The Travelling Salesman Problem: Find the Shortest Round Trip

Your route–
Rule of thumb: always go to the nearest unvisited city?
Shortest possible?

How many different round trips are there?

Cities	Round trips	Time to check them all*

* At a billion round trips per second. A round trip and the same trip driven backwards count once, which is where the ÷ 2 comes from. For comparison: the universe is about 13.8 billion years old.