Briefly

Bike ride

Bike ride

The map shows twenty-three major cities in Pennsylvania connected to each other by cycling routes. The problem is simple: start your summer vacation and go from Philadelphia to Erie passing once through each city and without going twice the same way.

It is all that needs to be done. The cities are numbered so that participants can describe the route to follow by means of a numerical sequence.

On this trip we will dispense with the usual practice of arriving at the destination by the shortest possible route. Just get there without paying attention to the odometer.

Solution

The only possible route to go from Philadelphia to Erie passing once through each city is by following the following route:

Philadelphia at 15, 22, 18, 14, 3, 8, 4, 10, 19, 16, 11, 5, 9, 2, 7, 13, 17, 21, 20, 6, 12 and finally Erie.