5.79 To guard a certain target, someone needs to be on duty day and night, so there are day shifts and night shifts. Personnel can be scheduled for a single day shift or a single night shift, or they can be scheduled for a continuous day and night shift. After working a day shift, a night shift, or a day and night shift, the personnel should rest for no less than 1 day and night, 1.5 day and night, and 2.5 day and night, respectively. If each shift requires 1 person, how many people are needed at a minimum to participate in the shifts?
［Solution］If there are 4 people taking turns on duty, each working 1 day and night and then resting for 3 days and nights, it is clearly sufficient to meet the requirements, so we know that 4 people participating in the duty is enough.
Below, we prove that having only 3 people on duty is insufficient.
(1) In the process of 3 people taking turns on duty, if someone works a day and night shift, they should then rest for 2.5 days and nights. However, the other two can work at most two consecutive days and nights (day shift, day and night shift, night shift, or day and night shift, day and night shift). Therefore, on the 3rd day after the first person works the day and night shift, the duty cannot continue.
(2) In the case where no one works the day and night shift, after the second person works the night shift, they should rest for 1.5 days and nights. However, the other two can only work one day and night consecutively, at which point the duty cannot continue.
In summary, at least 4 people should participate in the duty.