If a doughnut shaped house has two doors to the outside and three doors to the inner courtyard is it possible to end up back at your starting place by walking through all five doors of the house?

Yes, it is possible to end up back at your starting place by walking through all five doors of the doughnut-shaped house. You can enter through one of the outer doors, walk through the inner doors to the courtyard, and then return through the remaining doors in a way that allows you to complete the circuit. The arrangement of the doors allows for a path that connects all entrances and exits, enabling a return to the starting point.