In the land of Pi, there are six cities arranged in a circle. Each city is connected to every other city by a straight road. How many roads are there?
each of the six cities is connected to five others
but the road from A to B , is the same as the road from B to A
diagonals vs sides?
thanks R_scott for picking up on that.
Forgot to subtract the 6 sides from that total
To determine the number of roads in the land of Pi, we need to consider the number of possible connections between the six cities.
In this scenario, each city is connected to every other city, forming a fully connected graph. In a fully connected graph, every pair of vertices is connected by an edge.
To calculate the number of roads, we can use the formula for finding the number of edges in a complete graph. The formula is:
E = (n * (n - 1)) / 2
Where E represents the number of edges and n represents the number of vertices (or cities in this case).
Plugging in the values, we have:
E = (6 * (6 - 1)) / 2
E = (6 * 5) / 2
E = 30 / 2
E = 15
Therefore, in the land of Pi, there are 15 roads connecting the six cities.
The question basically becomes: How many diagonals does a hexagon have
which would be C(6,2) or 15