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 re: First guess by Charlie)

In addition to other assumptions made along the way, my multi-part posting of a solution included the assumption that the same day that one or more problems were posted or approved to be posted and thus new problems became eligible to be voted on, those that became eligible for voting that day would also be voted on by the hackers that same day. So for example as voter 11's thumbs up caused the third puzzle to be posted and the fifth and seventh to be approved for posting, three new puzzles on the queue became eligible for voting and were voted positively on that day by this voter 11.

If that assumption is not made, then, probably mostly due to missing initial votes by that positive first (eleventh, etc.) voter, which puts several on the approved list at a time, there are 3 rejections, contrary to the puzzle's asking that every problem get to be live on the site.

The last post still takes place on day 171, however. ... again still subject to the assumption that thumbs up and thumbs down cancel each other and the "every second" means skip one, vote one, etc.

Posted by Charlie on 2003-02-18 06:20:45