Divide the set {1,2,3,4, ....,n} into three disjoint subsets A , B , C whose sums of elements are equal.
For what values of n it is feasible?

(In reply to

half of it by Daniel)

You say:..".Thus it is possible to form A,B, and C for all even n>=6.."

**Not so**. Try n=10,16,22,28... etc and you will not be able to provide the desired partition.

**The sum of n numbers must be a multiple of 3 - otherwise you cannot create 3 equal parts.**

Now you have enough background to define precise criteria for the solvability of the division and (not asked in the post) describe the exact way of doing it for any given n , fitting those criteria.