There are 12 bastions on a wall of a fortress, and a watchman in each bastion. You don’t know neither the shape of the wall nor the distribution of the bastions on the wall. At midnight, every watchman starts from his bastion in a direction on the wall. Every watchman proceeds at constant speed, so that he would walk around the wall in 1 hour. When two watchmen meet, both turn back. They go through a bastion without any delay. Prove that at noon, every watchman arrives to his original bastion.