Example 10. As shown in Figure 6-1, it is a part of a city's street map, with five roads running both longitudinally and latitudinally. If one walks from point $A$ to point $B$ (only from north to south, and from west to east), how many different ways are there to do so?
Solution: Because the number of different ways from the top-left vertex of each small square to the endpoint equals the sum of the number of different ways from the two adjacent vertices to the endpoint, we can deduce the data at the top-left corner of each small square in Figure 6-4, which represents the number of different ways, and thus conclude that there are 70 different ways from $A$ to $B$.

Analysis: Let's first simplify the complex grid of routes to Figure 6-2. We can see that there are $1+1$ $=2$ ways to go from $E$. Then, expanding Figure 6-2 to Figure 6-3, we find that there are $3+3$ $=6$ ways to go from point $H$. Through observation and analysis, we can derive the following rule: the number of different ways from the top-left vertex of each small square to the endpoint equals the sum of the number of different ways from the two adjacent vertices to the endpoint.