The ministry of transportation of Lampukistan just made the following announcement: From Jul 1st, the country-wide inter-city bus service will be organized by the ministry.
The service will be organized in the following way:
- Every city is to be connected to every other city by exactly one line.
- Every line will serve exactly three cities.
The service will have more than one line. At least how many cities does Lampukistan have?
Bonus points if you give a formula for all possible numbers of cities.