[en] During the training of the Ukraine team to qualify to compete in the International Physics Olympiad 2018, the problem of oscillations of a mechanical system consisting of four charged massive balls connected by inextensible threads was proposed. It turned out that the problem has a paradoxical solution, which can be found in various ways. This paper discusses several ways of finding a solution to this problem. Kinematic relations, Newton’s laws, conservation laws, and Lagrangian formalism are used. The considered methods of solving the problem may be useful to students in studying mechanics and electrodynamics. (paper)