The Travelling Salesman Problem
?A salesperson has to visit a number of cities
?(S)He can start at any city and must finish at that same city
?The salesperson must visit each city only once
?The number of possible routes is (n!)/2


Combinatorial Explosion
A 10 city TSP has 181,000 possible solutions
A 20 city TSP has 10,000,000,000,000,000 possible solutions
A 50 City TSP has 100,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000 possible solutions
There are 1,000,000,000,000,000,000,000 litres of water on the planet