A interesting question I got from MathWorks!

I found a interesting question the other day.The question is:

Partition X={1,2,...,16} into two sets of equal sums, equal sums of squares,
and equal sums of cubes. Here's a formal statement of the problem:
find a subset A of {1,2,...,16} that satisfies the following three
properties:
o Sum_{a in A} a^1 = Sum_{a in X \ A} a^1.
o Sum_{a in A} a^2 = Sum_{a in X \ A} a^2
o Sum_{a in A} a^3 = Sum_{a in X \ A} a^3.

Somebody said that this problem can be solved by using recursive. Any suggestions?