Question 23
Lily pads in a row are numbered $0$ through $11$. A frog starts at pad $0$, while snakes occupy pads $3$ and $6$. From pad $N$ it independently jumps to $N+1$ or $N+2$, each with probability $\dfrac12$. What is the probability that it reaches pad $10$ without ever landing on $3$ or $6$?