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forum.virtualchallengemeets.com • View topic - 2010 USAMO 2

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2010 USAMO 2

Posted: Wed May 05, 2010 6:01 am

by stupidityismygam

There are [unparseable or potentially dangerous latex formula] students standing in a circle, one behind the other. The students have heights [unparseable or potentially dangerous latex formula]. If a student with height [unparseable or potentially dangerous latex formula] is standing directly behind a student with height [unparseable or potentially dangerous latex formula] or less, the two students are permitted to switch places. Prove that it is not possible to make more than [unparseable or potentially dangerous latex formula] such switches before reaching a position in which no further switches are possible.