2013 USAMO Problems/Problem 2
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For a positive integer plot equally spaced points around a circle. Label one of them , and place a marker at . One may move the marker forward in a clockwise direction to either the next point or the point after that. Hence there are a total of distinct moves available; two from each point. Let count the number of ways to advance around the circle exactly twice, beginning and ending at , without repeating a move. Prove that for all .
