The Rogain Problem

There are only 30 points to find. Assuming you were to go to all points, there are only 30!=30x29x28...x2x1 possible routes you could take to visit them. So why not compute the distance between each and every point then work out which one is the shortest? It would take even the worlds fastest computer a very long time to compute all these distances.

This problem is called the Traveling Salesman Problem (TSP) and is one of the well researched mathematical computing problems. No one has yet found a solution which does not require substantial computing time. Lucky for us, humans can do quite well at working out a pretty good solution (if interested see this issue of the Journal of Problem Solving).

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