Gulf Mathematical Olympiad 2013 - Problem 3
Source: Gulf Mathematical Olympiad 2013
April 5, 2013
vectorfunctionmodular arithmeticrotationgeometrygeometric transformationcombinatorics unsolved
Problem Statement
There are people standing on a circular track. We want to perform a number of moves so that we end up with a situation where the distance between every two neighbours is the same. The move that is allowed consists in selecting two people and asking one of them to walk a distance on the circular track clockwise, and asking the other to walk the same distance on the track anticlockwise. The two people selected and the quantity can vary from move to move.Prove that it is possible to reach the desired situation (where the distance between every two neighbours is the same) after at most moves.