Assume there are $n$ coins in a circle. They show Heads with probability $1/2$ and Tails with probability $1/2$.
One of the coins that shows Heads is randomly chosen and this coin and its two neighbors (the coin on the right and the one on the left from it) are flipped again. The probability of showing Heads for any coin from now on is $p$.
This procedure repeats.
We need to find the function of the expected number of iterations to get all Tails in the circle.
Can you help me with this? Is there any elegant way to proceed?