That time between Thanksgiving break and Winter break... that time when students everywhere go to sleep, visions of sugar-plums dancing in their heads.  Sugar Plums and Doctor E. that is!  They dream of the $60, $40, and $20 prizes going to top scorers, the handsome certificates, suitable for framing, going to all who qualify, the wonderful extra gifts from the folks at  Kadon Enterprises, makers of fine-gamepuzzles since 1980.  They dream of being eligible if they are UNI students or Iowa high-school students.  Sweet dreams, everyone, and we will see you next semester.

Turning in the correct solution to this week’s puzzle by Wednesday, December 19 will earn 2 puzzle points.

Turning in a correct solution along with a long word with no repeated letters will earn 3 puzzle points.

A graph is a series of points, called vertices and connections between them, called edges.  All that matters is how the vertices are connected.  In other words, the following four graphs are all considered to be equivalent.

Do you see it?  Each one is a 3 cycle and a four cycle, with a double-edge going between the 3 cycle and the four cycle.  Another way to think about it is that I can number the vertices of each graph (numbering them one through seven) such that in each graph, corresponding vertices are connected to corresponding neighbors.  If two graphs are not equivalent, then they are considered distinct.

Your task is to find out how many distinct graphs there that fit the following description:

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

As always, feel free to email if you have any questions.  The answer is bigger than five, and smaller than twenty.

The deadline for sending in solutions has expired.  But feel free to take some time to work on this one, and click here to see the answer.   Alternatively, click here to see the current challenge.

Web Page design: Doug Shaw