Königsberg

Legend has it that the 'gentlefolk' of Konigsberg would spend their Sunday afternoons walking around the town. It is believed they were attempting to cross each of the seven bridges, that join the north and south of the river to the two islands, once and once only without retracing their steps.

You might find it easier to study a more diagrammatic representation below (green dots represent the land to the north and south of the river and blue dots the two islands):

Can you succeed where the people of Konigsberg failed, and solve the problem of the seven bridges? If not, can you explain why not? If you can, explain how you know that you have all the solutions?