魔術猜牌-由再生訊息延伸推展猜中比值之研究
本研究是藉由數學手法探討；如何由一疊 36 張四種花色的撲克牌中，尋找出保證可猜中最多張花色的方法。研究過程是以在適當的猜牌時機，以邏輯推理、二進位、分析與歸納 … … 等數學原理與方法，搭配巧妙的策略運用而達到目的。 猜牌方法：先約定好猜牌規則，助手將 36 張牌背圖樣相同但非對稱的撲克牌，以旋轉牌背的方向傳達訊息。在本研究中得出「經由巧妙的猜牌方法保證可以猜中不少於 26 張花色」，並得出「當總張數趨近於無窮大時，保證可以猜中不少於 81 . 07 ％的牌，並且證出若僅使用獨立的訊息猜牌，無論任何猜牌方法皆無法猜中多於 87 . 37 ％的牌」 · 其中一個猜中多於 80 ％的例子是‘「當總張數等於 23006 張時，保證可以猜中不少於 1 8405 張牌（18405/23006 > 4/5）」 ·The study is mathematically based with reasonable explanations behind it. We are to correctly guess as many cards as possible from a deck of 36 cards, with random numbers and four different suits. We will apply mathematical methods, such as logic inference, binary system, and analytical reduction, upon right timing. Using careful arrangement of the principles and reasoning, we can reach our ultimate goal. To state guessing: Conference between the guesser and the assistant about the guessing rules, the assistant will have 36 cards with the same exact pattern on the back but not symmetrical. The pattern of the cards will be different when rotated 180o. The only communication between the two is by rotating cards. In this study, we can prove that through mathematical method, we can assure 26 or more cards can be correctly guessed. Furthermore, when the total amount of cards is close to infinity, we can assure 81.07% or more of the cards can be correctly guessed, and prove that if the cards are guessed from independent information, no more than 87.37% of the cards will be correctly guessed by any guessing methods. One of the examples, which 80% of the cards are correctly guessed, is that when the amount of the cards is 23006, 18405 or more of the cards can be correctly guessed. （18405/23006 > 4/5）
高中各學期成績與指定考科相關性
在升學主義越來越興盛的社會中，考試成績成為人人關心的重點，這\r 次研究就是藉由數理資優班同學的各學期在校成績和指定考科成\r 績，透過迴歸分析，找出各學期成績與指考成績之間的關係，並利用\r 圖表來解釋各種科目在各學期的課程，在高中三年所學的重要性，在\r 藉由此結果，希望能對目前老師的教育重點及學生學習方式能有所幫\r 助，亦可了解學生在高中求學過程中，哪些階段對指考成績較有正面\r 影響，進而強化該學習階段，以有助在指定考科時能充分發揮所學。\r \r In a society that emphasize on degrees, examination scores become the\r spotlight, and the ultimate goal for a high school student who had worked\r so hard for three years is to achieve high scores in the J.C.E.E. In the\r three years of high school, each subject has different topics each semester,\r but which semester has the most decisive effect on the J.C.E.E. score?\r This research is to study the effect of each semester on the J.C.E.E. by\r analyzing the grades of a science and math talented class in Senior High\r School using Regression analysis to find out the connections between\r term grades and the J.C.E.E. Then finding out which term grades had the\r most decisive effect in each subject. By using the result, we hope it can\r help teachers in their teaching and students in their learning. Also, it can\r provide the information about which stage in high school has positive\r effects on J.C.E.E. grades, therefore enabling students to emphasize on\r that stage in order to perform well on the J.C.E.E.