You can't get there from here

Optimization

        sub travelling_salesman {
          my ($cities, $airfare, $budget) = @_;
          for my $itinerary (all_permutations($cities)) {
            if (cost_of($airfare, @$itinerary) < $budget) {
              return $itinerary;
            }
          }
          return undef;
        }

How long does this take?
There are a lot of possible itineraries

Cities Itineraries

         3                                    6       
         4                                   24
         5                                  120
         6                                  720

continued...