Answer :

The roads not used are omitted.
The traveller can go as far as seventy miles in fifteen turnings. 
The turnings are all numbered in the order in which they are taken.
He never visits nineteen of the towns. 
He might visit them all in fifteen turnings, never entering any town twice, and end at the black town from which he starts but such a tour would only take him sixty-four miles.

Math Genius