## Realated Questions

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?On May 1, 2007, two organisations (A and B) were formed with n members each. On the first day of each subsequent month, m members join A while the number of members in B gets multiplied by p. On October 2, 2007, both organisations have the same number of members. If m = 20n, find p?

A total of 15 teams participated in a tournament. Each team plays with every other team exactly once. A team gets 3 points for a win, 2 points for a draw and 1 point for a loss. The team which scored the least got 21 points. The scores of all the teams were distinct and at least one match played by winning team was drawn. Which of the following is always true for the winning team?