link如何解决如下矩阵生成难题

将1~N*N放入一个N*N的矩阵，要求矩阵每行每列以及对角线的和相等。请问怎么实现？

这是算法题， 和LINQ没有关系

 using System;
using System.Collections.Generic;
using System.Text;

namespace MagicMatrix
{
    class Program
    {
        int[,] mm;

        static void Main(string[] args)
        {
            do
            {
                Program p1 = new Program();
                int n;
                Console.WriteLine("请输入矩阵的大小:");
                n = int.Parse(Console.ReadLine());

                if (n == 0)
                {
                    Console.WriteLine("请按Enter键离开!");
                    break;
                }

                if (n % 2 == 0)
                {
                    Console.WriteLine("请输入奇数!");
                    break;
                }

                p1.mm = new int[n, n];
                p1.AssingValue(n);
                p1.PrintOut(n);
                Console.WriteLine("\n");
            } while (true);
            Console.ReadLine();
        }

        void AssingValue(int n)
        {
            int assingValue = 1;
            int p = n - 1;
            int column = p / 2;
            int row = 0;

            for (int i = 0; i < n; i++)
            {
                for (int j = 0; j < n; j++)
                {
                    mm[i, j] = 0;
                }
            }
            mm[row, column] = assingValue;

            do
            {
                assingValue++;
                column--;
                row--;
                if (column < 0 && row < 0)
                {
                    column++;
                    row++;
                    row++;
                }
                else
                {
                    if (column < 0)
                    {
                        column = p;
                    }

                    if (row < 0)
                    {
                        row = p;
                    }

                    if (mm[row, column] != 0)
                    {
                        row += 2;
                        column += 1;
                    }

                    if (row > n - 1)
                    {
                        row = 0;
                    }

                    if (column > n - 1)
                    {
                        column = 0;
                    }
                }
                mm[row, column] = assingValue;
            } while (assingValue < n * n);
        }

        void PrintOut(int n)
        {
            for (int i = 0; i < n; i++)
            {
                Console.WriteLine();
                for (int j = 0; j < n; j++)
                {
                    Console.Write(mm[i, j] + "\t");
                }
            }
        }
    }
}