MathDB

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)

Problem Statement