Evilhubert

OK, let's say that a repeated pattern of lit/unlit lanterns is a win for the devil, regardless of the position of the angel and devil. Let's also say that if the angel and devil make a complete circuit of the path without either of them changing any lanterns, the devil wins (otherwise the angel can just stall indefinitely without ever getting any closer to his goal). In this scenario, the solution is: To explain the winning strategy, I'll first point out the following: So, to win the game:

There's a solution that I find simple and elegant enough to be satisfying In my explanation, I'm going to think of the lanterns as numbered. The first lantern our celestial beings come to after starting the game will be Lantern 0. The next will be Lantern 1, then L2, L3 and so on. The last lantern can be referred to as LT, with T = Total number of lanterns minus 1. Each time they walk round the lanterns and return to L0 will be referred to as a circuit. So who wins? So what's the winning stragegy? But how can we prove the strategy will always work for any number of lanterns? I just want to give a big thank you to witzar for posting the problem - I really enjoyed this one!

I give up. What is the answer?

Can I ask for a bit of clarification? There are a few things that could be interpreted in a couple of different ways When you say "or", do you mean AND/OR or Exclusive OR? When you say "IF" do you mean simply "IF", or "IF and only IF"? If the IF condition in a character's statement is not met (e.g. A says "If B is lying, then C is involved", but B is actually telling the truth), is that character considered to be telling the truth, lying, or neither? (obviously this becomes clear if the IF statements are interpreted as 'if and only if', but I'm asking in case they are not)