A hospital is infected with 16 patients. The patient number 13 is recovered from coronavirus

Question: A hospital is infected with 16 patients. The patient number 13 is recovered from coronavirus and want to say goodbye to all the remaining patient by visiting every patient exactly once. If the recovered patient enters any room twice, he will get infected again.

What path must the patient number 13 take to escape from room 4?

Answer: You do get, that it’s impossible, right?
The thing is to prove why…

Imagine a chessboard like colouring on the rooms.
If his room is white, then the room where je to exit is white.

You always change from a white to a black room and vice versa.
So taking 15 steps while going from white to white is impossible.

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