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There are 1600 people sitting around a circular table. The first person (person 1) has a sword and kills the second person then hands it to the next alive person (in this case person 3). Person 3 stabs person 4 and gives the sword to person 5. This goes on until person 1599 kills person 1600. Then person 1 kills person 3 and so on. This is repeated until there is only a single person remaining.
Who remains in the end?
(Credit goes to my wonderful 10th grade math teacher, a brilliant man with many great riddles!)