There are 12 towns grouped in four zones with three towns per zone. It is intended to connect the towns with a telephone lines such that each 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 ?  Pick.
A) 72 B) 90 C) 96 D) 144 E) 128
Explanation :   There are 3 towns.   Each town connects with the other town in 3 lines.   Hence total number of lines is 3 x 3 = 9.   Hence 1 zone has 9 direct links within it.   So 4 zones have 9 x 4 = 36 direct links within it.   Now, between zones/ interzone:   Consider a town in Zone 1. There are 9 towns outside this zone.   Hence 9 lines are required to connect between this town and the other 9 towns.   Similarly, there are 12 towns, each with 9 towns outside its own zone.   So, totally, there will be 9 x 12 / 2 = 9 x 6 = 54 lines inter zone (Divided by 2 comes here because, after half, it is repeated).   So, the total number of lines will be 36 (within zone) + 54 ( inter zone) = 90.   Answer : 90
<result>B</result>
There are 12 towns grouped in four zones with three towns per zone. It is intended to connect the towns with a telephone lines such that each 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 ?