Seven bridges of Konigsberg - solution

Have a go at the problem. Is it impossible?

I'm afraid that this one is a cheat, and it IS impossible. The fun part is working out why.

This problem started mathematicians thinking in a different way. It's not the distances or angles that matter in this problem, it's the relationship between the banks and islands and bridges. This type of mathematics is called Topology. In fact, you could think of the banks and islands as dots, and the bridges being lines joining them. That means that we can think of the diagram on the right.

Now, whenever you arrive at a dot by one bridge (or line), you have to leave it again by another. That means that if the problem is possible, there must always be an even number of lines at each point, apart from the start position and the end position. If you count the lines at each point, there are 5 lines at one point (the left-hand island) and 3 at all the rest. That means no matter where you start, there will always be at least one bridge that you can't reach.

You can solve the problem if you remove one bridge. For example, if you remove the bridge between the islands, there will be 4 bridges (or lines) from the left-hand island (or dot) and 2 from the right-hand one. The top and bottom banks both have 3 bridges. So if you start from one bank, you can walk onto, and off, the islands, ending up on the other bank.