A long time ago, there were only four towns in all of Numland. These cities had been connected by a network of roads respecting a very particular organization. There was only one road that led to Unville. Exactly two roads served Deuville. Three were coming and going from Troiville. And four roads, ultimately, served the metropolis of Quatville.
Faced with demographic growth, however, it was agreed to found Cinville and the ministers of Numland decided to continue with the same logic. Even if it meant destroying certain already existing roads, we sought an organization such that Unville, Deuville, Troiville, Quaville and Cinville would be served by 1, 2, 3, 4 and 5 roads respectively. However, after weeks of studies, no way of doing things could be found that would satisfy the ministers' request.
Could you explain to the Nuland engineers the reason for their failure?
A few decades later, the foundations of Siville and Septville were decided in quick succession. We then wondered if the rule could be respected again.
What do you think the engineers responded?
Today, Numland has grown considerably and has exactly 2024 towns. Is it possible for all of these cities to be connected in a way that complies with the rule?
