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!
