Puzzle versions can be found in several African folktales where they are taken
not to be diffi cult problems but only pleasant stories. In the Swahili tradition, a
visitor from another region visits a sultan but refuses to pay tribute. He is
confronted with a challenge: He must carry a leopard, a goat and some tree
leaves to the sultan's son who lives across a river, and he must use a boat that will
hold the visitor and two other items.
A Winter Stroll, Gibsons
The problem, of course, is that no two items
can be left on the shore together. (This is diff erent from the version mentioned
by Alcuin, which gave the option of leaving at least the wolf and cabbage on the
shore together.) The visitor, aft er mulling over the problem, decides to carry first
the leaves and goat, return with the goat, and then carry the goat and leopard
together to the son.
Matlock Bath, Gibsons
Graph version in which the landforms could be seen to constitute a network of
vertices, and the bridges as paths or edges. As we discussed briefl y above, a
network can have any number of even paths in it, because all the paths that
converge at an even vertex are used up without having to double back on any
one of them. For example, at a vertex with just two paths, one path is used to get
to the vertex and another one to leave it.
Mike Jupp, I Love Autumn, Gibsons
Both paths are thus used up without
having to double back over either one of them. In a four-path network, when we
get to a vertex, we can exit via a second path. Th en, a third path brings us back to
the vertex, and a fourth one gets us out.
All paths are once again used up. In an
odd vertex network, on the other hand, there will always be one path that is not
used up. For example, at a vertex with three paths, one path is used to get to the
vertex and another one to leave it (as mentioned briefl y above). But the third
path can only be used to go back to the vertex.
Harvest Feastival, Gibsons
To get out, we must double back
over one of the three paths. Th e same reasoning applies to any odd vertex
network. Th erefore, a network can have, at most, two odd vertices in it. And these
must be the starting and ending vertices.
Th e relevant point here is that Euler's
brilliant puzzle made it possible to look at the relationships among elemental
geometric systems in an abstract fashion in order to determine their structure
and their implications.
Corfe Castle Crossing, Gibsons
Richeson ( 2008 : 107) puts it as follows:
The solution to the Konigsberg bridge problem illustrates a general mathematical
phenomenon. When examining a problem, we may be overwhelmed by
extraneous information. A good problem solving technique strips away
irrelevant information and focuses on the essence of the situation. In this case
details such as the exact positions of the bridges and land masses, the width of
the river, and the shape of the island were extraneous. Euler turned the problem
into one that is simple to state in graph theory terms. Such is the sign of genius.