Learning about different problem solving strategies and when to use them will give you a good start. Problem solving is a process. Most strategies provide steps that help you identify the problem and choose the best solution. There are two basic types of strategies: algorithmic and heuristic.
It should be 'No vacancies' (plural). Vacant means empty/free. Vacancy is the state of being empty, therefore 'no vacancies' = no empty rooms.
Before the One (meaning the Source--not the number) there is only Void, or non-being; thought; the ultimate mystery, the incomprehensible Absolute. Begins with meanings such as, Non-existence; nothingness; the unmanifest; the unlimited; the eternal. The absence of all quality or quantity.