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'Lengthy Journeys' printed from http://nrich.maths.org/
Here is a simple map showing the
positions of 5 cities:
We could be making some car journeys between these towns and so
here is a chart giving us some information about distances and
These numbers show us direct routes. But now, suppose
we go on journeys involving three or four cities.
For example, we could go from Norwich to Oxford but go through
Cambridge on the way.
Or, we could go from London to Leicester but go through Oxford on
What other journeys involving three or four cities can you
When you have some of these answer these questions:
1. What is the total distance of your journey in
2. How many minutes long is your journey?
3. How much longer (in terms of time) is the journey
when passing through another city or other
cities along the way compared with the direct journey between the
starting city and the final destination?
Now you could try and find the longest route (in terms of distance)
for visiting all five cities.(We might decide that we will only
visit each city once.)
What about the shortest route for visiting all five cities?
How much longer does it take to travel the longest route compared
with the shortest route?