**1**

Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?

**2**

In a tournament, there are n team T_{1} , T_{2} , ...., T_{n} , with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common: T_{1 }& T_{2}, T_{2} & T_{3} , ....., T_{n-1} & T_{n} , and T_{n} & T_{1} . No other pair of teams has any player in common. How many players are participating in the tournament, considering all the n teams together?

**3**

Consider the set S = {2, 3, 4, ...., 2n + 1), where n is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X - Y?

**4**

Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint is nearest to

**5**

A function f (x) satisfies f (1) = 3600, and f (1) + f (2) + ... + f (n) = n^{2} f (n), for all positive integers n > 1. What is the value of f (9)?