Sunday Times Teaser 2707 – Good Times

by H. Bradley and C Higgins

A bus travels on a straight road between two towns, passing through six others on the way. The distances between adjacent towns are all different whole numbers of miles with the longest and shortest differing by six miles. The average of the distances between adjacent towns and the average of the distances between any pair of towns have the same two digits but in a different order.

How long is the bus route?