  We prove, using the coordinate Bethe ansatz, the exact solvability of a model
of three particles whose point-like interactions are determined by the root
system of g_2. The statistics of the wavefunction are left unspecified. Using
the properties of the Weyl group, we are also able to find Bethe equations. It
is notable that the method relies on a certain generalized version of the
well-known Yang-Baxter equation. A particular class of non-trivial solutions to
this equation emerges naturally.
