40410 楊輝的六階幻方

★ 終極密碼為0到100之間 ★

### 一、 引言

(也可見維基百科詞條: https://en.wikipedia.org/wiki/Conway%27s_LUX_method_for_magic_squares)。

### 二、 LUX法構造過程

$$\left[\begin{array}{cc} ~4~&~1~\\ 2&3\end{array}\right]\\(4a)$$ $$\left[\begin{array}{cc} ~1~&~4~\\ 2&3\end{array}\right]\\(4b)$$ $$\left[\begin{array}{cc} ~1~&~4~\\ 3&2\end{array}\right]\\(4c)$$

### 三、 LUX法與楊輝幻方的對比

 $$\left[\begin{array}{cc} 2&3\\ ~4~&~1~ \end{array}\right] \\ (7a)$$ $$\left[\begin{array}{cc} 2&3\\ ~1~&~4~\\ \end{array}\right] \\(7b)$$ $$\left[\begin{array}{cc} 3&2\\ ~1~&~4~ \end{array}\right] \\(7c)$$

### 四、 更一般的推廣

 $$\left[\begin{array}{cc} ~1~&~4~\\ 3&2 \end{array}\right]\\(9a)$$ $$\left[\begin{array}{cc} ~4~&~1~\\ 3&2 \end{array}\right] \\(9b)$$ $$\left[\begin{array}{cc} ~4~&~1~\\ 2&3 \end{array}\right]\\ (9c)$$
 $$\left[\begin{array}{cc} 3&2\\ ~1~&~4~ \end{array}\right] \\ (10a)$$ $$\left[\begin{array}{cc} 3&2\\ ~4~&~1~ \end{array}\right] \\(10b)$$ $$\left[\begin{array}{cc} 2&3\\ ~4~&~1~ \end{array}\right]\\ (10c)$$

$$\left[\begin{array}{cccccccccc} ~17~&~92~&~24~&~99~&~1~&~76~&~8~&~83~&~15~&~90~\\ 67&42&74&49&~51~&26&~58~&33&65&40\\ 23&98&5& 80&7&82&14&89&16&91\\ 73&48&55&30&57&32&64&39&66&41\\ 4&79&6&81&88&13&20&95&22&97\\ 54&29&56&31&63&38&70&45&72&47\\ 85&10&87&12&19&94&96&21&78&3\\ 60&35&62&37&69&44&71&46&53&28\\ 86&11&93&18&100&25&77&2&84&9\\ 36&61&43&68&50&75&27&52&34&59\end{array}\right] \\(11)$$ $$\left[\begin{array}{cccccccccc} ~67~&~42~&~74~&~49~&~51~&~26~&~58~&~33~&~65~&~40~\\ 17&92&24&99&1&76&8&83&15&90\\ 73&48&55&30&57&32&64&39&66&41\\ 23&98&5&80& 7&82&14&89&16&91\\ 54&29&56&31&63&38&70&45&72&47\\ 4&79& 6&81&88&13&20&95&22&97\\ 60&35&62&37&69&44&71&46&53&28\\ 85&10&87&12&19&94&96&21&78&3\\ 36&61&43&68&50&75&27&52&34&59\\ 86&11&93&18&100&25&77&2&84&9\end{array}\right] \\(12)$$

### 參考資料

---本文作者為上海華東理工大學金融學系博士生---