2013 USAMO Problems/Problem 2

Revision as of 17:48, 11 May 2013 by Yuler1818181818 (talk | contribs) (Created page with "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 ...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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 .