学步园

今天有个以前的朋友去面试,里面有个2个算法题.他不会,让我帮忙看看,一看我自己都傻了.
1题:
1-1000放在含有1001个元素的数组中，只有唯一的一个元素值重复，其它均只出现
一次。每个数组元素只能访问一次，设计一个算法，将它找出来；不用辅助存储空
间，能否设计一个算法实现？
这个我倒是会,但不知大算法是否够好,求更好的算法

 1static void Main(string[] args)
 2        {
 3            int[] list = new int[1001];
 4
 5            for (int i = 1; i < 1001; i++)
 6            {
 7                list[i - 1] = i;
 8            }
 9
10            Random random = new Random();
11
12            list[1000] = random.Next(1, 1000);
13
14            int sum1 = 0;
15
16            int sum2 = 0;
17
18            foreach (int i in list)
19            {
20
21                sum1 = sum1 + i;
22            }
23            for (int i = 1; i < 1001; i++)
24            {
25
26                sum2 = sum2 + i;
27            }
28
29
30            Console.WriteLine("重复的数字是:"+(sum1 - sum2).ToString());
31            Console.Read();
32        }

2: 四个女人过桥，夜间有一火把，每次最多过两个，必需带火把，
过桥速度不一样
no.1 1min
no.2 2min
no3 5min
no.4 10min
两个人过用最慢一个的速度，火把不能扔
如何在17min内四个女人都过桥
问题难点: 如果从需求中抽象出对象,并用程序输入
我写了很长代码怎么都得不到17, 求高人指点
个人代码

 public class CrossBridge
    {
       public int CrossTime
       { get; set; }

       public bool HasFire
       { get; set; }

       public string WomanID { get; set; }
    }

算法:

 static int Sum;
        static void Main(string[] args)
        {
            int total = 100;
            while (total > 17)
           {
               Sum = 0;
               total = GotIt(NewList());
               
           }
            Console.Read();
        }

        static ArrayList NewList()
        {
            CrossBridge woman1 = new CrossBridge();
            woman1.CrossTime = 1;
            woman1.WomanID = "1";
            CrossBridge woman2 = new CrossBridge();
            woman2.CrossTime = 2;
            woman2.WomanID = "2";
            CrossBridge woman3 = new CrossBridge();
            woman3.CrossTime = 5;
            woman3.WomanID = "3";
            CrossBridge woman4 = new CrossBridge();
            woman4.CrossTime = 10;
            woman4.WomanID = "4";
            ArrayList womanLists = new System.Collections.ArrayList();
            womanLists.Add(woman1);
            womanLists.Add(woman2);
            womanLists.Add(woman3);
            womanLists.Add(woman4);
            return womanLists;
        }
       
        static int GotIt(ArrayList lists)
        {
            Random r1 = new Random();
            int i=r1.Next(0, lists.Count-1);
            CrossBridge w1 = (CrossBridge)lists[i];
            lists.Remove(w1);
            int j=r1.Next(0,lists.Count-1);           
            CrossBridge w2 = (CrossBridge)lists[j];
            lists.Remove(w2);
            CrossBridge temp ;
            Console.WriteLine("走过去的是: 第" + w1.WomanID.ToString() + "女人and " + "第" + w2.WomanID.ToString() + "个女人");               
            if (w1.CrossTime < w2.CrossTime)
            {               
                temp = w1;
            }
            else
            {               
                temp = w2;
            }
            Sum = Sum + w2.CrossTime + w1.CrossTime;
            lists.Add(temp);
           
            if (lists.Count != 1)
            {
                Console.WriteLine(temp.WomanID + "走回去了");
                Console.WriteLine("现在的时间是:" + Sum.ToString());
                GotIt(lists);
            }
            else
            {
                Sum = Sum - temp.CrossTime;
                Console.WriteLine("总时间是:" + Sum.ToString());
                System.Threading.Thread.Sleep(2000);
            }
            return Sum;
        }