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.
All Acronyms. NCNS - No Complications, No Sequelae [Internet]; Sep 1, 2017 [cited 2017 Sep 1]. Available from: https://www.allacronyms.com/NCNS/No_Complications%2C_No_Sequelae.