Also, this problem isn't solved by induction. It's solved by recognizing the pattern. You don't need to establish the base case via the outside observer. All yo

Also, this problem isn't solved by induction. It's solved by recognizing the pattern. You don't need to establish the base case via the outside observer. All you need to know is that the day-based formula works for any number of islanders. It'd be like proving x^2 - 1 = (x+1)(x-1) for all x by starting with 1 and walking up the integers... Which is to say, not a bad way to prove it, but not necessary when you can logic it out otherwise.