How to meet every patient once?

[Genady]

This little hospital has 16 rooms connected as shown in the picture. There is one patient in each room. The patients in the rooms 2 to 16 are bedridden, but the patient in room 1 is fine and ready to go home. This patient wants to meet every other patient once, and only once, and then to exit the hospital from the room 16, as shown. How can it be done?

 

 

[Danijel Gorupec]

Spoiler

I was only able to do this by starting with either 1->2->1->5 or 1->5->1->2 (after this, there are many possibilities). Is there any other way?

 

[Genady]

7 minutes ago, Danijel Gorupec said:

Is there any other way?

Not that I know of. +1