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.
Following the same rules that gave my solution of the last posting on day 181, of original queue position puzzle 38, and rejection of #35 along the way, via on any given day voting before any posting, and then posting the earliest in the queue meeting the criterion of +3 or more net thumbs up, I added the new puzzle every third day to the queue (day 3, day 6, etc.)
On day 62 the status of the ten being voted on is 220222X00X, where the X represents 1, which next occurs again on day 422. Both these days are congruent to 2 mod 10, so the voting patterns will repeat from there also. The difference, 360, is a multiple of 3, so even the addition of new problems to the queue will repeat in this cycle of 360. By day 62, there are 47 problems in the queue, 13 have been posted and none rejected, but over the course of the 360day cycle, 120 puzzles have been added, while 86 additional have been posted and 2 rejected, resulting in the queue growing by a net of 32.
This continues indefinitely with 86 postings, 2 rejections and the queue growing by 32 each 360 days. Day 62 is the first day in which the cycle is entered.

Posted by Charlie
on 20030304 03:46:00 