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.
I get a very different answer than the previous posts, so either I'm over-simplifing or their over-complicating the problem. My assumptions are
1) all 40 problems begin with a clean slate
2) 3 Thumbs up immediately removes the problems from the voting queue, and places it in a posting queue, to be released one per day.
3) 3 thumbs down immediately removes the problem from the queue, and it is deleted
4) thumbs up and thumbs down do not cancel out
in the first five days, each of the first ten problems receives 3 up and 2 down - and all are to be posted. The next five days sees problems 11-20 deleted with 3 down to 2 up. The next 5 days sees problems 21-30 accepted for posting and the NEXT 5 days problems 31-40 are rejected. This gives 20/40 problems the posting status. The first problem will be posted on day 6, and each day thereafter (at least) one problem is ready, so no days are skipped. This means that the last accepted problem(30) is posted on day 25.
So where'd I go wrong