1. Determine if the set {1,2, ..., 96} can be partitioned into 32 sets of equal size and equal sum.
This was part a (The much easier part) of China Girls Math Olympiad 2008. It actually is not all that hard...
If anybody wants to know, this is the somewhat harder part:
b) Determine if the set {1, 2, ..., 99} can be partitioned into 33 sets of equal size and equal sum.
A hint for b:
 Spoiler:

The answer for b is true. You just have to fid the set. Do some experimentation! it will work!
Clarification: The problem is just asking whether is it possible to divide the set into subsets with 3 elements each such that the sum of the elements in each subset is the same.