Given a segment $AB$ of length $2003$ in a coordinate plane, determine the maximal number of unit squares with vertices in the lattice points whose intersection with the given segment is non-empty.
Source: Serbia 2003 1st Grade P2
Tags: geometry, combinatorial geometry, combinatorics
Given a segment $AB$ of length $2003$ in a coordinate plane, determine the maximal number of unit squares with vertices in the lattice points whose intersection with the given segment is non-empty.