Question

There are three cities A, B and C. Each of these cities is connected with the other two cities by at least one direct road. If a traveller wants to go from one city to another city she can do so either by traversing a road connecting the two cities directly, or by traversing two roads, the first connecting the origin to the third city and the second connecting the third city to the destination. In all there are 33 routes from A to B. Similarly there are 23 routes from B to C. How many roads are there from A to C directly?

Answer 1

There are 33 roads from city A to city C directly.

Step-by-step explanation:

Let's assume that there are x direct roads from A to C.

From the given information, we know that there are 33 routes from A to B and 23 routes from B to C.

Since each of the three cities is connected to the other two cities by at least one direct road, there are x routes from A to C directly. This means that there are x routes from A to C directly and an additional (33-x) routes from A to C through B.

Therefore, the total number of routes from A to C is x + (33-x) which is equal to 33. Simplifying this equation, we have:

x + 33 - x = 33

33 = 33

So, the number of roads from A to C directly is 33.