The Puzzle of the Map: Seven Bridges of Königsberg (today Kaliningrad)

I'm bad at math. Like, really bad. This is hard on my father who is a mathematician with the degrees to prove it. He keeps trying to get me interested in math, and his latest attempt is to tell me about the problem of the seven bridges of Königsberg, today Kaliningrad, Russia.

Here's the issue, and a colourful 1732 map of the city available for purchase here (as always no affiliation between me and the seller of any kind, simply giving credit where it's due), to help illustrate it.

As you can see, the city in 1732 had seven bridges, which I've highlighted in yellow. Residents used to like to play a game. They would try to take a stroll around the town attempting to cross each bridge exactly once and start and end in the same spot.

This is the point where you may want to take out a piece of paper and try to sketch this out on your own. 

Meanwhile, I can also show you this fabulous map of the city from sometime in the 1580's before the city's seventh bridge was built. This map is no longer for sale, as it was sold by Sanderus Antiquariat, as you can see here. It looks like if there were a seventh bridge on this map, it would be obscured by the couple standing in the foreground. 

WARNING

SPOILERS FROM HERE ON

One of the wonderful things about the beautiful map above, is that having six, instead of seven bridges, is basically the only way it would be (sort of) possible to accomplish this bridge-walking map puzzle. It's impossible to do it with seven bridges, and possible with six bridges if you end up somewhere other than where you've started, and this is where the math comes in.

My father suggested I write about this because of the famous mathematician Leonhard Euler. Euler essentially reduced the problem to a graph. Now, this is where my lack of mathematical knowledge shows, but from what I understand, you have to almost forget about the bridges for a moment, and imagine the various points or nodes you'll be going to. Looking at the map above, imagine for example that you start at the church on the central island, you can cross to the south bank of the river, use the other bridge to get you back to the central church, then cross to the north bank, walk along it to get back to the central church, cross to the orchard in the east, and then back up to the north bank.

Like this:

Euler explained that in order for the puzzle to work, each location, point or node (the central church, the north and south bank and the orchard, must have either exactly zero or two points of contact with each other. If there are more, and (I think) especially if it's an odd number, then it doesn't work. 

Anyway, I don't want to pretend to know anything about math, so I'll happy link to a few good sources of information about the puzzle. Here, here and of course, wikipedia, here.

Meanwhile, to soothe your frustration, enjoy these beautiful maps. They're really great.