# 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?

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As pointed out by Peter below, the teaser is OK. My original code (now corrected) was based on an incorrect assumption.

With some analysis, a much faster version is possible:

This is one of the best teasers we have seen recently.

There is nothing wrong with this teaser and it has a solution; indeed, a unique one.

Re-examine your assumptions.

Yes, when I woke up this morning I realised what was wrong. 🙂