$2007$ points on a circle
Source: All-Russian 2007
May 4, 2007
algorithmcombinatoricscircleRussiagametrick
Problem Statement
A. Akopyan, A. Akopyan, A. Akopyan, I. Bogdanov
A conjurer Arutyun and his assistant Amayak are going to show following super-trick. A circle is drawn on the board in the room. Spectators mark points on this circle, after that Amayak
removes one of them. Then Arutyun comes to the room and shows a semicircle, to which the removed point belonged. Explain, how Arutyun and Amayak may show this super-trick.