give me Short cut method of mathematics

attain the lectures and do practice

There are 12 towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required?

90 1 city will be connected with other 2 cities of its own zone by 3 lines each so 6 and further 3 lines for each zone ie 1 for each city.so 6+3*3=15 lines from each city. so total lines =15*12 but 1 line is shared by two cities so lines required=180/2=90 🤓