In class we considered this scheduling$/$hiring problem: the upper management in a hospital wants to schedule the night shifts of the nurses as follow. Each nurse will take a night shift for five days in a row, then rest for two days in a row. Knowing that the hospital will need at least $10$ nurses to show up every night, find the minimum total number of nurses required for this schedule.

This type of problems in general requires some nontrivial techniques that will be discussed later on in the course. However, the numerical data in this particular problem make not so difficult to guess the solution. What is the solution to this problem?