http://mathfactor.uark.edu/2012/03/ho-crazies-on-the-plane/ The Math Factor Podcast Site Fri, 08 Aug 2014 12:52:06 +0000 hourly 1 https://wordpress.org/?v=4.9.25 http://mathfactor.uark.edu/2012/03/ho-crazies-on-the-plane/comment-page-1/#comment-1003 Thu, 22 Mar 2012 17:40:26 +0000 http://mathfactor.uark.edu/?p=1424#comment-1003 I discovered an interesting cool ‘fact’ about this. The last person on the plan always sits in either my seat or their own.
In general, if my assigned seat was no 1 and the nth person was supposed to sit in seat n, then the last person always sit in seat 1 or their own seat. And in general, using this ordering of the seats, everyone either sits in seat 1 or a seat number greater or equal to their assigned seat!
 
 

]]> http://mathfactor.uark.edu/2012/03/ho-crazies-on-the-plane/comment-page-1/#comment-1000 Mon, 19 Mar 2012 06:05:18 +0000 http://mathfactor.uark.edu/?p=1424#comment-1000 It seems to me that [spoiler] if we sort of think about this in a pseudo-backward-induction type way, we know that seats 2-99 are going to be filled by the time the last passenger arrives regardless of which seat Passenger 1 sits in. So the last passenger is either going to sit in his seat or the first passenger’s seat. Since each displaced passenger moves randomly, either seat is equally likely to have been taken. So the last passenger has 1/2 probability that he will sit in Seat 1, and 1/2 probability that he will sit in Seat 100 (the correct seat). [/spoiler]

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