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.