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.

(In reply to new info solution - the sequel by Cory Taylor)

Based on the same set of assumptions I've now got exactly the same answer as Cory - phew!

However, considering Levik's post about 'how the voting works' and the constraint in the question that only one question can be posted per day I think we're still not working on the right set of assumptions. I think that the revised/additional assumptions are:

1. Only 1 problem posted per day. If more than 1 problem reaches +3 on the same day then only the first is posted, the others are voted on the next day prior to possible posting. What this means is: some problems will reach a score of +3 and subsequently be voted down to +2; some will reach a score of +4 (or more) before posting; and some will stay on +3 for more than 1 day before posting.

2. The question says that all questions are posted and Levik said that when a score of -3 is reached then the problem CAN be deleted, not that it IS deleted. Presumably then this is a manual, rather than automatic, process. So for the purposes of this problem we should assume that no problem is deleted (either due to apathy or benevolance?!?). Therefore a problem could reach a score of -3 (or even lower) before eventually increasing to +3 and getting posted.

OK now to solve the problem (again) - I may eventually get to the extra challenge!

Posted by fwaff on 2003-02-18 23:38:02