a pawn is moving on a strip of unit squares
Source: Dutch NMO 2000
October 22, 2005
geometrygeometric transformationinduction
Problem Statement
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 "" to the square numbered "", and vice versa;
(2) from the square numbered "" to the square numbered "", and vice versa.
Show that the pawn can reach the square numbered "" in a finite number of moves.