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.

Being a mere student I don't fully understand how the thumbs up/down all works so I had to make a couple of assumptions:

Assumption 1: downs and ups don't cancel each other out - ie if a problem received ududu then it would be posted. (the alternative is that ududu=u)

Assumption 2: once a problem has received 3 ups it can no longer be voted on. ie effectively there is a 'to be posted' queue.

With these assumptions in mind I reckon that the last problem is posted on day 81. Also of the original 40: 33 are accepted and 7 are rejected.

Now for the extra challenge....

Posted by fwaff on 2003-02-18 02:45:25