1. In the land of Königsberg, everything is made up of one, continuous line. Here’s how to figure out if something belongs in Königsberg.
- Click on any vertex (dot).
- To create a line, click on another vertex.
- Try to trace the whole picture by clicking on the vertices.
- You can only trace each edge (line) once.
This trace of the sailboat that started at the green dot didn’t work. Can you start at a different vertex and find a way to trace the entire sailboat?
Now try tracing the animals on the next puzzle.
Which ones belong in Königsberg?
2. The most treasured objects in Königsberg are ones that can be traced in more than one way. In fact, the more ways, the better! For the rest of the puzzles, try to answer the following questions:
a. Is it possible to trace each edge of the object once?
b. If so, mark where you start and end. Do you end where you started?
c. Can you start in the same place and end somewhere else? If so, show
d. Can you start somewhere else and trace the whole object? If so, show
e. Are there more than two different places where you can start? If so,
3. It’s your turn to draw some new items for the people of Königsberg. Try to draw a different item for each of the situations below or come up with your own Königsberg drawing challenge!
a. with 6 vertices that does not belong in Königsberg.
b. with 12 edges that does belong in Königsberg.
c. with 8 vertices that can be traced in more than two different ways.
d. with 10 vertices and 15 edges that belongs in Königsberg.
e. that does not belong in Königsberg and has the smallest possible number of vertices and edges.
f. that does not belong in Königsberg unless you remove one of its edges.
g. that does not belong in Königsberg and still won’t belong even if you remove any one of its edges.