No. B does not make sense without prior context. D is the answer. IMHO B & C both form viable solution, of equal lack of sense but require some prior context to make them make sense. A is just wrong.

If D were not a choice, B is indeed better than A or C, but is still not a very good choice. "No one knew the better solution to the problem" sounds incomplete. It might work if you said "No one knew which (of two choices) was the better solution to the problem."