= Solution
The <bipyrimidine> ligand has two distinct N,N-chelating pockets. It can use one pocket as a terminal <bidentate ligand>, or use both to bridge two Eu centres. Take all three nitrates per Eu to be bidentate O,O donors.
A consistent structure for B is \b[$\mathrm{Eu(NO_3)_3(bpm)_2}$], with two terminal, singly chelating bpm ligands. Six nitrate <oxygens> plus four bpm <nitrogens> give \b[<coordination number> ten]. The unused pocket of each terminal bpm points away from that Eu centre.
For C, use a dimer \b[$\mathrm{Eu_2(NO_3)_6(bpm)_3}$]. Place one bpm between the metals, chelating each Eu through a different N,N pocket. Add one terminal bidentate bpm to each Eu and three bidentate nitrates to each Eu. Each metal again has $2+2+6=10$ donor atoms, while the overall Eu:bpm ratio is $2:3$. In this model all four <nitrogens> of the bridging bpm are used, but only two of each terminal bpm are used.
Both structures have their accessible coordination sites occupied by multidentate ligands, and the <chelate effect> favours retention of those donors over adding or exchanging a solvent molecule. This accounts for the absence of coordinated solvent while allowing a higher <coordination number> than the <thiocyanate> example. Stoichiometry alone does not exclude polymeric alternatives or different nitrate binding modes; the monomer/dimer pair is an explicit internally consistent prediction.
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