# 永不妥協

2008年

## 摘要或動機

(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。

(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。

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].

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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