Quoted By:
Because you start on the outside of every room (other than your start room), and you end on the outside of every room (other than your end room), you must enter every other room the same number of times you exit it, so each room except for your start and end room must have an even number of doors. Therefore, you can have a maximum of two rooms which have an odd number of doors (your start and end rooms). However, there are more than two rooms (three to be exact) which have an odd number of doors: the top left, the top right, and the bottom middle.
Therefore the puzzle is unsolvable.
