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Problem: Find the Winner of the Circular Game

Explore how to implement a solution for the circular game problem using a queue in C#. Learn to simulate the elimination process by rotating and dequeuing elements, and determine the last remaining friend as the winner efficiently.

Statement

A group of n friends is seated in a circle, numbered from 11 to n in clockwise order. Specifically, moving clockwise from friend i leads to friend i + 1 for 11 \leq i << n, and moving clockwise from friend n wraps back to friend 11.

The game proceeds as follows:

  1. Begin at friend ...