Question 10
Beaverland has 12 cities. Highways labelled A to O connect them as shown.
A group of cities is called an **economic community** if every pair of cities in the group is connected either directly by a highway or indirectly through one or more other cities in the group. In the diagram, all 12 cities currently belong to one economic community.
Because of the Covid-19 outbreak, the mayors decide to block two highways to split the country into three separate economic communities. To minimize economic disruption, the smallest community must contain as many cities as possible. The mayors quickly find a way to meet these requirements. How many cities are in the smallest of the three resulting communities?
A group of cities is called an **economic community** if every pair of cities in the group is connected either directly by a highway or indirectly through one or more other cities in the group. In the diagram, all 12 cities currently belong to one economic community.
Because of the Covid-19 outbreak, the mayors decide to block two highways to split the country into three separate economic communities. To minimize economic disruption, the smallest community must contain as many cities as possible. The mayors quickly find a way to meet these requirements. How many cities are in the smallest of the three resulting communities?