件辦理 (B) 應憑出口商提供之交易文件辦理 (C) 應憑國內顧客提供之交易文件辦理 (D) 應憑國外同業委託之文件辦理",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "20.依土地登記規則第 56 條規定，下列何者非屬登記機關應以書面敘明理由或法令依據，通知申請人於接到通知書\n之日起十五日內補正之事由？\n(A)不屬受理登記機關管轄者\n(B)未依規定繳納登記規費者\n(C)登記申請書記載事項，或關於登記原因之事項，與登記簿或其證明文件不符，而未能證明其不符之原因者\n(D)申請人之資格不符或其代理人之代理權有欠缺者",
"role": "user"
}
]
| $A$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "2. 下列哪一種疾病較不可能導致高血鈉症？\n(A) 橫紋肌溶解症 (B) 嚴重腹瀉(C) 嚴重大面積燒燙傷 (D) 抗利尿激素分泌不當症候群",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "44 下列有關glycerinated gelatin栓劑基劑之敘述，何者有誤？\n(A)它是一種油性基劑(B)它具有吸濕性(C)它具有延緩藥物釋放之功能(D)它是一種水性基劑",
"role": "user"
}
]
| $A$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "6. 一個矩形的最大面積是多少，其頂點的坐標滿足方程式 $|y-x|=(y+x+1)(5-x-y)$，並且其邊與直線 $y=x$ 和 $y=-x$ 平行？請在你的答案中寫出找到的面積的平方。 $\\quad(12$ 分 $)$",
"role": "user"
}
]
| $432.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "23. 有一位投資組合經理人手上持有價值$10 百萬美元，修正存續期間為 6.8 年的債券投資組合，\n需要避險三個月。目前債券期貨價格為 93-02，名目本金為$100,000。假設其修正存續期間可\n用最便宜的交割債券的修正存續期間 9.2 年衡量，則其最適買或賣的期貨避險口數為何？\n (A)買71 口 (B)賣71 口\n (C)買79 口 (D)賣79 口",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "11.下列何者可能出現負的時間價值？\n (A)深價內歐式賣權\n (B)深價內歐式買權\n (C)價平美式買權\n (D)深價外歐式賣權",
"role": "user"
}
]
| $A$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "10. 有關催產素挑釁試驗檢查結果「陽性」之敘述，下列何者正確？\n (A) 10 分鐘內有 3 次宮縮，每次收縮持續 40 秒，且宮縮時並無伴隨胎心率晚發性減速 (B) 10 分鐘內有 3 次宮縮，每次收縮持續 40 秒，且宮縮時並無伴隨胎心率變異性減速 (C) 宮縮時，有 50%以上伴隨有胎心率晚發性減速 (D) 宮縮時，有 50%以上伴隨有胎心率變異性減速",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "17 一土層之地下水位在地表，飽和單位重 20 kN/m ，地下 2 m 深，過壓密比為 16。何者可能是 2 m 深處的\n 水平有效應力？ (A)5 kN/m2 (B)10 kN/m2 (C)20 kN/m2 (D)40 kN/m2",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "23.票據執票人對前手之追索權，就請求權時效期間而言，匯票為支票之幾倍？\n\n(A)1倍\t(B) 2 倍\t(C) 3 倍\t(D) 4 倍",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "問題 1：一個序列定義為 $ x_1 = 1, x_2 = 4$ 和 $ x_{n+2} = 4x_{n+1} -x_n$，對於 $n \\geq 1$。找出所有自然數 $m$，使得數字 $3x_n^2 + m$ 對於所有自然數 $n$ 都是完全平方數。",
"role": "user"
}
]
| $1.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "找出所有大於 2 且不超過 10000000 的自然數 \\( n \\)，使其具備以下性質：任何與 \\( n \\) 互質且滿足不等式 \\( 1 < m < n \\) 的數字 \\( m \\) 都是質數。",
"role": "user"
}
]
| $3.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "53. 各機關主辦會計人員，對不合法之會計程序或文書，應使之更正：不更正者應拒絕之，並報告該機關長官。前項不法之行為，由於該機關主管長官之命令者，應以書面明異議：如不接受時，應如何處理？\n(A)報告監察院依法彈劾 (B)報告司法檢調單位依法處理 (C)報告該機關之主管上級機關長官與其主辦會計人員或主計機關 (D)報告該機關之主管上級機關長官、主計機關、審計機關",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "68.離心式冰水主機，裝於冷凝 器與蒸發器間之浮球閥或限流器，其功用為控制(A)壓縮機容量(B)\n 蒸發器過熱度(C)壓縮機過熱度(D)限流冷媒降壓膨脹。",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "兩位玩家正在玩一個遊戲。其中一位玩家想出一個整數序列 ($x_{1}, x_{2}, \\ldots, x_{n}$)，這些數字都是單位數，包含正數和負數。另一位玩家可以詢問總和 $a_{1} x_{1}+\\ldots+a_{n} x_{n}$ 的值，其中 $(a_{1}, \\ldots, a_{n})$ 是任何選擇的係數集。為了讓猜測者確定所想的序列，最少需要多少個問題？",
"role": "user"
}
]
| $1.0$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "58. 依國際無線電規則規定，由一分鐘內連發12長劃，每一長劃歷時四秒鐘，\n兩長劃間間歇一秒鐘所組成的無線電電報信號，為以下那一種信號？\n(A) 緊急信號\n(B) 安全信號\n(C) 警報信號\n(D) 遇隩信號",
"role": "user"
}
]
| $C$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "第31屆國際數學奧林匹克 1990 短名單 問題 1 是否存在一個正整數，可以表示為1990個連續正整數的和，並且可以以1990種方式表示為兩個或更多連續正整數的和？",
"role": "user"
}
]
| $是$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "30.下列何者常引起豬心內膜炎?\n(A) 大腸桿菌\n(B) 放線桿菌\n(C) 布氏桿菌\n(D) 豬丹毒桿菌",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "16. 近年來，微波通訊系統中的可攜帶式或汽車電話系統與全球衛星定位系統需求快速成\n 長，使得在通訊系統中扮演關鍵性零組件的介質諧振器與介質濾波器的需求日益增\n 加。為了因應此一需求，介電材料需降低傳遞的損失才能維持傳輸訊號的完整性，而\n 下列何者將會影響訊號傳遞的完整性？\n (A)介電常數；(B)導體損耗；(C)介電材料損耗；(D)以上皆是",
"role": "user"
}
]
| $D$ | true | zh-tw |
[
{
"content": "You will be given a problem or task from the user. Begin by reasoning step by step in an inner monologue, thinking through the problem thoroughly until you reach a conclusion. Then, write a self-contained summary that includes all critical steps needed to arrive at the answer. Use Markdown and LaTeX to format your response. Your final answer should be clearly marked within \\boxed{}. Both your inner monologue and summary should be written in the same language as the user’s input.\n\nYour thinking process must follow the template below:\n<think>\nYour thoughts or/and draft, like working through an exercise on scratch paper. Be as casual and as thorough as you want, but limit yourself to doubting your own reasoning at most three times before committing to an answer you believe is correct.\n</think>\n\nHere, provide a concise summary that reflects your reasoning and presents a clear final answer to the user.\n\nProblem:",
"role": "system"
},
{
"content": "9. 鋼筋混凝土強度設計法之基本設計要求為：\n(A) 強度折減因數\n\n計算強度\n\n載重因數\n\n使用載重\n(B) 強度折減因數\n\n使用載重\n\n載重因數\n\n計算強度\n(C) 強度折減因數\n\n使用載重\n\n載重因數\n\n計算強度\n(D) 強度折減因數\n\n計算強度\n\n載重因數\n\n使用載重",
"role": "user"
}
]
| $D$ | true | zh-tw |
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