## Introduction

Growing up I read a number of short articles about *The Seven Bridges Of Königsberg* written for children. I was intrigued and already hooked on math! I wanted to know more, but at the time not much was written on the problem and not much could be found in the local library. Now I can look even deeper into the problem with the information gathered below. Even if you are not interested in graph theory but are interested in mathematics, I suggest you take a look into a most intriguing problem.

## Problem

Way back in 1735, Euler heard about an interesting problem that the town of Königsberg was facing.

At the time, Königsberg was a city in Germany, and the city was built around a river called the Pregel River. This city thrived with its merchant economy and part of the reason that it did so well was because it was structured in a particularly interesting way. There were two large islands in the middle of the Pregel River, and they were each connected to one another, as well as to the two riverbanks on either side, which comprised the majority of the city. And how were they connected? By bridges, of course! Seven of them, in fact.

The citizens of Königsberg spent their Sundays walking around town, enjoying their beautiful city. In the process, they came up with a game — which, as it turned out, proved to be incredibly difficult to accomplish. The goal was to walk across all of the seven bridges crossing the islands only once, without ever repeating a single bridge in the course of one’s walk.

At first, when people asked Euler to solve this problem, he brushed it off, thinking that it had nothing to do with mathematics, and therefore wasn’t really worth his time. But the more that he thought about it, the more intrigued he became. In a letter to a mathematician friend of his, he wrote:

This question is so banal, but seemed to me worthy of attention in that geometry, nor algebra, nor even the art of counting was sufficient to solve it. In view of this, it occurred to me to wonder whether it belonged to the geometry of position which Leibniz had once so much longed for. And so, after some deliberation, I obtained a simple, yet completely established, rule with whose help one can immediately decide for all examples of this kind, with any number of bridges in any arrangement, whether such a round trip is possible, or not….

Letter Euler wrote to the Italian mathematician and astronomer Giovanni Jacopo Marioni

He was hooked. Euler was *so* entranced, in fact, that he ended up writing a paper later that year that would contain a solution to the bridge problem. But before we understand how Euler solved this problem, we need to cover a few basic graph theory rules first. ^{1}

## References

^{1} ⭐ Joshi, Vaidehi. “Königsberg: Seven Small Bridges, One Giant Graph Problem”. 2017. *Medium*. https://medium.com/basecs/k%C3%B6nigsberg-seven-small-bridges-one-giant-graph-problem-2275d1670a12.

## Additional Reading

al Conocimiento, Ventana. “Euler And The Königsberg Bridge Problem | OpenMind´s Puzzles”. 2022. *OpenMind*. https://www.bbvaopenmind.com/en/science/mathematics/euler-konigsberg-bridge-problem/.

“Activity: The Seven Bridges Of Königsberg”. 2022. *mathsisfun.com*. https://www.mathsisfun.com/activity/seven-bridges-konigsberg.html.

“Eulerian Path – Wikipedia”. 2022. *en.wikipedia.org*. https://en.wikipedia.org/wiki/Eulerian_path.

“Eulerian Path And Circuit For Undirected Graph – GeeksForGeeks”. 2013. *GeeksForGeeks*. https://www.geeksforgeeks.org/eulerian-path-and-circuit/.

Joshi, Vaidehi. “A Gentle Introduction To Graph Theory”. 2017. *Medium*. https://medium.com/basecs/a-gentle-introduction-to-graph-theory-77969829ead8.

Paoletti, Teo. “Leonard Euler’s Solution To The Konigsberg Bridge Problem | Mathematical Association Of America”. 2022. *maa.org*. https://www.maa.org/press/periodicals/convergence/leonard-eulers-solution-to-the-konigsberg-bridge-problem.

Patowary, Kaushik. “What Mathematics Has To Do With The Seven Bridges Of Königsberg”. 2022. *amusingplanet.com*. https://www.amusingplanet.com/2018/08/the-seven-bridges-of-konigsberg.html.

Sethi, Rahul. “The Seven Bridges Of Königsberg”. 2020. *Medium*. https://medium.com/stamatics-iit-kanpur/the-seven-bridges-of-k%C3%B6nigsberg-268f73122e82.

“Seven Bridges Of Königsberg – Wikipedia”. 2015. *En.Wikipedia.Org*. https://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg.

St. Clair, Natalya. “Graph Theory Problems, The Seven Bridges of Königsberg Problem”, 2015. *mathcircle.berkeley.edu*. https://mathcircle.berkeley.edu/sites/default/files/archivedocs/2015/lecture/Graph%20Theory%20Intermediate%20I%20and%20Ii-2.pdf.

⭐ I suggest that you read the entire reference. Other references can be read in their entirety but I leave that up to you.