摘要
本研究利用顏色拉丁方陣取代數字集合為0、n、2 n、......、( n - 1) n的拉丁方陣，然後與數字集合為1、2、......、n的拉丁方陣作結合，成為一個有n種顏色且數字集合為1、2、......、n的拉丁方陣。此種作法可將原本的一組希臘拉丁方陣解變成多組解，同時也增添了視覺性與趣味性。這種結合顏色的拉丁方陣具有希臘拉丁方陣的特性，若藉由行互換、列互換的調整，使主對角線的和也成為定和，就會成為對角希臘拉丁方陣。此時，只需根據對角線出現的顏色，指定顏色的值，就可得出魔方陣，本研究將此填製魔方陣的方法命名為「顏色管理填製法」。使用該填製法只須想辦法讓每行、每列的數字與顏色都只出現一次，再藉由行互換、列互換的調整，使主對角線和也成為定和，就可得出魔方陣。
關鍵字：魔方陣、拉丁方陣、希臘拉丁方陣。
ABSTRACT
This study will use colors instead of numbers to solve the magic square. Thus, the Latin square composed of numbers 0, n, 2 n …… (n-1) n will be replaced by colors and combined with the Latin square with numbers1, 2, …… n to form a new Latin square which has n colors and numbers1, 2, …… n. This method can convert thesolution of Graeco-Latin square into multi-solutionwith aninteresting way. This coloring Latin squarealso has property ofGraeco-Latin square.By exchanging rows or columns can make a certain sum of diagonal numbersto turninto the orthogonalGraeco-Latin square. Further, designating certain value based on the colors appeared in diagonal can obtain the magic square.The methodused to fill the magic square in this studywas called “filling method by color management”. Therefore, this filling method can make the number and color appear only once in each row and each column.
Keywords: Magic Square; Latin Square; Graeco-Latin Square
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