Your question is Frog on Lily Pads: Cover Time. Take a moment with it on the right.
Talk me through your thinking if you like. When you're confident, submit your answer and I'll grade it like a real screen (7/10 or better passes).
Suppose there are n lily pads on a unit circle, and a frog jumps to an adjacent pad with probability 1/2. Find the expected time to visit every lily pad.