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 Sorry by Alan)

As the original extra challenge lengthens the queue by 1 every 11 and a fraction days, we could say it lengthens by .0875 per day (exactly that in the latest rules of posting used). As that is based on .3333... problems being added per day, we presumably would need to subtract at least .0875 from the .333... average add-on per day giving .2458333... problems could be added per day to maintain a constant size queue. That in itself is an interval of more than 4 days between problems being added, so 1 problem added per 5 days should shrink the queue.

Posted by Charlie on 2003-03-13 18:37:47