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paciguard

留个脚印，学习了。

香川群子

Problem 1207 - average number of different buses

Thelma drives shuttle buses.  There are 60 of them in the yard numbered 1 to 60. Each day that she works she is randomly assigned a bus.  After 40 days of working, on average how many different buses has she driven?  For example:  If she just happened to be assigned bus number 9 each of her 40 days then she will have only driven one bus, or if she just happened to be assigned bus number 9 or bus number 3 on each of her 40 days she will have driven only 2 different buses.
Round your answer to 2 decimal places.
Solution Format/Example: 15.37

问题1207：平均开过几辆不同的公车？

某公交线路有60个司机60台车编号1-60、每天随机驾驶其中1台车。
问40天内，平均每个司机开过几辆不同编号的公车？

答案=29.37

我写了两种解法，第2种计算精度高一点。

1. Sub test1()
   
2.     Dim i&, j&, m&, n&, r&, s&
   
3.     m = 60: n = 40
   
4.    
   
5.     For i = 0 To 10 ^ 4 - 1
   
6.         ReDim a(m - 1)
   
7.         For j = 1 To n
   
8.             r = Int(Rnd * m)
   
9.             a(r) = a(r) + 1
   
10.         Next
    
11.         
    
12.         For j = 0 To m - 1
    
13.             If a(j) Then s = s + 1
    
14.         Next
    
15.     Next
    
16.     Debug.Print s / i
    
17.     Stop
    
18. End Sub
    
19. 
    
20. Sub test2()
    
21.     Dim i&, j&, k&, m&, n&, r&, s&
    
22.     m = 60: n = 80
    
23.     ReDim a(m - 1)
    
24.     For i = 0 To m - 1
    
25.         a(i) = i
    
26.     Next
    
27.    
    
28.     For i = 0 To 10 ^ 3 - 1
    
29.         ReDim b(m - 1, m - 1)
    
30.         Randomize
    
31.         For k = 1 To n
    
32.             For j = 0 To m - 1
    
33.                 r = Int(Rnd * (m - j)) + j
    
34.                 t = a(r): a(r) = a(j): a(j) = t: b(j, t) = b(j, t) + 1
    
35.             Next
    
36.         Next
    
37.         
    
38.         For j = 0 To m - 1
    
39.             For k = 0 To m - 1
    
40.                 If b(j, k) Then s = s + 1
    
41.             Next
    
42.         Next
    
43.     Next
    
44.     Debug.Print s / m / i
    
45.     Stop
    
46. End Sub
    

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香川群子

Problem 1199 - Fair Chance

You and your friend are flipping coins, but on the next toss instead of flipping a coin you decide to randomly select a number between 0 and N inclusively. If the chosen random number has 5 as any of its digits your friend wins, otherwise you win. What should the number N be so as to allow each of you a 50% chance to win this game and make it fair? There are multiple numbers N that fit this criteria, what is the smallest?

Second question: once the number N is chosen you convince your friend that since all digits are pretty evenly distributed it won't matter what digit you are looking for, and instead of looking for 5 you want to look for digit X. So when a random number is chosen between 0 and N inclusively if it contains X as any of its digits your friend wins otherwise you win. What should the digit X be to skew the game most in your favor?

Submit your answer separated by a comma: N, X
Solution Format/Example: 493, 7

问题1199 - 公平猜数：

你和你的朋友喜欢玩扔硬币,但这次你们决定随机选择0到N范围内的一个数字。
如果选择的随机数任何数位上含有5，那么你的朋友赢了,否则你就赢了。
N数应该是多少能让你们每个人都有50%的机会赢得这场比赛,这公平吗?
可能有多个数字N,符合这一标准的最小的N是什么?

第二个问题:一旦N选择好之后，你欺骗说服你的朋友,说我们另外定一个数字x，如果随机选择的0-N范围内的数中任意位上含有X那么你的朋友赢了否则你赢了。数字X应该选什么可以使得该游戏对你最有利?

回答格式由一个逗号分开:N,X
例子:493,7

答案：590489,0

1. Sub test4()
   
2.     Do
   
3.         n = n + 1
   
4.         If InStr(n, 5) Then m = m + 1: If m > n \ 2 Then Debug.Print n: Exit Do
   
5.     Loop
   
6. End Sub

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peng115

mark！一下