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: new info solution - the sequel by fwaff)

OK so given the previous assumptions I reckon that the last problem is posted on day 182. The reason that this isn't 10x+1 is because the final two problems reached +3 on day 181 and the second of them had to wait until day 182 as only 1 problem can be posted per day.

Regarding the extra challenge then the queue will never reach zero. The reason for this is that in any 10 day period there are 17 thumbs up (10 on day 1, 3 on day 3, 2 on day 5, 1 on day 7, 1 on day 9) and 10 thumbs down (5 on day 2, 2 on day 4, 1 on day 6, 1 on day 8, 1 on day 10). This gives a net increase of +7 over the 10 days.

Therefore in any 30 days there is a net increase of +21. However, in any 30 days there are 10 new problems added which need +30 to approve them. Which means that on average the queue of problems pending grows by 3 problems every 30 days.

Alan: are we anywhere close to solving the problem you intended yet?

Posted by fwaff on 2003-02-19 04:44:05