A Maths Puzzle: Euler Trail and Solution

[Kazutoification]

Ah, so there are 16 lines.

[iZehro]

To me you never really gave us the answer you just told us the different ways of drawing through the boxes which to me comes fairly naturally....other words easily

[xXOrangutanXx]

Go through corners.

[DeshGTP]

Fold the paper

[TheNebraska402]

i thought of it as each box has four sides, and with that said it's able to be solved. what i don't get is why the middle rectangle gets passed through five times instead of only four. to me this is an easy way to make something impossible to solve. it isn't too hard to put in so many instructions and rules to make something unsolvable.

[911shortee]

@TheNebraska402 The puzzle is more meant to be thought of as a house, where each of the black lines is a wall, and each of the little red lines he added in @ 1:42 is a door, you must then go through every door once and then close it behind you, no opening closed doors

[xXACarmine37Xx]

theres like the vertical line thats not crossed

[MentalLemur]

I missed the line in the middle on the top half

[114Freesoul]

Can't we use the superposition principle and cross one of the angles of the figure, thus crossing two lines that have one common dot? That would be a little cheating, probably, but still a solution.

[hooloovoo1st]

You're not the guy from numberphile are you ...?

[HappyEskeemo]

Annoying sophistocated sir, you're voice throws off my chi balance.

[BettterSkatez]

It's tough to solve.

[wvboarder2005]

lol i spent hours upon hours in school trying this even though its impossible its still a good time waster

[crazylaxgoalie13]

no there is a solution you make the puzzle small and you draw a highlighter through it

[mickeyyeung0528]

Finally a serious explanation on this puzzle.

[Salfordbluemoon]

...and I still fucking tried to solve it !!

[Salfordbluemoon]

I don't get it...if there's no solution, why bother showing it? it's like a joke with no punchline. you go on and on for ages about fuck all . a crap puzzle that's not really a puzzle. what's green and red, only comes out at night and sounds like a cat? FUCK ALL.

[ThePieDemon]

@Salfordbluemoon Being able to prove the impossibility of a puzzle is also very important and is a puzzle in itself. Many fields of research have been created just because a person tried to disprove a puzzle

[Salfordbluemoon]

@ThePieDemon I get what you're saying but, we already all know that there is no solution...so what's the point?

[ThePieDemon]

@Salfordbluemoon It's fun watching your friends agonize over a problem that you already know is impossible ;) If you're talking about the video, the point was to show the maths behind the disproof

[Salfordbluemoon]

@ThePieDemon You mean your EX-friends.

[bolmeteussteeldragon]

as expected, singingbanana is the best mathematician

[monggomen123]

can you pass through a line you made

[applebroz222]

---

[DamnAllWhoApposeMe]

i finished this its easy

[outofpeanuts]

@DamnAllWhoApposeMe Great. Now divide by zero.

[nosrale]

13 People did not understand

[kandikid2308]

It is impossible

[forinner]

if it's easy, why isn't there a solution? trace the wall in the center? that's cheating

[Cnurc]

Hello singingbanana. As always you explained everything perfectly and it was riveting to watch. I have one question, however. Have you encountered the puzzle where you draw a square and an X in the middle of it without picking up your pencil? Is the explanation of why that puzzle is impossible the same as this one (4 corners and a midpoint making 5 points)? It has always "puzzled" me :).

Thank you for the videos.

[singingbanana]

@Cnurc It is the same. A square with a cross would have four corners with an odd number number of lines.

[thepspdaxter]

@Cnurc theres a trick with the puzzle you can fold the paper and draw on that so you dont "pick up the pencil" while having th ability to jump its cheap bu thats the only way

[GPinkBandit]

this was really easy for me o-o

[99MrNoodles]

To bad that wasnt a curved line

[Tricksy214]

I THOUGHT IT WAS SUPOSED TO BE MADE WITH ONE CONIOUS LINE????

[sashakepoes]

@Tricksy214 are you even listening what he says? -_-

[Tricksy214]

@sashakepoes my volume doesnt work

[megansrp]

I've solved it. Didn't take that long to figure out...

[edaman1231]

i beat it in 2 trys.. within 5 min..... so easy

[SuperWhatever111]

=.= the top is one line it self. same as the sides and bottom. Who ever made this puzzle is tricking you :D

[mixttime]

Furthermore you can count the inside as another "box" and that has nine paths in and out. So there are actually 4 events of having an odd number of paths and as you mentioned it is only possible to overcome 2.

[MetroAdventures]

Konigsberg!

[ideallyyours]

I hereby offer a SOLUTION. Is it illegal to roll the paper into the shape of a torus? If not, I think that could possibly work. Thinking outside the box, as so many have clearly not done.

[23TennisGirl23]

I thought you had it for a second and I got all excited and then I was disappointed when you proved me wrong :/

[singingbanana]

@MrJoeybeans81 No need to shout. You are, however, mistaken.

[imacreeperlol]

@singingbanana how is he mistaken all puzzles do have a solution nomater how hard

[hugili3]

@singingbanana how is he mistaken? it works if you start inside the box!

[skaterboo33]

@MrJoeybeans81 You're wrong, This is actually a famous puzzle. It's not called Houdini's last trick, The guy that created this puzzle was a mathematician. He has another one with 7 bridges called the seven bridges of something but i forgot the whole name. But he made this puzzle to be impossible for a reason. He did it to prove a point to his students and other mathematicians about angles, given properties, and properties that can be put in place.

[hotstuff80000]

@MrJoeybeans81 word u r so right

[Albion105]

@MrJoeybeans81 you were shouting and acting stupid in other video's regarding this, dude, you need to calm down :/

[Cationification]

@MrJoeybeans81 Who said all puzzles have a solutions? There are real life puzzles in and out of this world that don't have a solution yet? but I'm sure there are somethings out there that do not have a solution.. and never will have a solution as this is what can make life so interesting.

[Jeetard2]

@MrJoeybeans81

hey i have a puzzle for you.. i'll make a maze with no exit

have fun

it's still a puzzle though lolzz

[pivotman64]

@MrJoeybeans81 then try it

[PACMANnot]

I learned about this from my 5th grade teacher.

[zeergy]

16 lines divided in 5 boxes = 3,2

[AwakeBenihime]

I thought it was physically impossible without lifting the pen. I guess Euler trail is different to "Houdini's last trick" (if that's what it's called).

[4lifevideogames]

got it

[marq3993]

There is a solution. It was shown in the 1940s at the old "Believe it or Not" place.If i can remember will try to post.

[878amelia]

i solved it BEFORE the suloution came up. i am 10. i am very clever

[Lolwuut101]

@878amelia same, im 11... lol

[99FeeBee99]

@878amelia post a video of you doing it and I'll believe you.

Anyway you shouldnt be on youtube, kid

[rh27un]

ok, now can we see the solution in english?

[kiyla29]

Cant you NOT lift the pen?

[kiyla29]

i'm proud to say i solved it without seeing the solution first :)

[ItsXXnotXXme]

can i cross my own line

[DIEofLAUGHING]

OR PLEASE ANYONE TEACH ME HOW TO UPLOAD VIDEO ON YOUTUBE!!!!!

[DIEofLAUGHING]

I HAVE THE PICTURE BUT I DONT KNOW THE WAY TO SHOW YOU GUYS PLEASE THE VIDEO CREATOR GIVE ME HIS EMAIL AND I WILL SEND HIM

[DIEofLAUGHING]

I DID IT IN JUST 29 SECONDS

[cadavillo1]

can you start and end inside the box???

[cadavillo1]

can you start inside??

[richdar99]

this has been mathematically proven hat its not possible to do this

[cheti1337]

thumbs up if the squeaking of the marker gave u chills

[boss18887]

nice

[realmadjis]

Ive solved it with out that thing

[kidzilla1123]

i solved it

[AbysmalSamurai]

But what if you join the lines?

[wyrmbuster]

so your telling me i spent 30 minutes on an unsolvable puzzle?!?!12!@1/?

[MrBigawesome1]

FAIL!!!!! a box has four lines so how can you go through the bottom of the box twice???

[nicekiller888]

i did this..it took me all of 15 seconds to solve it :P

[reecemarr123]

@nicekiller888 prove it

[ERV7081]

oh yeah I did it in one day. Solved it on accident.

[ERV7081]

@singingbanana GUESS WHAT I FUCKING DID IT PEOPLE!!!!

GONNA BE UPLOADING IT RIGHT NOW, IT'S AT 7 PERCENT COMPLETE ,GOSH DARN IT!!

[TheAxepro]

sdsds

[ragna120k]

this has been solved..

[gnomex11]

woooo!!! i got it in 5 tries :D!

[PullarBearBear]

Are we allowed to overlap lines?

[PinqReneqade]

My 2nd grade teacher showed the class this puzzle about 7 years ago. Fascinated by the puzzle, i have promised myself to solve it. 7 years later, i watch this video and realize how much of my life i have wasted. ;---;

Thanks mate.

[mrtierney2]

What if you start by using the corners instead of in the middle of the lines...that could change the outcome and the number of lines

[mrmrhihi1]

sinse when the hell did youtube have sound in their ads?

[singingbanana]

@acer1827 Haha. Irony.

[joshhix18]

@acer1827 He's pronouncing it correct. In case you didn't know, he's a mathematician so I would guess he knows a little about what he's talking about. If you still doubt me, just ask any math professor. I think YOU should do some research next time before trying to prove someone else wrong and making yourself look like a fool.

[Haelstrome]

@acer1827 "Leonhard Euler (German pronunciation: [ˈɔʏlɐ], English approximation, "Oiler";[1] 15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist." - Wikipedia page on Leonard Euler.

[GillesDM1993]

@acer1827 has it ever occured to you that english is not the only language in the world? euler is a german name and in germany it's pronounced "oiler"

[themrice11]

@acer1827 it is pronouced Oiler trail. it is spelled like euler and he did say it right

[nicholishere]

IT IS NOT IMPOSSIBLE!!!

[TheEgg185]

oilers...trail ?

[demonnn09]

how many paper did u spend ?

[TheD3g3n3rat3d]

what i still didnt get: does the line has to be outside of the box to "win" or better say solve this puzzle or can it be inside?

[dougie98710]

easy

[cornelllevi1]

Ugh, the sound of expo on paper sends chills down my spine.

[MrGiratinaORIGINAL]

Oh,wait,just realised.Sorry.

[MrGiratinaORIGINAL]

On the first time he realised he nearly solved it so he purposly done something stupid.Noticed that?

[airsoftslayer95]

chuck norris can do that in his sleep

[2BROVIDEOS]

Its easy by the way Im Bro 2

[2BROVIDEOS]

He almost had it he just needed to go in one line he missed its possible

[cakesofdeath]

You lost me mate!

[mazur87]

@cakesofdeath It's so simple... pfrrr

[cujodee09]

I can do that easy

[DannyFatSack]

first try.

[gaunzabeast]

ok first of all THANK YOU!!!! no joke i've been at this flipping thing for 5 years since freshmen year and it has litterally been the most anoying brain teaser ever for me id forget about it for a while then bam its like i had to solve damn thing, but quick side note couldnt u just draw a circle connecting to the ends of the lines on the outside and could that just be considered one line if not who cares and by the way yeah im even laughing at myself why it only took me 2 sec to find this video

[You2beer4eva]

it is possible but you have to think in 3D..... there is your solution :)

[gamesbok]

I was studying this problem so hard that I fell off a bridge in Konigsberg.

[wlSimplelw]

You're suppose to start inside one of the boxes...

[theoneandonly1305]

I did it on my first try... x)



[JonagerTv]

:48 you cheated... you picked up your marker

[dannyville211]

@JonagerTv you're dumb. Get off youtube.

[JonagerTv]

@dannyville211 WOW i got told off

[JonagerTv]

:50  you picked up the marker

[aziminshafie]

why everybody is too stupid. the solution is like this.

first - fold the paper-make it half diagram

second- solve the diagram

then- fold back the paper. note- u should use tracing or any transparentt

paper

[grandtheftauto5588]

it is possible! watch?v=Dh5HR8knUgA

[charlloss123]

i did it acidently and in matter of seconds on video before xD

[johnsonville1brat]

I CHALLENGE YOU Now i'm going to link it.

[johnsonville1brat]

I'm 16 years old and I did it my 3rd try.

[yangstahboi2]

lol i just did it on the second try, i think.......... O.o

[yangstahboi2]

lol i just did it on the second try

[Jaline52879]

i used the corners when i got stuck...

[Fortevn]

Well it's a "think outside the box" puzzle. I put the whole thing in 3D, which looks like a frame, then simply draw the line on the 3rd coordinate (z, as I built it in x-y) so the drawline will go to a block without crossing any line then go through the last line.

Like how burglars said "If you can't break the wall, dig a hole or from the chimney".

[acdcrox23]

if you have a PC then go to start, all programs, accessories, paint, then press the Print Screen/SysRq button above insert (on your keyboard) then in paint press edit, then paste, then you can crop it and save it to your pictures......if you have a PC

[Lycanthrope3390]

I figured it out after he put the lines on each line. It is simple when you do that.

[KRAZYLAUGHTER]

hhaha nevermind i messed up

[anticorncob6]

1) Can you do this if you're allowed to fold the paper over ONCE?

2) Is this possible if you have to go over every line except one?

[anticorncob6]

@anticorncob6

1) Yes I've tried that

2) EASY

Now can someone tell me how to send this comment to the past me?

[TheHarryshan1]

That is a waste of time and paper

[flap4000]

hii, I'm 16 years old, I bet with my father that he would not solved this puzzel for 50 euro's.

You know what, he solved it, I couldn't believe my eyes and I lost 50 euro :s.

I'l putt the screen shot at youtube :)

[anticorncob6]

@flap4000 Please show it to me I don't know what "screen shot at youtube" means!!!

[marmjtin]

Interesting.

Pulgar arriba.

[kasunovinfinity]

I solved it, because it didn't say anything about corners, and the lines HAVE to make up the corners, so they are still part of the lines, therefore crossing a corner is crossing a set of lines at once if crossed 'properly'... therefore I used MS paint to present my solution, using a single pixel set drawing, nothing is impossible :D -> imageshack.us/photo/my-images/­715/unledut.png

[newgrounder2]

danbal759 is 13 years old and proved he is a retard in less then a minute.

[KRAZYLAUGHTER]

its not impossible i solved it

[sevenriches]

@KRAZYLAUGHTER Prove it...... Didn't think so.....

[anticorncob6]

@KRAZYLAUGHTER Where's your solution?

[KRAZYLAUGHTER]

@anticorncob6 its nowhere because i hid it underground where nobody could find it bwuahaha!! but seriously i did it wrong ha

[danball759]

never mind i am stupid proved my self wrong but how ever i must say you people are mean i am just 13 damn calm dow so sorry every one

[orcyngiser]

@danball759 well your a fucktard cuz first u think ur smarter then a university level mathematician then you realize you were wrong.

And on top of that , it says ur 22 on ur account.

[danball759]

hey everone this is danball759 i did it agian and the way i did it was go through my line not the puzzles lines so there it is possible so fuck off bitch

[rokusho0100]

@danball759 you can't cross your own line...

[slovakmath]

@danball759 You come on here ridicule the poster of this video, claim you did it easily twice, and then tell everyone to "fuck off bitch" because we merely asked you to show proof. At your age, 13, I'd already taught myself derivative based calculus from books my teacher let me read...and had just begun to work on integrals & simple PDE's. I doubt youll ever understand (or even just see) a very simple PDE for the rest of your life. So yes you are stupid & I hope you feel bad too. You should.

[navigator758]

ok except you have explored every possibility of xing the lines when you have you may discover the solution ! Hint think outside the box, euler.

[Gwindios]

sorry guys nevermind I see now that i forgot 1 line soo myn is also now solution ( if you could read it and follow it ) so nevermind ;P

[Gwindios]

Do you know that if you at 0:47 DON'T go up but go left then down from the out side go left in the same box do got out and then up en right done.

[Muki13]

impossibility doesn't exist, in a world with a concept called infinite.

[Muki13]

I solved this puzzle within 2 minutes, 2 years ago, It takes a mastermind or basic outside the box logic thinking to solve it. Nothing is impossible, its just tricky to think of.

Figure it out for yourself, trust me it not impossible, singingbanana has absolutely no logical sense what so ever.

[L3irus]

@Muki13 Oh ho ho. Can you make a video of it please. I'm dying to see you stumble twice over the same line or missing out a line to cross.

Jeez people nowadays. There are already a bunch of morons who said they solved it and missed out a bunch of lines while they stumble all over the lines.

[Muki13]

@L3irus my solution is so easy its mind-boggling. Making a video would be pointless and a complete waste of my time.

Hint: The solution is the puzzle

Read the rules over and over in your head and look at the puzzle, the answer should come to you instantly. If It doesn't your an idiot.

"In a world with a concept called infinite, there absolutely no such thing as impossibility." - muki13

[L3irus]

@Muki13 Not being able to show the answer clearly proves that you have none. The way you talk even makes you worse than all those people out there who put up videos of what they call an "answer" to this.

[Muki13]

@L3irus I already gave you the answer below. The hint that i gave you, is the fucken answer. How stupid can you be?

[L3irus]

@Muki13 Okay, maybe I'm too stupid, now tell me the answer and not some ridiculous "hints".

[ZOMGxTAKEDOWN]

I solved it in 12 seconds when I paused the video at the start and looked at it and I have never seen it before :D

[Nutzername36]

this puzzle can´t be solved in 2D but in 3 Dimensions and higher it can :D

[AnimeBelover]

@Nutzername36

... The of course ... you can solve it easily in 3D but the point is that this is a house with 5 rooms where you can only exit through doors. If you do it in 3D, it is missing the point -_-

[33879528]

es imposible no tiene una solucion lo intento resolver desde los 13 años cuando me lo enseñaron tengo 22 en la actulaidad si alguien save como resolverlo por fabor digame