Problem des Handelsreisenden

You have a chance to become a travelling salesman on the map and globe. You need to find the shortest circular route passing through all the towns marked by pegs. The route is indicated by a string showing its length and a mark signposting the shortest possible way. The problem can be resolved by testing the length of all the possible routes and selecting the shortest one. This method is termed a brute-force solution. However, with the increasing number of towns the number of routes rapidly increases. For example, for 28 towns we have the incredible 5 444 434 725 209 176 080 384 000 000 options.