Exercise 3.

Edward A. Mouse has just finished his brand new house. The floor plan is shown below:

A rectangle subdivided into seven smaller rectangles, with three on top, and four below. The top-left rectangle has gaps leading to the top-middle and bottom-left rectangles. The top-middle rectangle also has gaps to the two bottom-middle rectangles and the top-right rectangle. The top-right rectangle has gaps leading to the bottom-right rectangle and the bottom-middle-right rectangle. The bottom rectangles have gaps leading to the bottom rectangles adjacent to them.

  1. Edward wants to give a tour of his new pad to a lady-mouse-friend. Is it possible for them to walk through every doorway exactly once? If so, in which rooms must they begin and end the tour? Explain.

  2. Is it possible to tour the house visiting each room exactly once (not necessarily using every doorway)? Explain.

  3. After a few mouse-years, Edward decides to remodel. He would like to add some new doors between the rooms he has. Of course, he cannot add any doors to the exterior of the house. Is it possible for each room to have an odd number of doors? Explain.

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