If I take a spare day and some sandwiches, program my gps/satnav for home and take the opposite of whatever it tells me, where will I go? On a grid system it looks like I will just move away from home in the same direction as I was to start with, but the roads round here are not in a grid. Most roads join at T junctions so there is only a choice of right or left. If travelling north when my home is directly east, the gps will say turn right so I will turn left. The next T junction will take me either north or south again and possibly for some miles (it isn't a grid) so I wonder if I could end up circling around my destination rather than just moving away from it.
Is it possible to have a road system where doing the opposite of the shortest route to home leaves you circling round it?