Suppose there are 20 problems on the site the Sunday evening a user looks at the site the first time. She doesn't read the newest problem of the day, but instead ONLY reads problems that come up on the "Random Problem" page. She reads 5 random problems each day, always in the evening. The only problem is she can see the same problem more than once.
The other problem is problems continue to come in from the infinite queue. Two per week day and one per weekend.
What is the probability she will have read all the problems after her next Sunday evening check? What is the probability she will have read all the problems after the Sunday evening after that?
Note: The problems displayed when you click on "Random Problem" are independent of each other. There isn't anything to make sure that you are getting five different problems if you click on random problem five times.
(In reply to About Flooble
Gamer: "...any problems were already posted [when she starts selecting her 5 random problems on any given night]".
Thanks. I guess the flooble veterans like Charlie would have known that. Then the problem is not as difficult as it would have been with my assumptions, but it probably still requires a software program to be written to solve it. If there are 20 problems the first Sunday night, and she clicks 5 times, there are a lot of possibilities, ranging from getting the same problem 5 times, to getting 5 distinct problems. On the following Monday night, when she clicks 5 times, not only do I have to worry about duplicates among these 5, but also about problems being duplicates of those of the previous day. On Tuesday I have 2 previous days to contend with. The complications mount up, and a program is probably required to sort them out.
btw...why is the protaganist of your puzzle a female? Did you have anyone in particular in mind ?
Posted by Penny
on 2004-02-09 19:01:02