quasar

A rectangular building consists of two rows of 15 square rooms (situated like the cells in two neighbouring

rows of a chessboard). In each room there are three doors which lead to one, two or all the three

neighbouring rooms. (Doors leading outside the building are not counted.) The doors are distributed in

such a way that one can pass from any other room to any other one without leaving the building. How

many distributions of the doors (in the walls between the 30 rooms) can be found so as to satisfy the

given conditions?

Source: Austrian-Polish Mathematics Competition

rows of a chessboard). In each room there are three doors which lead to one, two or all the three

neighbouring rooms. (Doors leading outside the building are not counted.) The doors are distributed in

such a way that one can pass from any other room to any other one without leaving the building. How

many distributions of the doors (in the walls between the 30 rooms) can be found so as to satisfy the

given conditions?

Source: Austrian-Polish Mathematics Competition