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    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/124870


    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/124870


    Title: 關於一個秤重問題的探討
    The study about a weighing problem
    Authors: 王昱翔
    Wang, Yu-Hsiang
    Contributors: 李陽明
    王昱翔
    Wang, Yu-Hsiang
    Keywords: 秤重問題
    決策樹
    數學歸納法
    Weighing problem
    Decision tree
    Mathematical Induction
    Date: 2019
    Issue Date: 2019-08-07 16:35:45 (UTC+8)
    Abstract: 本文欲探討，在已知一枚硬幣重量有誤而其他硬幣重量皆相同的情況之下，利用無砝碼天平秤n次，最多可以從多少枚硬幣中找到重量有誤的那一枚硬幣並且知道是較輕還是較重。第二章分別討論「已知一枚硬幣較重」、「已知一枚硬幣較輕」和「已知一枚硬幣重量有誤但不知道是較輕還是較重」三種情況，利用決策樹和數學歸納法證明之，第三章給予實際操作的過程。
    This article wants to find : under the condition that one coin is wrong in weight and the other coins are the same weight, using a scale without weight, what is the maximum number of coins that we can find from the coin with the wrong weight ,and know that it is heavier or lighter ? In chapter 2, we will discuss the following three cases : there is a heavier coin, there is a lighter coin, and there is a coin of wrong weight but not sure the coin is heavier or lighter, separately. we will use the decision tree and mathematical induction to prove them. In chapter 3, we will show the practical process.
    Reference: 中文文獻
    (1)謝維馨，分類工具(3)─決策樹（Decision Tree），上網日期2018年3月1日，檢自：http://yourgene.pixnet.net/blog/post/118211190-%E5%88%86%E9%A1%9E%E5%B7%A5%E5%85%B7(3)%E2%94%80%E6%B1%BA%E7%AD%96%E6%A8%B9%EF%BC%88decision-tree%EF%BC%89。
    (2)CH.Tseng，決策樹 Decision trees，上網日期2017年2月10日，檢自：https://chtseng.wordpress.com/2017/02/10/%E6%B1%BA%E7%AD%96%E6%A8%B9-decision-trees/。
    (3)林宥廷(2014)，有關三源數列的探討，國立政治大學，應用數學系碩士班，臺北市。
    英文文獻
    (1)Alan Tucker(1994)，Applied Combinatorics(5th edition)，John wiley&Sons Inc.
    (2)C.L.Liu(2000)，Introduction to Combinatorial Mathematics(International editions 2000)，McGraw-Hill.
    (3)Susanna S.Epp(2003)，Discrete Mathematics with Applications，Cengage Learning.
    Description: 碩士
    國立政治大學
    應用數學系
    105751006
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0105751006
    Data Type: thesis
    DOI: 10.6814/NCCU201900333
    Appears in Collections:[應用數學系] 學位論文

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