I need some help on this question please.

The set {1, 2, 3, 4} can be partitioned into two sets {1, 4} and {2, 3} of the same size. Notice that 1+4 = 2+3.

Question
Jane says she can partition the set {1, 2, .........16} into two subsets S and T of the same size so that:
- the sum of the numbers in S equals the sum of the numbers in T
- ther sum of the squares of the numbers in S equals the sum of the squares of the numbers in T
- the sum of the cubes of the numbers in S equals the sum of the cubes of the numbers in T
Is Jane right or wrong? Clearly explain your answer.

I would appreciate any help.