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
