1. The traveling salesman problem A traveling salesman has to go to Amsterdam, Alkmaar, The Hague, Hilversum, Utrecht, and IJmuiden. What is the shortest route he can take to visit all these places? This question is an old problem known as thetraveling salesman problem. Using brute force and trying every single solution is an option, but if the number of places to visit grows, the number of solutions to go through grows as well and becomes prohibitive. Also choosing the route, so you visit every place once only, is not easy to solve. As a matter of fact, this problem is an unsolved problem. But finding an answer to this question is a matter of importance in modern technology, think for example of routing on a microchip. It is possible though to solve a simplified form of the traveling salesman problem with the Greedy algorithm. Assume an agent of a commercial courier service has to deliver five packages to five different addresses. The agent wants to be home as early as possible to celebrate his daughter's birthday so he needs to find the shortest route to deliver his freight. See the graph pictured below. In the graph A to E denote the addresses, with A being the home of the agent and B to E the delivery places. The edges between the addresses represent the roads, the numbers are the distances. The agent delivers the packages in a certain order and tries to travel the shortest distance between the addresses.
   1. Determine the shortest route to travel for the agent if he wants to be home early.
   2. Are there other routes the agent can travel that are of equal length to be home early?
   3. Assume the agent has to deliver 42 packages to 25 addresses. How many different routes can he travel?