Four grasshoppers sit at the vertices of a square. Every second, one of them jumps over one of the others to the symmetrical point on the other side (if X jumps over Y to the point X′, then X, Y and X′ lie on a straight line and XY=YX′). Prove that after several jumps no three grasshoppers can be:(a) on a line parallel to a side of the square,
(b) on a straight line.(AK Kovaldzhy) geometrycombinatoricscombinatorial geometry