  We investigate a restriction of Paul Erdos' well-known problem from 1936 on
the discrepancy of homogeneous arithmetic progressions. We restrict our
attention to a finite set S of homogeneous arithmetic progressions, and ask
when the discrepancy with respect to this set is exactly 1. We answer this
question when S has size four or less, and prove that the problem for general S
is NP-hard, even for discrepancy 1.
