Exercise $12\mathrm{.}3$: Start by finding all possible routes to the ovals marked A and $B.$ To make listing the paths simpler, let's call a move down and to the left $0$ and down and to the right $1.$ To be clear, the full route shown by arrows in the opening diagram would be recorded as the string $001111010.$ It may be helpful to find all possible paths that occur in the ovals above A and B to break the problem down further. Lookfor patterns in the strings you give for each oval.