In the Garden of Eden, there is a circular pathway, where the Angel and the Devil enjoy an infinite stroll, walking side by side. There are lanterns placed along the pathway (a finite number of them). Each lantern can be in one of two states: on or off. The Angel, a servant of light, has control over the illuminated lanterns. Whenever they pass such a lantern, the Angel decides whether it remains on or off. Conversely, the Devil, a servant of darkness, has control over the lanterns that are dark, and can change their states as they pass.To alleviate their boredom, the Angel and the Devil decide to play a game. The Angel's objective is to bring all the lanterns into complete order, winning immediately if either all lanterns are turned on or all lanterns are turned off. To ensure the game eventually concludes, the celestial beings agree that the game ends if the lanterns return to a previously encountered state. In this case, the Devil is declared the winner.
Now, the question is: Who will emerge victorious, and what strategy ensures the win?