At flooble there are 40 problems in the queue. (this may not be true but lets just pretend it is.) A few crazy hackers somehow manage to promote themselves to scholars. On the first day the first hacker will vote thumbs up on all problems displayed.(The 10 most recent) On the second day the second hacker votes thumbs down on every second problem. On the third day the third hacker votes thumbs up on every third problem. And so on and so on. (When it gets to the eleventh day the eleventh hacker will do what the first hacker did)

How many days will it take for every problem in the queue to be live on the site?

Note: For those who don't know there are only 10 problems that can be voted thumbs up or thumbs down every day and these problems are the 10 least recent. Also a problem with three thumbs up will be posted to the site and taken out of queue. Only one problem can be posted to the site per day. Also if a problem gets 3 thumbs down it is deleted.

Btw: for those who like an extra challenge what if one problem is submitted every 3 days?

Also: A hacker will always vote before a problem becomes live.

Ok. For every person who wants to take one last stab at this puzzle these are the base rules.
1. a thumbs up will cancel a thumbs down.
2. If a problem reaches +3 it will be posted unless one problem has been posted on that day already.
3. As soon as a problem reaches -3 it will be deleted.

Basically to calculate it out you would have to do one of two things
Find some mathematical equation or write out a computer algorithim
2 work out step by step. To do this you would have to follow these steps.

At the start of a day the following happens.
The hacker votes then the oldest problem which has reached +3 is posted and -3's are deleted. Then the next day starts and the havker votes etc. O yeah levik. I started working it out(again) and so far in the first 30 days 5 probs have been posted and the problems in the queue are rated in their order of oldest to newest. 1 1 2 1 -1 0 0 -2 2 -1(These are the ratings one the problems in the queue on day 30, 5 probs have been posted so far) neways as an estimate if we assume every 10 days 3 probs get posted (I'm disregarding the fact that there was 1 problem per 10 days for the first two sets of ten days) then it would take around 145 days.

Posted by Alan on 2003-02-26 12:27:05