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.
House vacancies can be caused by death, resignation, declination, withdrawal, or House action, but the Constitution requires that they be filled by election. The law concerning Members elected to fill vacancies varies according to when the vacancy occurs and applicable state law.