算法一枚

        /// <summary>
        ///  Find all sub number groups that sum equal to a given number
        /// </summary>
        /// <param name="list">sorted list</param>
        /// <param name="total">total number</param>
        /// <returns>all sub number groups</returns>
        private static IEnumerable<List<int>> FindCombination(List<int> list, int total)
        {
            var found = new List<List<int>>();

            //[2,3,4]  total:1
            if (list.First() > total)
                return found;

            //[2]   total:1
            if (list.Count == 1 && list.First() != total)
                return found;

            //[1,2, 6] => [1,2]
            if (list.Contains(total))
            {
                found.Add(new List<int> { total });
                list.Remove(total);
            }
            //[1,2,3] => 1+2+3 =6
            if (list.Sum() == total)
            {
                found.Add(list);
                return found;
            }

            //travel every item to find combination
            for (var i = 0; i < list.Count; i++)
            {
                var seed = list[i];
                var subTotal = total - seed;

                var clonedList = new List<int>(list);
                clonedList.RemoveAt(i);
                var combinations = FindCombination(clonedList, subTotal);
                foreach (var item in combinations)
                {
                    item.Add(seed);
                    item.Sort();
                    if (!IsContainArray(found, item))
                        found.Add(item);
                }
            }
            return found;
        }

        /// <summary>
        /// To check if an list of list contains a list
        /// </summary>
        /// <param name="list"></param>
        /// <param name="item"></param>
        /// <returns>contains or not</returns>
        private static bool IsContainArray(IEnumerable<List<int>> list, IEnumerable<int> item)
        {
            return list.Select(l => string.Join(",", l)).Contains(string.Join(",", item));
        }

这个算法可以说是纯为实现而实现，没有经过任何精巧设计，但从测试结果来看，还没找到漏掉的。