Behold the solution to The Wright Challenge: Beyond the Puzzledome #5.   If you forgot the actual question, click here to see it again.

To date, there have been thirty Wright Challenge problems.  This is the first one that I've regretted.  I called Doctor E to complain, and this was what he said:

"Hi, this is Doctor E.  I'm currently travelling the world finding new and interesting problems for my puzzle contest.  Please leave a message at the tone."

Here is the issue:  As you recall, we were looking for graphs with the following properties:

1) The graph has six vertices
2) Three of the vertices are connected to 3 edges, two of the vertices are connected to two edges, and one vertex is connected to only one edge
3) The graph is connected - i.e. there is a path from every vertex to every other vertex

The intended answer was thirteen, and I gave the hint that the answer is bigger than five and smaller than twenty. 

The problem was that by my definition of graph, one could argue that either of the following solutions counted:

Can a vertex connect to itself?  If so, do you count it as being connected to two edges or one?  And what if you didn't notice that in my illustration, I had some verticies connected to other ones more than once?  And all of the permutations of these rules gave different answers.  Here are the thirteen solutions I was thinking of:

Lisa F. found 13 additional graphs with the rule that a vertex can connect to itself with the mutant edge being counted twice.  So the total, adding Lisa's, gives twenty-six graphs.

People sent in some very good long words with no repeated letters.  Doctor E. first posed this problem to his best friend, Stuart, thirty years ago when he was merely Young Master E.  Stuart came up with "GREYHOUND BUS" which had 12 letters, and you had to pretend that the Us weren't repeated.  Here are some of your answers:

Good job, all!

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