A forest lies between two parts of a city. How many unique routes are there to go from the west side to point A in the east side without retracing any portion of the route?
Show Hint
In path problems, always look for distinct routes that avoid retracing and check for any intersections or barriers that affect the path.
Step 1: Understanding the problem.
We are asked to find how many unique routes there are from the west side of the city to point A on the east side, without retracing any portion of the route. This is a typical problem in graph theory, where each route can be considered a path between two points, and retracing means using the same path more than once.
Step 2: Analyzing the graph.
From the image, we see that there are several paths between the west and east sides, and the forest acts as a barrier. The key is to count how many unique ways we can move from the west to the east side while avoiding retracing the same path. We need to look at the different possible combinations of routes.
Step 3: Identifying the unique routes.
By examining the diagram, we see that there are 3 distinct routes to reach point A from the west side without retracing any portion of the route. This includes paths that follow different combinations of bridges and tunnels, all starting from the west side and ending at point A.
Step 4: Conclusion.
The number of unique routes is 3.
\[
\boxed{3}
\]
