Question 39
Some soldiers are standing in a line in the east-west direction, each of them facing north. Their officer commands, "Right face!" They should now all be facing east, but, as they are at the very beginning of their military career, some of them get the order wrong and turn to the west. Every soldier who is then facing his neighbor immediately concludes that he has made a mistake and performs a $180^{\circ}$ turn within 1 second. The process continues, so that any two soldiers who are now facing each other perform $180^{\circ}$ turns within 1 second. Prove that after some time, the soldiers will stop moving.