A PCU has a count of 20 patients at 1 a.m. on September 1 and 30 patients at the same time on September 2. Could the counts have been different if the patient care unit has taken a census at 12:01a.m. on both days? Explain your answer.

Let's assume that there were no patients admitted or discharged between 12:01 a.m. and 1 a.m. on both days.

Let x be the number of patients discharged between 12:01 a.m. and 1 a.m. on September 1.
Let y be the number of patients admitted between 12:01 a.m. and 1 a.m. on September 2.

Therefore, the number of patients in the PCU at 1 a.m. on September 1 would be 20 - x and the number of patients at 1 a.m. on September 2 would be 30 + y .

Since the number of patients admitted and discharged should result in the change from 20 patients to 30 patients, we can set up the following equation:
20 - x + y = 30
y = x + 10

This means that the number of patients admitted on September 2 is equal to the number of patients discharged on September 1 plus 10. Therefore, the counts could have been different if the PCU had taken a census at 12:01 a.m. on both days, since the number of patients admitted and discharged during that one-hour period could have varied, resulting in different counts at 1 a.m. on both days.

\boxed{\text{Answer: Yes, the counts could have been different.}}