臺灣國際科展

永不妥協

科展類別
臺灣國際科展
屆次
2008年
科別
數學科
學校名稱
國立馬祖高級中學
指導老師
胡裕仁、洪儒
作者
林孟俞、陳紹宇

摘要或動機

本文籍由一套數學遊戲的必勝方法及其背後潛藏的數學原理,來作為研究目標。透過研究德國數學家E.Sperner 提出的方法所延伸的數學遊戲,來解決潘建強、邵慰慈兩位教授留下來沒有證完的遊戲結果[1],並將遊戲增廣至三維空間的探討且得到如下的結論:

一、平面棋盤

(1)不可換色,先下者恆勝,其最快獲勝方法,為依所下位置的三角形衍生子圖周界走。

(2)可換色,獲勝規則由棋盤的總頂點數決定,若棋盤的總頂點數為奇數,先下者獲勝;若棋盤的總頂點數為偶數,則後下者獲勝。

二、空間棋盤


(3) 不可換色,先下者恆勝,而最佳下法,則是下在大四面體本身內部的某一點,且其最快獲勝方法為,依正四面體稜邊所下位置走。

圖例說明

This study is mainly about an invincible method of a mathematical game and its theory
from which it is derived. We want to solve the problems left by Professor Poon,
K.K and Professor Shiu,W.C. and meanwhile extend it into three dimensions through
the method brought up by E. Sperner[1].

圖例說明

On two dimensional case, the first player will win the game forever on condition
that these two players can't change their chesses colors at will. And the fastest
way to win will be just putting the chesses that along the baby triangle boundaries.
If both players can change their chesses colors randomly, count the chesses number
before starting the game. It is calculated that if the number of the total chesses
is odd, the first player will win the game in normal and logical circumstances.
On the contrary, if the number of total chesses is even, the latter will win.

On three dimensional case, the first player will definitely win the game without
allowing changing chesses colors. And the best strategy is putting chesses in the
inner of the big tetrahedron; what’s more, going along the edge of the tetrahedron
will be shortest way to win the game.



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