How does he do this and exit from room 4?

Question

Hospitals have 16 isolation rooms. Each room has a patient with different illnesses. The patient in room 13 recovers from corona and now say goodbye to each patient and visits only once. If he entered twice in any room he will become infected again.

How does he do this and exit from room 4?

Answer 1

One of possible solutions given below:

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Answer 2

He walks into room 14 and says goodbye to the resident, then he goes back to room 13 and walks into room 9, then he follows the sequence: 10-11-15-16-12-8-7-6-5-1-2-3-4