Question

The downtown streets of a city on a hill are represented by the diagram. How many different routes moving downward at every step will take a visitor from bus stop A to the conference center B?

a) 2
b) 6
c) 8
d) 12

Answer 1

To find the number of different routes moving from bus stop A to the conference center B, we count the number of paths that only move downward at every step. There are 6 different routes that meet this condition. (option b)

Step-by-step explanation:

To find the number of different routes moving downward from bus stop A to the conference center B, we need to count the number of paths that go from A to B by moving only downward at every step. In the given diagram, the blocks represent the streets of the city. Each block is connected to the block beneath it, and the entire city is on a hill.

We can find the number of routes by counting the number of times we can make a downward move. We start at bus stop A, and for each block we encounter, we have two choices: we can either move downward to the next block or continue straight to the block below it.

Since there are 6 blocks between bus stop A and the conference center B, we have 2 choices for each block, resulting in a total of 2^6 = 64 different routes. However, some of these routes may not move downward at every step.

We need to eliminate the routes that have more than one consecutive block where we don't move downward. By following this condition, we can see that there are 6 different routes that move downward at every step. Therefore, the correct answer is b) 6.