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When Mr.Mike finally retires, he is going to have a party on a cruise ship with all 12,184 of his former students. Each of the students will be given a number as they board the carrier. All his former students will line up around the edge to cheerfully greet him. Mr.Mike will shake hands with student number one, then push number two overboard; shake hands with student number three and then push number four overboard; shake hands with number five and push six overboard. This pattern continues as he repeatedly goes around and around and around the whole ship, shaking then shoving, until finally there is only one student left. Which of the 12,184 students will that be?

This problem is different from the table one. You have a fixed amount of 12, 184 students.

Anyway, can anyone provide the explanation for this problem? I tried finding the solutions since this is identical to the Josephus problem.


marked as duplicate by Jaap Scherphuis, Rubio Apr 7 at 5:36

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    $\begingroup$ "Duplicate" here doesn't mean identical in all respects; it means the existing answer(s) to the other question can answer the current question as well. Which is the case for the question identified. $\endgroup$ – Rubio Apr 7 at 5:35
  • $\begingroup$ The wikipedia page on the Josephus problem has a complete proof of the general solution to the k=2 case. $\endgroup$ – Jaap Scherphuis Apr 8 at 3:10

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