Who Would Win in the 'One Potato, Two Potato' Game Without Full Elimination?

[gcsetma]

I'd like to hear any ideas on how to determine the eventual winner of "One potato, two potato" without going through the full elimination process.

Given n people in a circle, eliminating every 8th person left (which is the process in "One potato, two potato" although every mth person would be more interesting) and beginning again with the person proceeding the one that was eliminated, which person would win?

 

[awkward]

I'd like to hear any ideas on how to determine the eventual winner of "One potato, two potato" without going through the full elimination process.

Given n people in a circle, eliminating every 8th person left (which is the process in "One potato, two potato" although every mth person would be more interesting) and beginning again with the person proceeding the one that was eliminated, which person would win?

This is called the Josephus Problem. See

http://en.wikipedia.org/wiki/Josephus_problem