Taken from the Legendre's three square theorem page on wikipedia.
In mathematics, Legendre's three-square theorem states that a natural number can be represented as the sum of three squares of integers
n = x^2 + y^2 + z^2
if and only if n is not of the form n = 4^a(8b + 7) for integers a and b.
The first numbers that cannot be expressed as the sum of three squares (i.e. numbers that can be expressed as n = 4^a(8b + 7)) are
7, 15, 23, 28, 31, 39, 47, 55, 60, 63, 71
As trolls go I'd say this was a fairly sophisticated one. However it has the failing that anyone that is willing to attempt this question is more likely to know about the Legendre's three square theorem.
So I give points for intelligence, points for sophisticatedness of the trap but take away points for mis-judging your targets.
All in all I give this a 8/10. Wear it with pride.