“Soldiers are lined up along a line in the east-west direction, each of them facing
north. When the officer commands ‘right turn’ they should all turn towards the
east. Since they are at the very beginning of their military career, some of them get
the order wrong and turn towards the west. Each soldier who now faces his neighbor
concludes that he has made a mistake (disregarding the possibility that his neighbor
made the mistake), and he makes a 180° turn within 1 second. The process
continues in the same way: every soldier who faces a neighbor makes a 180°
turn within 1 second. Prove that the process will end in a finite number of steps.”