We play the following game in a Cartesian coordinate system in the plane. Given the input (x,y), in one step, we may move to the point (x,y±2x) or to the point (x±2y,y). There is also an additional rule: it is not allowed to make two steps that lead back to the same point (i.e, to step backwards).Prove that starting from the point (1;2), we cannot return to it in finitely many steps. analytic geometrycombinatorics unsolvedcombinatorics