In the early 18th century, the city of Königsberg (now Kaliningrad, Russia) was a bustling Prussian port built around the Pregel River. The river split the city into four distinct land areas — two riverbanks and two islands — connected by a total of seven bridges.
The citizens of Königsberg enjoyed strolling through their city, and a particular challenge became a favourite topic of conversation:
Is it possible to take a continuous walk that crosses each of the seven bridges exactly once?
You could start anywhere, end anywhere, and walk in any order — but you could not cross the same bridge twice.
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| Map of Königsberg in Euler's time showing the actual layout of the seven bridges, highlighting the river Pregel and the bridges (Image: Wikipedia) |
The layout
Imagine standing on one of the riverbanks. From where you are, you can see bridges leading to both islands, and from each island, more bridges leading to the other island and to the opposite bank. The arrangement is symmetric enough to tempt you into thinking a clever route must exist — yet tricky enough that many attempts end in frustration.
The puzzle is purely about the connections:
- Four land regions (north bank, south bank, and two islands)
- Seven bridges linking them in various combinations
No distances, no time limits — just the rule: cross each bridge once and only once.
Why it matters
At first glance, this is a pleasant riddle for an afternoon walk. But in 1736, the problem caught the attention of Leonhard Euler, one of history’s most influential mathematicians. His analysis transformed the question from a local curiosity into a new way of thinking about space, movement, and connectivity — ideas that would eventually form the basis of graph theory and influence fields as diverse as network design, logistics, and computer science.
Your turn to explore
Before we discuss Euler’s reasoning or the general principles behind such problems, you can try the challenge yourself. Thanks to modern technology, you don’t need to travel to Kaliningrad — you can attempt it interactively here:
Play the Seven Bridges of Königsberg puzzle
The rules are simple:
- Start anywhere.
- Cross each bridge exactly once.
- You may end anywhere.
Take your time. Try different starting points. See if you can find a route — or convince yourself that none exists.
Coming next
In the follow‑up post, we will examine how Euler reframed the problem, the mathematical structures he introduced, and the precise conditions under which such a walk is possible. That discussion will not only settle the Königsberg question but also open the door to a whole class of problems you can apply to maps, networks, and even puzzles of your own design.
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