using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            int[,] data = new int[,]
            {
                { 9, 8, 6 },
                { 8, 6, 4 },
                { 5, 6, 3 }
            };
            Debug.Assert(data.GetLength(0) == data.GetLength(1));
            var query = Arrange(Enumerable.Range(0, data.GetLength(0)).Select(x => x).ToList(), new List<int>())
                .Select(x => x.Select((y, i) => data[i, y]).Sum()).Max();
            Console.WriteLine(query);

        }

        static IEnumerable<List<T>> Arrange<T>(List<T> source, List<T> current)
        {
            if (current.Count == source.Count)
            {
                yield return current;
            }
            else
            {
                foreach (var item in source)
                {
                    if (!current.Any(x => x.Equals(item)))
                    {
                        foreach (var item1 in Arrange(source, current.Union(new List<T>() { item }).ToList()))
                        {
                            yield return item1;
                        }
                    }
                }
            }
        }
    }
}

------解决方案--------------------

C# code

public struct Cell
    {
        public int col;
        public int row;
        public int value;
    }
    
    static Stack<Cell> stack = new Stack<Cell>();
    static int colnum = 3;
    static int maxValue = 0;
    
    static int[,] data = {{9,8,6},{8,6,4},{5,6,3}};
        
    public static void RunSnippet()
    {

        
        for(int i = 0; i < colnum; i ++)
        {
            Cell cell = new Cell();
                cell.row = 0;
                cell.col = i;
                cell.value = data[0,i];
                SumMax(cell);
                stack.Pop();
        }
        WL(maxValue);
            
    }
    
    public static void SumMax(Cell cell)
    {
        stack.Push(cell);
        if (!Check())
            return;
        
        int row = cell.row + 1;
        
        if (row < colnum)
        {
            for(int i = 0; i < colnum; i++)
            {
                Cell next = new Cell();
                next.row = row;
                next.col = i;
                next.value = data[row,i];
                SumMax(next);
                stack.Pop();
            }
        }
        else
        {
            int cMax = 0;
            foreach ( Cell c in stack )
            {
                cMax += c.value;
            }
            
            if (cMax > maxValue)
            {
                maxValue = cMax;
            }
        }
    }
    
    public static bool Check()
    {
        bool rtn = true;
        foreach ( Cell c in stack )
        {
            foreach ( Cell c2 in stack )
            {    
                if (c.col == c2.col && c.row == c2.row)
                {
                    continue;
                }
                else
                {
                    if (c.col == c2.col)
                    {
                        rtn = false;
                        return rtn;
                    }
                }
            }
        }
        return rtn;
    }