Using topological abstraction he simplified the problem from this:
into the abstracted graph here:
Where each vertex is a land mass, and each edge is a single bridge. Then, using arcane Eulerian path maths he worked out you can't have a path between all nodes using each edge once. To simplify slightly, this is because every node bar two (the first and last) must have an even number of connected edges; pairs of one to get in and one to get out. However, as seen above, this example has all four nodes with odd numbers of connected edges, thus making the problem impossible. In this foul swoop he conjured up the sorcerer's art of graph theory, still plaguing CS undergraduates to this day. Read more
Interlude ~300 years
It's 2018 in the English city of Birmingham, now the Middle-Eastern exclave of Birmingstan, and I, probably the greatest visionary of the 3rd Millennium, am on a jog or something. Never mind I was playing Pokemon GO. It's still fun guys come back. Anyway, I came into the city's canal wharf area bit, where four canals all merge into one and there's a crane, the sea life centre and thousand or so pubs. My autism drive kicked in, and I decided to make a list of the 10 best bridges on Brum, which then morphed into developing a tour of the 8 bridges of the wharf area bit. I gave up on working it out out right there because I know could just work it out when I got home. I got home. On google maps I located the wharf area bit and screen-grabbed it into GIMP.exe where I could draw lines over it. Here's the map of the area, with the eight bridges marked on:
Now, in terms of turning this into a topological graph, the third most Easterly bridge can be discounted, as it doesn't really get you anywhere. After one layer of abstraction I had reached this point:
Now, at this point I had still no idea what I was doing, I knew about the Königsberg problem and reckoned the easiest way to figure out a route would be to turn it into a proper graph and go from there, using Euler's rules. However, upon one more layer of abstraction I shat my pants:
Fuck. It's literally the exact same. Just rotate it ninety degrees and it's identical. By complete coincidence the 8 bridges of Brum translated exactly onto the 7 bridges of Königsberg, topologically speaking. However, unlike in the former Prussian city, the bridges of Brum still stand, and you can go there today and try to walk the impossible route; don't worry if you get tired, you'll be within 5 foot of a pub wherever you are.
I'm copyrighting "Bridges of Brum" btw.