## Realated Questions

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 lies are required

Four brothers and three sisters sit in a single row, facing the photographer’s camera. If the three sisters always sit together, how many different photographs, having all of them, can be eliked?

PQRSTU is a regular hexagon drawn on the ground. Prashant stands at P and he starts jumping from vertex to vertex beginning from P. From any vertex of the hexagon except S, which is opposite to A, he may jump to any adjacent vertices. When he reaches S, he stops. Let S

^{n}be the number of distinct paths of exactly n jumps ending at S. What is the value of S^{2}k, where k is an integer?