Little math challenge (no complete automatism allowed)

[pier4r]

having
\[ 1^{2}, 2^{2}, 3^{2}, ... , 27^{2} \]

divide them in 3 groups (no duplicates) with the same sum.
Surely you can go and write programs to find the solution. The idea is, though, you solve it with pen and paper (or, dunno, drawings). At most one can use the equivalent of a simple calculator (no iterations or programmability).