Last one standing

100 people stand in a circle numbered 1–100. Starting the count at person 1, every second person is eliminated (2, 4, …) and the circle closes up, continuing until one remains. What is the survivor's number?

Show hints (2)+
  1. This is the Josephus problem with k=2k=2.
  2. Write n=2m+Ln=2^m+L; the answer is 2L+12L+1.

Answer

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