Balkan Mathematical Olympiad 2018 p2
Source: BMO 2018
May 9, 2018
algebra
Problem Statement
Let be a positive rational number. Two ants are initially at the same point in the plane. In the -th minute each of them chooses whether to walk due north, east, south or west and then walks the distance of metres. After a whole number of minutes, they are at the same point in the plane (not necessarily ), but have not taken exactly the same route within that time. Determine all possible values of .Proposed by Jeremy King, UK