洛书（九宫）

给出1，2，3，……，9，这9个数字，请将他们排成一个三行三列的数字方阵，它的每行，每列和每个对角线上三个数字之和都相等。

这里我写了一个思路比较简单的方法（C#）

public static void JiuGong()
        {
            //默认格式为:
            //   n1,n2,n3
            //   n4,n5,n6
            //   n7,n8,n9
            int i = 0;
            for (int n1 = 1; n1 <= 9; n1++)
            {
                for (int n2 = 1; n2 <= 9; n2++)
                {
                    for (int n3 = 1; n3 <= 9; n3++)
                    {
                        for (int n4 = 1; n4 <= 9; n4++)
                        {
                            for (int n5 = 1; n5 <= 9; n5++)
                            {
                                for (int n6 = 1; n6 <= 9; n6++)
                                {
                                    for (int n7 = 1; n7 <= 9; n7++)
                                    {
                                        for (int n8 = 1; n8 <= 9; n8++)
                                        {
                                            for (int n9 = 1; n9 <= 9; n9++)
                                            {
                                                if (n1 + n2 + n3 == 15
                                                    && n4 + n5 + n6 == 15
                                                    && n7 + n8 + n9 == 15
                                                    && n1 + n4 + n7 == 15
                                                    && n2 + n5 + n8 == 15
                                                    && n3 + n6 + n9 == 15
                                                    && n1 + n5 + n9 == 15
                                                    && n3 + n5 + n7 == 15
                                                    && n1 != n2
                                                    && n1 != n3
                                                    && n1 != n4
                                                    && n1 != n5
                                                    && n1 != n6
                                                    && n1 != n7
                                                    && n1 != n8
                                                    && n1 != n9                                                   
                                                    && n2 != n3
                                                    && n2 != n4
                                                    && n2 != n5
                                                    && n2 != n6
                                                    && n2 != n7
                                                    && n2 != n8
                                                    && n2 != n9
                                                    && n3 != n4
                                                    && n3 != n5
                                                    && n3 != n6
                                                    && n3 != n7
                                                    && n3 != n8
                                                    && n3 != n9
                                                    && n4 != n5
                                                    && n4 != n6
                                                    && n4 != n7
                                                    && n4 != n8
                                                    && n4 != n9
                                                    && n5 != n6
                                                    && n5 != n7
                                                    && n5 != n8
                                                    && n5 != n9
                                                    && n6 != n7
                                                    && n6 != n8
                                                    && n6 != n9
                                                    && n7 != n8
                                                    && n7 != n9
                                                    && n8 != n9
                                                    )
                                                {
                                                    i++;
                                                    Console.WriteLine("第{0}组排列方式", i);
                                                    Console.WriteLine(n1 + " " + n2 + " " + n3);
                                                    Console.WriteLine(n4 + " " + n5 + " " + n6);
                                                    Console.WriteLine(n7 + " " + n8 + " " + n9);
                                                    Console.WriteLine();
                                                }
                                            }
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
            Console.Read();
        }

 

结果显示为：