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: Seeing as how by fwaff)

I agree that if this asks for an addition to the extra challenge, that this would just add to the speed of increase in the size of the queue.

But, applying the change to the original problem, my solution is different from fwaff's in that I had switched to posting the latest puzzle voted on that day that met the criterion, and only if none such existed was the oldest one posted in preference to newer ones. As explained in comment 43: Looking Back at the Rules, this resulted in the emptying of the queue at day 201 already, and also resulted in all 40 being posted with none rejected.

There is a paradox also in changing that rule to allow 2 to be posted per day, with the same order of preference--last voted on that day that qualifies, and if there are less than 2 of those, the earliest eligible(s) not voted on that day. The time is reduced to 191 days, but the paradox is that two get rejected: nos. 33 and 40 (I made sure I counted columns correctly this time).

Posted by Charlie on 2003-03-13 09:12:16