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.
Vacancy rate of $7.85 per month ($13.70 per bill) may be granted for a single family residence that will not be occupied or used as a residence for at least 60 consecutive days. Garbage and recycling must not be set out for collection during this time.