From kelso's link
The insolubility of the 5 Room House problem can be proved using a graph theory approach, with each room being a vertex and each wall being an edge of the graph (see image opposite). In fact, this puzzle is similar to the famous “seven bridges of Königsberg” problem thanks to which the eminent Swiss mathematician Leonhard Euler laid the foundations of graph theory..
http://www.archimedes-lab.org/How_to_Solve/5_rooms.html
is kelso's link.
if you have ever studied graph theory, you will have seen this puzzle before. That's why I didn't bother. And mentioned graph theory, to point others to it on google.
there are "non-standard" out of the box ways to do it, as already mentioned in this thread.
anyone who had that should be a winner, if this is a competition.
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