At Quiz Master Shop Towers we have a square lawn surrounded on all four sides by the building. At each corner of the lawn there is a door in the wall, each leading to different wings of our commodious abode. Each side of the lawn is ten metres.
We are fed up with visitors wandering hither and thither across the lawn when going from door to door, and want to put down paths to reduce the wear on the grass.
The thing is, upkeep on these large country piles can be expensive, so we want to use as little paving as we can get away with. We want to put down the shortest total length of paths possible, while providing a route between every pair of doors.
Putting a path around the outside would provide the routes, but that's 40 metres of paving. Leaving out one side gets it down to 30 metres, but some recalcitrants would not walk all the way round when going between the pair of doors without a direct path. And this isn't the shortest solution.
But what is?
Answer at 9.00 on Monday