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 The flooble question (Posted on 2003-02-18)
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.

 See The Solution Submitted by Alan Rating: 4.0000 (10 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: First guess | Comment 6 of 51 |
(In reply to First guess by fwaff)

As mentioned in my previous reply I think it's a bad assumption to think downs and ups do not offset each other. In fact, if we assume that they do, then all the problems will in fact get to be posted, the last one on day 171. Again this assumes that "every second problem" starts by skipping 1, then voting one, etc.; "every third problem" means skip 2, then vote the third etc.

This assumption also simplifies the report: instead of the V code for being voted on, the current net vote is shown, 0 initially, 1 for 1 thumbs up, etc. Net thumbs down is indicated by X = -1 and Y=-2; -3 never needs be shown; if it happened, it would be shown as r for rejected.

1 1111111111qqqqqqqqqqqqqqqqqqqqqqqqqqqqqq
2 1010101010qqqqqqqqqqqqqqqqqqqqqqqqqqqqqq
3 1020111020qqqqqqqqqqqqqqqqqqqqqqqqqqqqqq
4 102X111X20qqqqqqqqqqqqqqqqqqqqqqqqqqqqqq
5 102X211X21qqqqqqqqqqqqqqqqqqqqqqqqqqqqqq
6 102X201X21qqqqqqqqqqqqqqqqqqqqqqqqqqqqqq
7 102X202X21qqqqqqqqqqqqqqqqqqqqqqqqqqqqqq
8 102X202Y21qqqqqqqqqqqqqqqqqqqqqqqqqqqqqq
9 102X202YP10qqqqqqqqqqqqqqqqqqqqqqqqqqqqq
10 102X202YP1Xqqqqqqqqqqqqqqqqqqqqqqqqqqqqq
11 21P0a1aXP20111qqqqqqqqqqqqqqqqqqqqqqqqqq
12 20P0P0aXP10010qqqqqqqqqqqqqqqqqqqqqqqqqq
13 20P1P0PXP20020qqqqqqqqqqqqqqqqqqqqqqqqqq
14 20P1PXPXP20X20qqqqqqqqqqqqqqqqqqqqqqqqqq
15 20P1PXP0P20X21qqqqqqqqqqqqqqqqqqqqqqqqqq
16 20P1PXP0P10X21qqqqqqqqqqqqqqqqqqqqqqqqqq
17 20P1PXP0P11X21qqqqqqqqqqqqqqqqqqqqqqqqqq
18 20P1PXP0P11Y21qqqqqqqqqqqqqqqqqqqqqqqqqq
19 20P1PXP0P11YP10qqqqqqqqqqqqqqqqqqqqqqqqq
20 20P1PXP0P11YP1Xqqqqqqqqqqqqqqqqqqqqqqqqq
21 P1P2P0P1P22XP201qqqqqqqqqqqqqqqqqqqqqqqq
to be continued...

 Posted by Charlie on 2003-02-18 05:37:05

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