Given n different positive integers not greater than 2n-2, we prove that more than n^2/12 consecutive integers can be represented as the sum of half of the given numbers. This confirms a conjecture of Lev.
CWI
CWI. Probability, Networks and Algorithms [PNA]
Networks and Optimization

Karolyi, G. (2008). Balanced subset sums of dense sets of integers. CWI. Probability, Networks and Algorithms [PNA]. CWI.