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.
OK, having CAREFULLY re-read the question I see wehere my Giant error is. Oh well, I never claim to have great reading skills... Anyways, the recently posted reality ofthe posing aside, I have a few things to say about this one. I can't grasp how the last day could be anything other than 10x+1. For example, if the last day were 64, then that means on the 64th day, someone voted thumbs down on the fourth problem, removing all from the queue. But what about the first three that made the voted out problem #4 in the queue? Second, I relaize that it is more elegant mathematically, but is it realistic to assume that the hacker voting on every third problem (for example) votes on 3,6 and 9 - rather than 1,4,7 and 10. Try this yourself - do you not start with a counter and then skip as required to produce the proper pick ratio?
Now woth the new info on voting, this problem gets much longer...
Finally, for the extra challenge, the queue will never expire. in ten days, there are a maximum of (10+5+4+3+2+2+2+2+2) 32 votes, or 3.2 votes per day. With 3 votes required to remove a problem from the queue, the conditions required to exhaust it are prohibitive. I'm not going to prove that at least three votes are wasted in any day day stretch to solidify this point, but you can see for yourself that the five votes cast by hacker 2 are already wasted...
oops
