- Euler finds out the solution
- Graph theory never gets invented
- We never have telecommunications or GPS
this post was submitted on 18 Jul 2025
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Is Köningsberg donut shaped?
A problem with this is that the river presumably goes all the way around the earth. Otherwise you could just travel west until you found its end. You really need a donut shaped earth, a sphere doesn't help much
But the river running round the whole planet does not matter in this case.
You run into it on the planet backside and then need another bridge, right?
What about an opposite bridge where you cross under the river? Some sort of tubular subterranean structure. We could call them opposite bridges.
That would make the earth a donut lol and would work!
Won't be in Königsberg anymore though, so that bridge won't count
Surely it a river doesn't go all the way around the earth. Rivers typically have one (or many) start points, where they are surrounded on three sides by land, meaning it's possible to cross from one side to the other. Otherwise it's just a strait or channel.
However, that assumes you are not on the land in between a fork in the river. In which case you would have to cross a bridge outside of Königsberg, and we might have to expand the problem to crossing every bridge on the continent once.
I mean that might be theoretically possible with some geothermal energy input at some point, but practically speaking all rivers I've observed do not do this.
It seems likely that there is land between the source and the mouth.
It should be fairly easy for someone to visit the sources of the Elbe to test this presumption with real science.
When you go to sleep tonight, Euler is gonna be under your bed.
but are there an even or odd number of bridges allng the circumnavigation
yes
Crossing oceans, which are continuous with the river, seems to make this about as meaningful at tunneling under the river.
I feel that leaving Koningsberg is already breaking the rules.
The original idea was taking a walk before a meal, so maybe if you were a really fast walker...
Don't let the sailors tell you you have to cross oceans to circumnavigate the globe! Just walking around the headwaters of the Pregolya River is equivalent.
While this would have worked in Euler's time, the puzzle in fact became unsolvable around 1873 when canals were built in the Masurian lakes effectively connecting a tributary of the Pregolya with a tributary of the Vistula to the south and cutting of this route. I assume the canals were constructed by mathematicians trying to close this loophole. Maybe hopping across lock gates when they're closed doesn't count as a bridge tho?
TBF, does the problem specifically state it has to take place on Earth and not some theoretical planet with contiguous landmass?
Why not just take a boat over the river? Last time I checked boats were not bridges.
Ahem Greetings. Can I have a go at it?
This must be the true reason the whole city got razed.
Allegedly, the Russians wanted to negotiate about Kaliningrad in 1990 but Germany was more horrified than interested. Straightforward decision at the time. No one wanted a reprieve of the whole Polish Corridor thing, especially without even Germans living there. Rather a mistake in hindsight.
especially without even Germans living there
Germans were brutally deported after WW2
I think there was a plan to settle volga germans there and re-recreate the volga german republic, of course only after the OG volga german republic thing failed.