Two divisions of Napoleon's army are camped on opposite hillsides, both overlooking the valley in which enemy forces have massed.
If both divisions attack their enemy simultaneously, victory is assured, but if only one division attacks alone, it will suffer a crushing defeat. The division commanders have not yet coordinated a joint attack time. The commander of Division A wishes to coordinate a joint attack time of 6 am the following day with the commander of Division B.
Given the stakes involved, neither commander will give an order to his troops to attack until he is absolutely certain that the other commander is also attacking simultaneously. The only way the commanders can communicate with each other is by courier. The travel time between the two camps is an hour's trek through enemy-held territory, exposing the courier to possible capture by enemy patrols.
It turns out that on that night no enemy patrols were scouting in the area. How much time will pass before the two commanders coordinate the attack? Justify your answer.