How To Actually Solve The Königsberg Bridge Problem?

A precursor to topology and graph theory!

Hemanth
Street Science

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The Königsberg Bridge Problem — An illustration showing seven brdiges connecting four landmasses. Island 1 (centre) is connected to the upper bank (north) and the lower bank (south) via two bridges each. Island 1 and Island 2 (east) are connected by a bridge. Island 2 is connected to the upper bank and the lower bank via one bridge each.
Illustration created by the author

The Königsberg bridge problem has its origins in the Russian city of Kaliningrad. Back when the problem originated, it was known as the city of Königsberg (Prussia). This city was cut into several pieces by the waters of river Pregel (Pregolya) flowing through it.

As you can see from the title image, the river Pregel cuts the city of Königsberg into an upper bank, lower bank, Island 1, and Island 2. Island 1 is connected to the upper bank and the lower bank via two bridges each. Island 1 and Island 2 are connected by a bridge. Island 2 is connected to the upper bank and the lower bank via one bridge each. In total, there are seven bridges.

As the residents of Königsberg traversed the tricky bridges in the early 18-th Century, a curious question popped up among them:

Given any starting point, would it be possible for a resident to travel through the city such that each bridge in Königsberg is used only once? If so, how?

Thus, the Königsberg bridge problem was born. It is now your turn to try and solve this little logic problem.

Spoiler Alert:

If you wish to solve this puzzle on your own, I suggest that you pause reading this…

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