Could the following "Surd Partition" problem be NP complete? Note that if the square roots are omitted in the following then the problem is well known to have a polynomial solution.
Surd Partition
Instance: A collection of positive integers $b_{i}, i=1,..,n$ such that $1 \leq b_{1}\leq b_{2}\leq..\leq b_{n}\leq n$
Question: Is there a subset S of {1,2,..,n} in which
\begin{eqnarray} \left| \sum_{i\in S} \sqrt{b_{i}} - \sum_{i\in S^c} \sqrt{b_{i}} \right| < 1? \end{eqnarray}