= Solution
Two bidentate <bipyridine> ligands provide four N donors and three terminal NCS ligands provide three more. Adding one water gives \b[$n=1$ and <coordination number> eight]:
$$
\mathrm{Eu(NCS)_3(bpy)_2(H_2O)}.
$$
Eight-coordinate arrangements, distorted between familiar ideal polyhedra, are plausible for a sterically crowded Eu(III) centre. A second water would give <coordination number> nine, which is not forbidden for a <lanthanide>; the requested value is a chemically motivated prediction, not something fixed by charge balance. Diffraction or a direct hydration-number measurement is needed to establish it uniquely.
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