A grasshopper hops from an integer point to another integer point in the plane, where every even jump has a length $\sqrt{98}$ and every odd one - $\sqrt{149}$. What’s the least number of jumps the grasshopper has to make in order to return to its starting point after odd number of jumps?
Problem
Source: VII International Festival of Young Mathematicians Sozopol 2016, Theme for 10-12 grade
Tags: Plane, combinatorics