How the Königsberg bridge problem changed mathematics - Dan Van der Vieren

View full lesson: ed.ted.com/lessons/how-the-kon...
You’d have a hard time finding the medieval city Königsberg on any modern maps, but one particular quirk in its geography has made it one of the most famous cities in mathematics. Dan Van der Vieren explains how grappling with Königsberg’s puzzling seven bridges led famous mathematician Leonhard Euler to invent a new field of mathematics.
Lesson by Dan Van der Vieren, animation by Artrake Studio.

[@isaacsmith6482]

Just remember: when you can't solve a problem, invent a new field of mathematics to explain why you can't solve it ;D

[@alexeikafe5388]

person211 or ask the soviets for help

[@kevinzhang5983]

1+1 oh no I can't solve it, so I defined it, 1+1 is now 4

[@anirudhpj8875]

No I think you are not really appreciating the genius of his discovery. The problem cannot be solved using normal mathematics. It requires something to be built up from pure logic. When he did this he found out that he can call it a new branch of mathematics because there is no other fields that this depends on. I don’t mean offence to you but would like you to know that he just did not do any gimmick and called it new maths. Euler was a great mathematician.

[@hoanglong5824]

Kevin Zhang you must also make sense bro

[@syedshahrukhraza2923]

@@anirudhpj8875 I think the other guy is joking. But you're right, this was absolutely ingenious by Euler. The "why" is the amazing part, not the answer itself. The explanation of nodal degrees is simply stunning.

[@adamn7409]

So if I'm struggling with a math problem,I can just bomb it?

[@ffggddss]

Only if you're the Soviet Air Force in WWII.

[@noname-sg6qx]

Or You could invent a new field in mathamatics

[@duckymomo7935]

You can invent a new field of math You can also just impose some more restrictions, which is similar to bombing.

[@thalespro9995]

Or u could start a war against that place

[@mirunastoica320]

yes

[@TheOswald42]

Königsberg and the seven bridges....sounds like a new disney movie...

[@awesomemantroll1088]

Since Disney owns everything, everything sounds like a Disney movie.

[@TheArklyte]

In alternate reality where Disney doesn't treat its vieweres as morons, why not?

[@ynntari2775]

And Snow White's story happens to take place in Germany

[@MrBubuStation]

It does even more when you translate the name literally to kings mountain

[@nazeefa2]

I remember watching this video two years ago and being so fascinated by the puzzle! Fast forward two years and here I am studying Graph Theory in my Mathematics degree... :)

[@virave]

Same, I'm in my second year of engineering and here I am studying this for my exam tomorrow

[@mikecostanza303]

Has minesweeper come up in it? It seems as if the two could be related.

[@blakeceej]

annd it became my thesis field of study.

[@ashharazim2223]

i am studying it for my CS degree, Graph Theory is Amazing

[@smallfryskilledge1550]

@@mikecostanza303I’m not sure if minesweeper was originally made with graph theory in mind but it most definitely can be used in game design in games like minesweeper or even map design for games.

[@castonyoung7514]

I knew there would be an out of the box solution, but blowing up two bridges goes just to far.

[@miko5742]

Blowing one bridge is fine, but two bridges? Like, come on! You have one job

[@danielwang4917]

too*

[@TeamTwiistz]

Dammit I spent 10 Minutes actually attempting to solve this one instead of being lazy!!

[@quarkyquasar893]

Lol, me too and as soon as I played again it said "Give up?" so I paused and tried again, but them after giving up it said it has no solutions. fml ;-;

[@m13m]

I already did the Hard work in the course i took in school on discrete mathematics?

[@Conglomeration]

omg I'm a subscriber

[@dionje5TV]

20min

[@dionje5TV]

+dionje5TV and i always thought i Know this isn't possible but there Must be a Solution if they Ask is that.

[@thegreatkwyjibo5529]

If you go the long way around the world then it's possible

[@abadlydrawnsnowman1648]

lol

[@All3me1]

😂😂😂

[@MichaelS95]

If you can't cross the water without a bridge, it's still not possible.

[@ancbi]

hopefully he will be able to get around the source of the river on some mountain without having to actually cross any bridges along the way.

[@Sidiciousify]

theres two ways to do it if i travel around the entire world.

[@frosted1030]

The answer is obvious.. you swim across, once.

[@woosanminsung7743]

Lmao 😂🙌🏻

[@prithabhattacharya8532]

haha good one!

[@helmiazizm]

Or just build another bridge

[@vardhanr8177]

+thanks haha LOL!!!

[@mimimomooxo391]

+thanks nah, building a wall is much better :p

[@ReySkywalker2]

"Give up? You should, it's not possible!" Oh you could have told me that before I paused the video and spent 10 minutes trying to solve it... Thanks... 🙃

[@lityum2779]

If someone asks you question like that, its 99% impossible to solve.

[@miguelalonso7520]

"Think about it for a moment." 10 minutes are many moments!

[@8bit_pineapple]

You still could have solved it by determining it is impossible. I paused the video for 10-15min and made a proof, though it wasn't as nice as the videos. My reasoning was that, because of symmetry the starting positions 1,2, 7 and 6 are equievlent, the same for 3 and 5. Which means checking just the starting positions 1, 3 and 4 actually checks all starting points. So I checked them and concluded it was impossible.

[@Eshiay]

I just came to the conclusion that you couldn't enter and exit the city 3 without breaking the rules. There were 5 bridges in the middle, and the only way that an odd number of bridges like that on a land mass would be able to be crossed with those rules there couldn't be any other bridges on other land masses. Probably a little wrong with, but I was right in the fact it was impossible.

[@barnabaslee2333]

Lord Plagueis lol

[@tinman2584]

I just looked up Konigsberg on Google maps its very easy to find. Also, the two bridges are gone just as they said on the video but there are now two more bridges on the other island! So now its impossible to solve again.

[@untruelie2640]

In German it's still sometimes called Königsberg, however the old city doesn't exist anymore. It was completely destroyed during and after the war. Kaliningrad was build almost entirely from scratch. Only some parts of the old fortifications, the cathedral and the nearby tomb of the philosopher Immanuel Kant survived. The german population fled the city or was expelled - now only former soviet ethnicities like Russians, Ukrainians, etc. live there and the area is an exclave of Russia between Poland and Lithuania.

[@jonas8975]

I also just looked it up and it seems so that there built another bridge on the bigger island and now you can solved it again quite easily.

[@NoriMori1992]

As of 2021: "Two of the seven original bridges did not survive the bombing of Königsberg in World War II. Two others were later demolished and replaced by a modern highway. The three other bridges remain, although only two of them are from Euler's time (one was rebuilt in 1935). Thus, as of 2021, five bridges exist at the same sites that were involved in Euler's problem. In terms of graph theory, two of the nodes now have degree 2, and the other two have degree 3. Therefore, an Eulerian path is now possible, but it must begin on one island and end on the other."

[@clawcross]

It will be returned to germany or poland aftet putin goes away and they will solve that problem

[@thor8152]

Königsberg will be remembered forever,because there is a german dish called "Königsberger Klöße",which is basicly Meatballs with Capers

[@NonSurvivorOne]

Klopse.

[@jalchi8367]

and because its a enclave of russia in the middle of europe

[@justinos2990]

@@NonSurvivorOne *Klöpse xd

[@MrExoticSnow]

@@justinos2990 Klopse ist kein falscher Plural.

[@Icetea-2000]

Jalchi That no one really cares about, with a different name

[@angieengi]

That town should be famous for not only this riddle but because of the fact that it is the town where Immanuel Kant was born. He also lived there till his death.

[@Michael-Hammerschmidt]

Andjela Popov Seriously!

[@alejandroojeda1572]

Wasn't he almost terrorized of Visisting other places? I've Heard he memorized the Mao of London but never went there

[@TheAutobotPower]

But hey, it's just a theory... A GRAPH THEORY! -I couldn't resist-

[@AnujMishra-jj5fc]

thanks for watching, i guess

[@MiahooJunk]

And.................................................. CUT!

[@emperoriziko4414]

Its a wrap everybody......!!

[@justlikedirt9634]

Insert meme here

[@YogeshwarSinghSisodiya]

this is used in computer science... have you ever heard of Graph Search...???

[@Aman-ix5tg]

Wow, I didn't know that Euler made the graph theory. All hail Euler!!

[@abdullahenaya]

Know*

[@zolfjustice]

+Abdullah Craft *no

[@abdullahenaya]

+Supah Doctor Muffin what? It's know not no

[@kjrbh]

+Abdullah Craft *no

[@Sunny-mo7fr]

#aman....whats the use of graph theory.... ...hope its not playing with bridge riddles.

[@RealYellowbeard]

My father showed me a similar puzzle 50 years ago. A single rectangle, bisected horizontally, with the upper half bisected into two even halves and the bottom half segmented into three equal boxes. I never knew this form of math had a name, and never knew you could prove that it couldn't be done. I used this video to come up with the node diagram, and proved that all the degrees were odd. (9, 5, 5, 3, 3, 3). Thank you for a most enjoyable diversion!

[@doodelay]

The fact that Euler didn't consider this a math question REALLY highlights how much math has matured. Wow

[@non-pe8xn]

If you did an in depth video teaching like maths and stuff I would actually watch it and it would be really really helpful for school and stuff

[@RochesterOliveira]

I have one word for you: Numberphile

[@gekylafas]

Also, 3Blue1Brown

[@8bit_pineapple]

Don't get me wrong, Numberphile is great, but it's mostly for introducing topics. For learning math Khan Academy is way better.

[@zaigamakhtar9237]

if only my math professor could explain this as this video did, I probably would have actually listened to him. please make more videos like this which simplifies complex topics with the aid of animation, we really need them.

[@ericwang6826]

Thank you Soviet Air Force, for creating a Eulerian path in the bridge problem no one actually knew about.

[@fishyeverything8530]

10th like to this comment

[@LethalPigeon7]

This is always a bit awkward.

[@Fatortu]

But they also destroyed the whole city. The island is a park now. It's not as important to get there anymore

[@ThePrikoki]

In Soviet russia the math solves you ( with a bomb).

[@thCentury-rx9di]

+Toxq Jam lol

[@tobiaskumutat4723]

Königsberg may also have gained some sort of popularity, because of Immanuel Kant, the famous philosopher having lived there as well. At least that is the reason why I know it. Greatings from Germany. 😁

[@xeonn01]

I love stuff like this that mixes history and math/science. Great video!

[@anukulkumar219]

No one back then could have even imagined the impact of the problem we have in modern day mathematics and computing..sometimes approaching a question is more important than the answer..thanks to mayor and euler..🙏

[@shine0nme135]

thanks a lot you just saved my motivation to do my discrete math worksheet, ted ed truly never disappoints

[@navalkumarshukla9447]

I appreciate the way you guys use animation to explain the concept.

[@TheAmir259]

1:03 - Give up? You should, it's not possible. Glad I didn't even bother pausing the video and try to solve it at all!

[@holydukk]

And that's how you cheat in mathematics, kids.

[@GarketMardener]

Ropsana Khanom ARE YOU LITERALLY NEW TO THE INTERNET

[@johnroy5169]

+GarketMardener Now now, let's use our inside voices here 😂😂

[@RK-ep8qy]

+GarketMardener well you spelt it wrong you tweed: it's what happens when your knowledge comes from the Internet

[@GarketMardener]

Ropsana Khanom dude i am aware of what the terrorist verbally spam out loud, and why. It's a joke. I am not trying to offend anybody with this anyway. also, unlike you, i can separate legit info from memes.

[@johnroy5169]

***** ok ok ok let's all hold hands and talk about how much me love each other, let's not hate

[@Aayush12211]

One of the best things I have seen on youtube in a long time.

[@robbyjulian311]

Whoa, along with Gauss, Euler has appeared many times in my classes in my electrical engineering major. Those dudes are brilliant.

[@rickrose5377]

And an interesting aside: Immanuel Kant lived his entire life without traveling more than a few miles from his native Königsberg.

[@michaelzheng5250]

Honestly, the Russians got the best solution, rename the city so that “Königsberg” doesn’t even have any bridges to begin with.

[@TheJukkis]

Make Kaliningrad Königsberg again ( ͡° ͜ʖ ͡°)

[@derherrdirektor9686]

Kaliningrad = King's Mountain; Königsberg = King's Moutain. You get the jist? it's not renamed. It's translated. That's an error in the video.

[@ousarlxsfjsbvbg8588]

Der HerrDirektor Kaliningrad does not mean kings mountain

[@Quintinohthree]

@@derherrdirektor9686 Grad means city or castle, Kalinin was the president of the Soviet union untill his death in 1946, after which the city was renamed in his honor and is derived from kalina meaning guelder rose. Nothing about the name is translation.

[@michaelzheng5250]

Der HerrDirektor Kalinin = a Soviet politician, Königs = Kings, thus Kalinin =/= Königs

[@cmdrtianyilin8107]

My A-hole elder sister asked me to solve this without any assistance and even giving me any prior knowledge and I was stuck with it for days. Thanks TED-Ed for the explanation.

[@cyrilcabo6646]

this video actually taught me a lot more on graph theory than my prof did.

[@moniquetabarnero692]

This is a cool video, hope you make the Hamiltonian too. Thanks. :))

[@runepower909]

Interesting. Hopefully, this channel will give me the inspiration I need to become a more productive person.

[@endrankluvsda4loko172]

Eh, being productive is over rated. Being kind and patient are better things to strive for :)

[@catface7133]

This is an old puzzle I learnt in primary school, where you draw a rectangle made up of 5 boxes. 2 on top, 3 on bottom and try to draw a line that passes through all sides only once. It's impossible but fun watching people think they've solved it

[@HIDlarissaTERRY]

lovely presentation!

[@SquareSquidStudios]

I found myself trying to solve it anyways~

[@rosastarbuxemburg]

i actually thought i found a correct answer :D

[@namanvashishth1284]

Mee too..... congratulation guyz....

[@mr.goblin3935]

I solved it. You take a boat

[@someweebwatchingcartoons4456]

same

[@snowfloofcathug]

I tried, but within seconds I realized it was impossible because they were all odd, and then he went on to explain just that xD

[@JoelJames2]

Huh, looks like learning Euler Paths in class saved me the time of wasting several minutes trying to solve that question :P

[@simplyerik41]

I have an exam on this next week, thanks Ted-Ed!

[@akshay5895]

Just learning Graph theory at School! This explains it in a much better way! Thanks!

[@LeviPenell]

my grandfather was from Königsberg :D sadly he died last year, so I can't ask him if he crossed the bridges ^^

[@annalittle4857]

I went to math camp over the summer and we covered stuff like this and it was actually a lot of fun

[@ASLTheatre]

My brain was picking at this puzzel off and on for days. Glad to finally know the answer.

[@kevinmcguire2040]

What is fascinating about this video is that as a Project Management professor, I paused the video at 2:11 and made the connection between the geography and a project management network diagram both being "graphs". For you PMs out there, you always had it explained to you that in looking at a network of tasks, you could go through the node or around it but not both as that was redundant. But as the networks get bigger, this becomes harder and harder to understand if you have over-constrained something. Here you go folks: Count the ins and the outs of each node. Get rid of one of edge 4 and edge 5 and one of edge 6 and edge 7. Thank you Mr. Euler. Your genius transcends the generations.

[@JM-us3fr]

Why do you say his name (Euler) correctly (Oi-ler) in the beginning, but pronounce the thing named after him (Eulerian path) incorrectly (You-larian path)?

[@raphielohnef4678]

Well, there can't really be an english version of "Euler" because it's the guy's name but the term "Eulerian path" was invented and can be pronounced as defined.

[@MissJCfaustino]

Graph theory is really my jam. 😍

[@dribrahimel-nahhal2477]

Great Vid!. I enjoyed it so much. It is highly informative and simplifying scientific graph theory and its relation to the graphs data structures in Computer science. Thanks for posting

[@MsClelia]

We spent weeks on the Euler theory in maths and you just explained it in 4 minutes thanks 😂

[@jannikdrescher1400]

I only konw Konigsberg due to their high specified meal: The Konigsberger Klopse^^

[@-.._.-_...-_.._-..__..._.-.-.-]

"Give up? You should have." --Dad

[@luminastarcrest7948]

I watched this video years ago, and now I'm studying Graph Theory in college and my professor used this video for the introduction :D

[@glory6998]

I 💙 that person voice🗣....it relax my mind....thank u TED-Ed for those great videos

[@TomJo-tu5rr]

The real question here is, Would it be considered cheating to walk over six of the bridges and then go around the source of the river in order to avoid crossing one bridge twice? Also thanks for the great video, and greetings from Germany(~300km/~180miles) from Königsberg

[@neighbourskid]

who are you so wise in the fields of science?

[@TomJo-tu5rr]

I made this comment like 5 years ago. I have absolutely no recollection of this.

[@neighbourskid]

@@TomJo-tu5rr I'm the only one to find this comment

[@user-js8tm5ff4r]

I always come to these videos hoping that I'd learn something new. End up not understanding 90% of them😂

[@abadlydrawnsnowman1648]

same

[@kittenmeister7858]

מה קורה?

[@red__guy]

there is a stereotype in Israel that stupid people use a Hebrew (Jewish letters) users name/nickname/Facebook name etc on the internet. where other use English names on the internet. Same as OS language.

[@user-js8tm5ff4r]

Omer Neu im not aware of such stereotype

[@user-js8tm5ff4r]

Clorox Bleach הכול סבבה מה ניש

[@carlos32195]

awesome info never knew who came up with the idea, I remember learning about graphs from the data structures curse I took at collage.

[@lexik4603]

Usually I skip past the few seconds it gives you to try and figure it out, but the ONE TIME I decide to actually try it ends up being impossible.

[@vaibhavgupta20]

didn't know that Euler is pronounced as oiler.

[@DS-Pakaemon]

yeah , or is it just us, with our Indian English

[@apw3ner]

+Debangsu Sarkar no it's a german name. "deutsch" (german for "german) is pronounced "doitch"

[@loreleihillard5078]

and "Europa" (Europe) is "Oi-rope-ah"

[@rainnne9786]

Vaibhav Gupta Did someone say OIL?

[@narmonteam9417]

rvb rvb FREEDOM

[@evehellod9776]

Who else doesn't get what he says because they're too dumb to understand but watches anyway because it's interesting? Just me?...

[@dominikastrauss5208]

Yeah...

[@superawesomecaptainmcfluff9506]

It is not that tough to understand, just note stuff down!

[@kvlpnd]

Its not that much tough. Atleast for me. :P

[@Nestor.555]

FeelsBadMan

[@Nestor.555]

But yeah, watch it a second time and you'll probably understand it :)

[@pebbles7003]

I have exam of graph theory 3 days later feels good to watch this. Seeing mathematics used in something 😀

[@TanmaiNiranjan]

holy cow,i did a presentation of this @ school last year and got me a trophy!!!!!!

[@tomsmith9707]

You know, the Earth is round, so you just walk the other way

[@pseudoproak]

Tom Smith There is something like oceans which you cannot walk over. Gigantic areas covered with seemingly blue and undrinkable liquid seperating our continents. You can cross the big places you can walk over, the continents, because there is solid ground.

[@elias486]

When you hyperfocus so hard help to invent a new field of maths by accident

[@nyssamurphy6103]

There was a version of this in a Maths test i took a while ago! It must've been slightly different because i could solve it but it was similar!

[@whatcoconut7871]

Love this. !! We are solving modern problems in computer vision, NLP and robotics using a field of maths, which was developed because one mayor was obsessed with bridges 300 years back.

[@paolorizzo7677]

Who knows Konigsberg for the almighty Immanuel 😎☝ ???

[@derschmiddie]

Königsberg isn't that hard to find on a map. It's just called Kaliningrad today or Калинингра́д in Russian and has half a Million Inhabitants.

[@championbally7570]

very good explanation. thanks

[@muhammadumair7377]

I was studying state space graph which led me to this and i'm not disappointed

[@kalvinsurtijo4313]

hello

[@Conglomeration]

hi

[@TheFranchiseCA]

Is it me you're looking for?

[@nitro5401]

You just have to follow the river to the source, and to bypass it. I should maybe phonecall this Euler.

[@marie-lynnissa656]

i just love this channel

[@joryjones6808]

You know it’s going to get good when you hear the name Euler.

[@carsontroeh127]

"you'd have a hard time finding the medieval city Königsberg on any modern maps" HMM I WONDER IF IT'S THE RUSSIANS' FAULT OR SOMETHING

[@claypl7021]

Królewiec?

[@avivastudios2311]

I watched it this in highschool years ago. It was nice.

[@ekosetiawan_indo]

Wuawwww, watch it for several times and still impressing me

[@muhammadvitra2716]

konigsberg now called Kaliningrad

[@zolderkamercommunist9227]

Have you watched the entire video?

[@SexyArty]

Konigsberg is long time gone. There is another city built on it's place now. Abomination that is all soviet architecture, which they now call Kaliningrad. I don't mind ruskies ruining their own cities, but why turn once beautiful Prussian capital into... whateverthefuck it is now? The worst thing is soviets didn't even try to repair the city, they just dismantled what was left for building materials. Upsets me a lot.

[@zolderkamercommunist9227]

+SexyArty ok

[@Rocsanse]

+SexyArty At least the castle is being reconstructed.

[@cobaltdust22]

Koenigsberg is gone due to Adolf Hitler's mesmerizing Germans into obedient and suicidal force, to kill and destroy many places around Europe (and especially in USSR) . And due to British calousness and cruelty. Because it is not Soviets who destroyed this city but British RAF with Air Chief Marshal Arthur "Bomber" Harris in charge.

[@TickedOffPriest]

It was cheap of Ted to give a riddle that cannot be solved.

[@smallfryskilledge1550]

I’m taking a Discrete Math final exam tomorow, I wish we had time to look at real life applications of math in class like this. Very cool stuff, this problem was just the right challenge to review right before the exam.

[@aviralsinghal5937]

Damn Same! Even I have discrete math in a month and this practical application makes it so much more fun! Do you mind if I get to talk to you a bit more about discrete math and the combinatorics side of things?

[@smallfryskilledge1550]

⁠​⁠@@aviralsinghal5937sure, my student sized brain forgot a lot of the stuff, but if you have questions about discrete math feel free to ask.

[@NaturallyAnnaMarie]

Can you please do a Ted video on anxiety? I would be really interested to watch!!

[@Pikazilla]

spoilers; it's impossible. now you don't need to waste hours to solve the puzzle

[@Ghost-kr9nr]

Its like a trap.

[@navaryn2938]

"you'd have a hard time finding Königsberg on a map" Bruh not if you did at least elementary school in europe

[@vdagr8795]

Yeah, but he was probably saying that the city's name now is Kaliningrad

[@ramshankaryadhunath9302]

This was brilliant! Much better than my discrete math teacher!

[@jitendersingh5205]

This video can through your fear of math out from your body very brilliant video

[@jitendersingh5205]

Like please

[@AdamSmith-gs2dv]

I wish Kaliningrad was still German but I guess its too late for that.

[@Suyamu]

Why, did you want to live there?

[@Pilbsu]

+Centurion III One is an example of the creation of an imperial colony and the other is an example of the destruction of an imperial colony. Is it ethical for the Roman empire to colonize Londinium and for Russia to colonize Kaliningrad? It's a question of ethics, and the answer is simple: if it is right for London to be English then it is right for Königsberg to be German (or the reverse).

[@claypl7021]

I wish it was Polish. Or even better, Lviv.

[@Batnoodles]

Adam Smith there's still hope

[@daev3000]

I wish it still belonged to the Old Prussians. Too late. It's totally Russian now.

[@RinoaL]

0:40 sounds like an unimportant question that would only bother a mentally disturbed person. i dont see the need for finding such a path in the first place.

[@ayle1312]

Rinoa Super-Genius you don't sound like you've ever met a mathematician

[@sanjay.skumar7467]

This is an amazing video

[@eijiroukireeshima7222]

That's just awesome :3

[@gooseguse]

Too bad half of us already need a calculator for addition and subtraction alone... graph theory? ROTF.

[@blonded0532]

Königsberg is rightful German clay!

[@lewisprice8616]

Can you do the invention of the hamiltonian path soon?

[@DK-tv6rk]

Isa ito sa mga dahilan kung bakit hilig kong pag-aralan ang palatalangguhitan.

[@OkimeOlvx]

Give Königsberg back to Germany

[@osqq420]

will never happen

[@jakubcesarzdakos5442]

it should be rather Lithuanian...

[@g.55centaurosimp18]

Give it to Poland

[@3snoW_]

If the germans didn't want to lose lands to russians they shouldn't have started a war with them.

[@heinrichvonhahnrei7323]

@@3snoW_ if they had not you really think nothing would have happened?

[@kilinich]

Soviet bombing Königsberg? ORL? Common, TechEd, check you history book. Soviets bombing it like 4 times with few bombers but the Royal Air Force use 174 bombers first and 189 second time, dropping more than 500 tons of bombs and killing more than 4000 citizen, whole city was completely destroyed and rebuilded by Soviets. Shame on you, TechEd!

[@chattw6885]

Funny thing, on that snippit of the map this guy has in the hand, there is actually a town called Königsberg, its just the Hessian one and not the Prussian one. I found that funny because that is literally the only other place which is named that way and you happened to probably randomly include it.

[@moniquejhoienyllaxina290]

This thing actually showed up in our computer book and spent the whole class trying to solve it XD

[@nokostunes]

Swim over the rivers if you have to cross one again. Solved :P

[@bbrinergaming3694]

No. 280 view but who cares?

[@gilgameshe.e2079]

no one.

[@bbrinergaming3694]

Gilgamesh E.E207 Good that no on cares

[@gilgameshe.e2079]

can you logically explain the cause behind your comment in the first place?

[@bbrinergaming3694]

Gilgamesh E.E207 Bcause I want to comment for fun as it is midnight for me

[@Hoch134]

You must be fun at midnight.

[@glennowen4940]

I was lucky since, had learnt it in my Data Structure & Discrete Math class :P Straight forwardly knew it was impossible since Euler's circuit can't be used on odd nodes...

[@memine226]

miss your voice so much! finally you are back! Addison Anderson!