A Topological Type Problem—I Think…what Is It

[SaxonViolence]

Friends,

 

Imagine a round room. The room has 3 one-way entrances and 3 one-way exits. 

 

Pick an exit at random and it will led you to another round room.This room also has 3 entrances—including the one that you just came through—and 3 exits.

 

Can I hook a number of round rooms together in such a way that they form a closed loop and my path will inevitably lead me back to the original room?

 

Connections can be a wooly-bear worm—so assume that the doorways teleport you. or that some connecting corridors are much longer than others...

 

Or quit being so damned literal and just think of it as an abstract topological space.

 

I assume that if it is possible to turn the rooms into one interconnected net, there should be a minimum number of rooms required before the rooms can become an interlinked network...

 

What is the minimum number of rooms and what is the minimum number of rooms that I must transverse to return to my starting point?

 

Can I make larger networks larger than the minimum number?

 

Just exactly what kinds of equations or visualizations do I need to handle this problem?

 

Thanks.

 

…..Saxon Violence

 

BIG PS:

 

Can the equation be expanded to include a system of round rooms with 5 entrances and 5 exits each? How about 7 entrances and exits?

Edited June 2, 2019 by SaxonViolence