HMMT 十一月 2009 · 团队赛 · 第 10 题
HMMT November 2009 — Team Round — Problem 10
题目详情
英文原题
- [ 4 ] Suppose that instead there are 6 rooms with 4 doors. In each room, 1 door leads to the next roomin the sequence (or, for the last room, Bowser’s level), while the other 3 doors lead to the first room.
Now what is the expected number of doors through which Mario will pass before he reaches Bowser’slevel?
解析
英文解析
- [ 4 ] Suppose that instead there are 6 rooms with 4 doors. In each room, 1 door leads to the next roomin the sequence (or, for the last room, Bowser’s level), while the other 3 doors lead to the first room.
Now what is the expected number of doors through which Mario will pass before he reaches Bowser’slevel?
Answer: 5460 This problem works in the same general way as the last problem, but it can bemore succintly solved using the general formula, which is provided below in the solution to the nextproblem.