  We describe a procedure to solve an up to $2N$ problem where the particles
are separated topologically in $N$ groups with at most two particles in each.
Arbitrary interactions are allowed between the (two) particles within one
group. All other interactions are approximated by harmonic oscillator
potentials. The problem is first reduced to an analytically solvable $N$-body
problem and $N$ independent two-body problems. We calculate analytically
spectra, wave functions, and normal modes for both the inverse square and
delta-function two-body interactions. In particular, we calculate separation
energies between two strings of particles. We find that the string separation
energy increases with $N$ and interaction strength.
