山东大学学报（理学版）
山東大學學報（理學版）
산동대학학보（이학판）
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
2014年
12期
76-80
,共5页
纵横图%纵横图编制方法%对偶行间数字交换%对偶列间数字交换%对角数字交换%混合数字交换
縱橫圖%縱橫圖編製方法%對偶行間數字交換%對偶列間數字交換%對角數字交換%混閤數字交換
종횡도%종횡도편제방법%대우행간수자교환%대우렬간수자교환%대각수자교환%혼합수자교환
magic square%method making up magic square%interchanging digitals between the dual rows in one column%interchanging digitals between the dual one row%interchanging digitals on the diagonal angel line%hybrid digital switching
纵横图是个古老的组合数学问题。本文以1～n2个连续自然数构成的n行、n列的方形阵列作为n阶纵横图的基数字阵列，研究了其结构特点与纵横图特征（各行、各列及对角线数字和相等）的关系，提出了一种编制任意阶纵横图的通用性方法———对偶数字交换法。应用举例表明，该方法使用便易，不受纵横图的阶数约束，而且易于衍生出诸多种新的纵横图来。
縱橫圖是箇古老的組閤數學問題。本文以1～n2箇連續自然數構成的n行、n列的方形陣列作為n階縱橫圖的基數字陣列，研究瞭其結構特點與縱橫圖特徵（各行、各列及對角線數字和相等）的關繫，提齣瞭一種編製任意階縱橫圖的通用性方法———對偶數字交換法。應用舉例錶明，該方法使用便易，不受縱橫圖的階數約束，而且易于衍生齣諸多種新的縱橫圖來。
종횡도시개고로적조합수학문제。본문이1～n2개련속자연수구성적n행、n렬적방형진렬작위n계종횡도적기수자진렬，연구료기결구특점여종횡도특정（각행、각렬급대각선수자화상등）적관계，제출료일충편제임의계종횡도적통용성방법———대우수자교환법。응용거례표명，해방법사용편역，불수종횡도적계수약속，이차역우연생출제다충신적종횡도래。
A new method making up magic square is presented by analyzing the relation between the structure of n ×n natural numbers array and the basic characteristic of any order magic square.The method is as follow:n/2 digitals of all dual rows or dual columns will be interchanged.If n is odd,adjusting the structure of the array is necessary,that is, the ordered series of numbers on the reverse first diagonal angle line,on the second diagonal line,on the central column and on the central row should be replaced respectively by the central column,the central row,the first diagonal angel line and the second diagonal angel line in the new array.Finally,some examples are given to show the advantage of this method,and many new kinds of magic squares will be generated by using this method.
