Consider an infinite strip of unit squares. The squares are numbered "1", "2", "3", ... A pawn starts on one of the squares and it can move according to the following rules:
(1) from the square numbered "n" to the square numbered "2n", and vice versa;
(2) from the square numbered "n" to the square numbered "3n+1", and vice versa.
Show that the pawn can reach the square numbered "1" in a finite number of moves. geometrygeometric transformationinduction