Report Lanterns of Eden. in New Logic/Math Puzzles Posted February 8 3 hours ago, k-man said: These are some trivial and uninteresting examples and I'm not sure how they help. These trivial examples show that for small values of N (the numbers of lanterns) the Angel wins. You seem to be claiming that that the Devil wins for larger values of N, and that all it takes is two OFF lanterns that are not adjacent. So lets analyze the case of three lanterns that are initially OFF, ON, OFF. If the Devil does not switch the 1st lantern ON, then the Angel switches the 2nd lantern OFF, winning immediately after. If the Devil switches the 1st lantern ON, the the Angel does not switch the 2nd lantern, and the Devil cannot switch the 3rd lantern as this would lose immediately. So after the first "pass" the lanterns are in state ON, ON, OFF, and from here the Angel wins by flipping the first two lanterns. But maybe this case is also "trivial and uninteresting", but then what is the smallest N where the Devil can actually win, and what is the initial state?