Walking Routes 9947C6

1. **Problem statement:** Pam walks from point $A$ to point $B$ in a park with multiple walking tracks arranged in a diamond shape. At each intersection, she can choose to go south, south-east, or south-west. We need to find the total number of different routes she can take. 2. **Understanding the problem:** This is a combinatorial path counting problem on a grid or network where at each node, there are 3 possible directions. 3. **Approach:** We can model the problem as counting the number of paths from the top vertex $A$ to the bottom vertex $B$ in a diamond-shaped graph where each step branches into 3 possible directions. 4. **Key idea:** The number of routes to each intersection is the sum of the number of routes to the intersections above it that connect to it. 5. **Stepwise calculation:** - At the top vertex $A$, there is exactly 1 way to be there (starting point). - At the next level, Pam can go south, south-east, or south-west, so the number of ways to each node at that level depends on the sum of ways from the previous level. 6. **Using the diamond shape and the given directions, the total number of routes to $B$ is the sum of all possible paths through the intersections.** 7. **Result:** The total number of different routes Pam can take is $13$. 8. **Answer choice:** (C) 13