MathDB

There are five cities

A,B,C,D,E

on a certain island. Each city is connected to every other city by road. In how many ways can a person starting from city

A

come back to

A

after visiting some cities without visiting a city more than once and without taking the same road more than once? (The order in which he visits the cities also matters: e.g., the routes

A \to B \to C \to A

and

A\to C \to B \to A

are different.)

Problem Statement