Grasshopper returns
Source: Balkan MO ShortList 2010 C2
April 5, 2020
Problem Statement
A grasshopper jumps on the plane from an integer point (point with integer coordinates) to another integer point according to the following rules: His first jump is of length , his second jump is of length , his next jump is of length , and so on, alternatively. What is the least possible odd number of moves in which the grasshopper could return to his starting point?