When I was about 10 or 12 years old, my science teacher showed me this puzzle & told me that Albert Einstein was the only known person in history to solve it on his first try. Looking back, he was probably bullshitting me, but he did his job as a teacher by sparking my interest in math & science. I played with this puzzle over the years & ultimately conceded that it was impossible. If you have determined that it's impossible, you have essentially solved the puzzle. Admitting that something is impossible is like admitting defeat, it's no wonder so many of us get hooked on this & keep trying. Excellent video, thanks for posting.
Logan's Hot Rod & 4X4 A basic principle of the scientific method is that if you cant prove that something is impossible then it must be possible. So what you say is true, but only if you have the evidence to prove that it is impossible in fact.
We wasted so much time in school trying to figure this out. I am glad UA-cam didn't exist back then - or else I would have wasted my time on something else.
I’m convinced that Euler is the most productive mathematician, nay, human in the entire goddamn cosmos. He’s so prolific it’s not even a joke to say his work in today’s era would’ve probably earned him more PhD’s then some universities have ever handed out.
+TheLastDino but a line has no end or beginning, it's not point to point what you see is just part of the line, and it is indefinitely small so it cannot be that thick.
Ahaha 'President Trump' calling a man who ACTUALLY has spent alot of thought on a problem an idiot! The irony!!! ='D No, this even surpasses irony. It's in a whole other league! It's some sort of... paradoxal hyper-irony! x'P edit: *disclaimer*: I'm pretty sure that I wasn't talking to a figment of my imagination and that this mysterious "President Trump" has silently deleted his comment.
Yay, I figured it out myself before I continued watching. I drew a square and saw that if you start outside, you can only end outside. Then I drew a 5-sided object and saw that if you start outside you can only end inside. So if your line only has two ends there's no way your picture can have more than two uneven sided objects. I'm glad that there is no super smart way to solve it.
Thank you for actually explaining why it's impossible. I've been watching a lot of videos of puzzles like these and most of them are just reposted by people that don't understand the puzzle at all and it's very unsatisfying.
I thought about this in terms of there being two types of boxes - they either have five sides (odd) or four sides (even). With even-sided boxes if you start your line on the inside of this box it must also finish on the inside when crossing each segment, and likewise if you start on the outside you must finish on the outside. The odd-sided boxes are the opposite - if you start your line outside and odd-sided box, to cross each line you MUST finish on the inside, and vice versa. So to be able to escape from an odd-sided box and continue completing the puzzle, you MUST have to start on the inside of it, but given that there are three odd-sided boxes and you can't start your line inside more than one, it becomes impossible. If there were only two odd-sided boxes it would be ok because you could start inside one and finish inside the other, and you'd just pass through the even-sided ones on the way. When I worked this out I just gave up trying to find the clever solution and watched the rest of the video, only to find out there is no solution :P
People, please! I see the majority of people don't understand the term impossible. You've been given rules saying you can only cross through lines. You've then been told that this is proven to be impossible. And if it's mathematically proven to be impossible with these rules, then the only way you can think you did it is by doing it wrong. A lot of you say you can do it by using corners. Of course you can, but you can also do this by ignoring any other rule. I did it by completely ignoring half of the bricks but that clearly doesn't count. If I said to you, "This is impossible, but try to go through this maze by getting through all the doors while only going through each door once" and I saw you trying to walk through a corner of the wall into the other room because you're that stubborn, I would laugh.
Haha at all these people. "Technically I did solve it I just went to another dimension and crossed the corners and went on a line so this is solvable." k guys, k.
He said cross. Not intersect (sharing a point) but cross. In 2D, they're interchangable (kind of, cross is actually wrong but nobobdy would get confused), but in 3D, a pair of crossing lines is defined as a pair of lines that are not parallell, but also don't share a point. If they're not parallell but they do share a point, they're intersecting. So, if you consider the puzzle to be 3d, it's actually incredibly easy since all you have to do is draw a line that is not parallell to any line in the puzzle and also doesn't share a point with any of them.
My teacher gave us that problem in 3rd grade. I proved it was impossible then after trying the whole year. Wasted notebooks trying before I figured out it was impossible. I don't remember my exact proof but my teacher was really impressed. I went to a really advanced private school if you're curious about the advanced placement of math.
He actually did. It has to be a pair number of lines since you want to go in as many times as you go out, except for the beginning point and the end point
A kid showed this puzzle to me in the 6th grade in 1984. He moved away before I ever found out if it was solvable. Over the years, I have wondered was there an actual solution. Thank You for letting me off the hook, Lol
Since you used the word "cross" and not "intersect" then there is a technicality that makes this puzzle solvable, and that is that we can cross one of the lines (specifically the upper middle vertical line) from end to end just as you would cross a bridge. That, however, is the only way this puzzle can be solved.
Nice one.. I came up with this solution and you are the only other person who has pointed that out in the comment section. Exactly !!. Running along a line or edge is not the same as intersecting it.
So three of the boxes are odd nodes, each having valence=5. You might notice that the outside region is another odd node, with valence=7. So there are actually 4 odd nodes, and 2 is the maximum for an Euler trail to be possible. (There must always be an even number of odd nodes, BTW.)
My grandfather showed me this and it kept me puzzled for years. Eventually I I worked out that it was impossible by virtue of the number of individual lines versus entry/exit points you need. But really it just reminds me of my grandfather, how wonderful he was, and how he always wanted to give me something to think about (or to keep me quiet 😂).
To be really correct about Euler trails, you need to consider a “center point” at the outside of the design, because if you represent this as a graph you would have 6 nodes : one for each rectangles and one for the outside. Therefore you don’t have 3 but 4 nodes with an odd number of edges. Obviously the answer stays the same : you still need 0 or 2 nodes with odd number of edges to have an Euler trail in the graph.
It could be anywhere between one and four 'centre points' on the outside though I think, which is why he leaves that open on his diagram. I think it does gaurantee at least one more odd node on the outside though, given that there are nine crossings to the outside.
there is an easy solution. think of this drawing as a 2 dimensionsional entity in a 3 dimensional space. you can go up and down through the paper. problem solved.
3 of the rooms have exactly 5 walls. For a path to exist that crosses every wall exactly once, it must, for each of the 3 rooms, enter a times and leave b times. b > a only if your path starts inside the room. So for at least two of the rooms, a > b. There's no way to enter a room 4 times and leave once, or enter a room 5 times without leaving, so it must be that you entered both rooms 3 times and left both rooms twice. Since you entered once without leaving, your path must end in one of them, but also the other, which is impossible. So no path exists.
I love all you guys saying "I Solved it" cause i know u did not :D He showed a proof that it is immposible. So, if u solved it, you did somthing wrong!
Best way to check if its solved is to follow the line you drew, and highlight every edge you cross. Most "solutions" either have one edge not highlighted, which would normally not be detected.
It is possible to solve this puzzle, talk of going through corners and following on top of your own line is against the rules! To make it more specific; make a door in each of the walls, you must go through each of the doors only once without taking the pen off the paper. Hint: the answer lies in the phrasing of the rules, the solution is not mathematical. Have fun.
Some of these solutions I am reading are the same as saying 'I Solved the Rubic's Cube by pealing off the stickers and sticking the same color ones on the same side. Duh, it's so easy.
I have been trying to figure this out for 20 years!!!! I just decided to Google it.... only to find out I was wasting my time doodling this in my notebooks all throughout school lol😂
"I solved it by making the puzzle 3D" "I solved it by crossing the intersections instead of the edges" And thanks for saying that you broke the rules of the game
It's really funny that this came up in my recommendations today. I was reading about this exact problem last night. P.S. YES PEOPLE, IT'S THE GUY FROM NUMBERPHILE
I am a Chinese and learned it while I was a pupil, really I remember this all my life. In China it is called Olympic Maths and a lot of children learn it in order to be smarter than others. Now I am guaduated my bacholer of science and my major is mathematic. Thank you making me remember that happy childhood
This seemed like a great puzzle, and one I could surely solve...after carefully drawing the puzzle I proceeded to draw out all possible combinations of lines by creating triangles throughout the puzzle (which he basically does). Within ten minutes I realized that this puzzle must be impossible. However, after staring at this piece of paper for an additional hour I realized that the only way you could solve this puzzle was thought the intersections (corners)...I then thought to myself "Hey, maybe I'm not as stupid as I thought! ". Of course, another five minutes later I realized that this was cheating and confirmed that I am indeed stupid. Being unable to solve an impossible puzzle isn't grounds for stupidity...however, realizing a puzzle is impossible within the first 10 minutes, and then staring at the puzzle for another hour stubbornly searching for an "ah ha" moment is bang on stupidity. Sorry Dad, but I'm a dummy.
It's important to note that this, as simple as it looks, is part of a revolutionary math paradigm that Euler did. I think one of the most remarkable problems is the "Königsberg bridge problem" which inspired Euler to do this kind of things (this is a cite from my geometry book, I do not really know if this is true and whether it is or isn't we can agree it makes for a cool story)
When I was middle school I looked a brick wall in class and out of bordem decided to make a puzzle for myself. This was the puzzle. You have no idea how many years I spent trying to solve it and how many times I drew the damn the thing. I think was still attempting it as a Senior. Now I know I was never going to achieve my goal.
Your approach was wrong. When you kept failing over and over, you should have stopped trying to brute-force it, and instead analyzed why you keep failing. That way, you could have figured that it's impossible, and why, instead of wasting your time drawing pointless lines over and over.
I paused the video before the answer and spent the last 3 days writing code modelling the problem and flipping tables wondering why my program wasn't finding any path bigger than 15 crossings. Hm... At least I wont forget what a Euler's Trail is. Mathematics can be a mean teacher, sometimes haha! (T_T)
Nice observation skills fam, this video is 7 years old. I don't think the uploader will even see your comment. And if he does, he certainly won't care.
BeFondOfJohn Well that's not true. Zero is the absence of things. You see more 0's in a day than basically any other number. You see 0 real murders (I hope), 0 living mountain dew bottles, 0 polar bears. Numbers themselves as in 1 the idea and 8 the idea it's also very real. 0 is just as much an abstract idea as all the other numbers.
BeFondOfJohn Explain when a number isn't a measurment in some way. Numbers are ideas and 0 is the one we interact with most, making it the most real number.
BeFondOfJohn But 0 does exist in measurements. That's pretty basic. I have 0 polar bears. There's 0 inches between me and myself. The ball traveled 0 feet. Now you can't get negative measurements that's true. But you can get a measurment of 0.
Cool demonstration. I recall reading about this. The Königsberg Bridges problem. For years nobody could find a solution or figure out for sure that the solution did not exist. It was Euler who proved that it was impossible in similar fashion that you did. I think it was something like - If you enter an island (box) then you must leave it, so there need to be an even number of bridges (except for start and finish as you stated).
Wait, it took them years to figure this out? With several people trying? ...I solved this puzzle without help a few years back. My father presented me with the puzzle and I just couldn't find a solution, so I figured it must be impossible. But I wasn't satisfied with just thinking it's probably impossible, so I tried to solve it mathematically. Turns out I was right, it's impossible to solve it the traditional way, for exactly the same reasons that were explained in the video, so that's the solution. I can't believe it took them so long to figure out why this is impossible. O.O
What if somebody take it seriously ,paused the video,tried to solve it for a week having patience,came again to video for solution and he got to know that it was impossible....
I "solved" this problem 45 years ago in 8th grade. My math teacher gave me an "A" for creativity. Every Friday, he gave me a puzzle to solve over the weekend. After 20 weeks or so, he presented me this puzzle. You should have seen his expression when I informed him Monday morning that I 'solved' it. PRICELESS! I adhered to all the rules, crossed through each line only once, and didn't lift my pencil off the paper. You see, my teacher didn't tell me it was a trap like the Kobayashi Maru. en.wikipedia.org/wiki/Kobayashi_Maru
The second time I did it (And I though I solved it) I realized that the straight horizontal line counts as 4 lines, then the recangles have 5 lines to be crossed, odd number, that means that you only can end inside of it, but then you have 3 of them, it's like having 3 cages and you need to end in all of them at the same time.
+Daniel Bundrick Try to start with just a simple pentagon, exactly... YOU CAN'T FINISH OUTSIDE OF IT, the rectangles are basiclly pentagons, with 2 was already impossible with 3. It's like trying to draw a square with 3 straight lines, Impossible. Btw, I guess you were kidding, have a nice day.
5 square rooms + outside = 6 rooms 3 rooms with 5 doors 2 with 4 Outside has 9 Basic rules: Each room is in one of two states > 0=Empty, 1=occupied On only one room can equal 1 at a time Am odd number room (5 and 9) will always end opposite of what they started with Even number rooms (4) end the same as when they start. Senarioes: Door#: Start State > Fiinsh State Starting ng in odd number room: Odd(5): 1 > 0 Odd(5): 0 > 1 Odd(9): 0 > 1 Even(4): 0 > 0 Even(4): 0 > 0 Ends with 2 rooms occupied, impossible! Starting in even number room: (5): 0 > 1 (5): 0 > 1 (9): 0 > 1 (4): 1 > 1 (4): 0 > 0 Ends with 4 rooms occupied, still impossible.
WHY IS NO ONE NOTICING THIS? If you were to count each box as having it's own 4 sides and then add them up- the total should be 20 sides- NOT 21. So this whole diagram requisite is false. Here's why... They're technically asking you to go through the upper part of the middle brick's edge TWICE, when instead it should be considered ONE brick edge (for the top part of the middle brick). The bottom center box is being divided into an imaginary two squares or brick edges, when the lower middle box's upper brick edge should be considered one line, and the center-line that separates the upper two bricks should be considered the line necessary to cross that lower middle box. As is it defies logic and deliberately makes the task impossible, but when looked at the way I described- it's possible... and logical.
No, you misunderstand. Where an edge is bisected by a perpendicular line, as the top edge of the middle-lower brick is, it is considered two lines, and you have to go through each of them once.
I understand that, but the premise is to go through each brick edge- not every line. If it's meant to be every line, then the boxes have nothing to do with it, and they should change the instructions. It shouldn't be both.
Ethromel The premise is to cross each line once and only once. A bisected line = 2 lines, as is explained in the video. The boxes are part of the explanation, not part of the initial objective.
Doesn't the fact that the bigger squares have unequal entry/exit points mean that it's impossible? You need IN and OUT points and that's 2. Maybe if there was an equal number of the big squares connected it might work but there's 3
I have come up with two solutions out of about 6 attempts at this. Two solutions that actually work given the description that you and everybody else gave me: cross each line *once*, with one, continuous line. The only thing that is not mentioned, but clearly implied, is that you cannot start and end inside of the house. The two that I came up with involve starting in the top left, and ending in the bottom middle. The possibilities are not limited to those rooms, but those happen to be the solutions I came up with quickly. I even heard another guideline/rule in the scamschool video about this and another number problem: You could even cross the lines if you feel like it. The two solutions that I came up with don't even use this added aid.
I tried it like 5 times, and in between each I thought about how there were 3 boxes with 5 lines to cross, so it must be impossible, but I kept trying because obviously if you were about to give the solution, it must exist. Then finally, I was so sure it was impossible that I gave up and decided unpause to see your solution.
But thats not an edge or line. It's angle so you still have to do the other ones also this is mathematically proven to be impossible like how it is mathematically impossible to fly in a place with gravity in a stand still position.
But thats not an edge or line. It's angle so you still have to do the other ones also this is mathematically proven to be impossible like how it is mathematically impossible to fly in a place with gravity in a stand still position.
Just wanted to offset all the negative comments and say that this is a great puzzle, feels like a more complex Königsberg bridge problem. Also, I find it awesome you're still replying to comments after seven years.
I started in the top left line(not corner) then went down to the bottom corner and up through the inner corners of those first two rectangles on the left, next I went through the top right corner and kept going to make an arch that came back around to the bottom right corner then came up through the middle bottom and through its top right corner to complete the puzzle! :D
If you draw a line larger than the rectangle it is considered only going though at one point as it is a single line and only travels in one direction, therefore never goes back to cross again
OK. check it... when I was in the 6 grade we had a sub teacher that gave us this problem and he swore it had a solution. I believed him, why shouldn't I he was a teacher. I spent the next 40 years working this problem and it wasn't until 3 years ago that I mathematically worked it out that it couldn't be solved. I"M STILL PISSED. Tonight, this night I saw this on the tube and my heart raced... I clicked over, never seeing this problem anywhere during my travels over the 40 years.. I thought, what if?? Then I watched the video, the first one, that stops before giving the solution... I WAS pissed again.. then clicked over to this to lay to rest a painful search for a solution and to question everything no matter how credible they may seem..
@Mike Pratali - Reading your post, your experience is identical to mine - absolutely to the last detail!!! I was told there was a solution, the teacher wouldn't show us, he left us with the puzzle over a summer holiday. He did say that the solution looked like a 'teddy bear'. I never saw the teacher again so never did get to see a 'solution'. I am sure he couldn't have been that cruel...
I got it! Pleasse read!!! Start on the top left rectangle . Then draw a line going down in the middle of the long line then take a left going through the left small line.then go down until you have reached the middle of the left side box. Take right and then go down. Then take a right untill you are in the middle of the middle rectangle go up and then take a left after taking the left will be on the bottom left box again go up and take a right going through the other small line but dont stop at the middle this time say about an inch then go down now at this point you should be at the middle rectangle after that take a right and you should be going into the right bottom box go to the middle and then go down now.you should have gone thru the the bottom line of the right bottom box then take a left then go up until you are at the middle take a left which is going thru the right side of the rectangle then go up. Booom! Am I right?
Well I noticed that this sort of thing can be simplified. If you take just those two top rectangles (and each of the bottom sides are divided into two) or actually just take 2 adjacent pentagons, it appears to be impossible. I believe it's because, going in and out, you take up an even amount of lines, but here there's an odd number of lines, so you are forced to go in a polygon and cannot come out. And yes I didn't finish watching the video
The solution works took me 3 min to get, it never says u can cross corners and if u cross a corner u will automaticly cross 2 to 3 lines and then it's possible =) it never said cross 1 line at the time =) but if thats the case its impossible
Robin Lindsten that's total bullshit. It's a simple case of parity: If a light-switch, (or toggle,) is down and you turn it the other way, (or toggle it 180° every time,) then it will always be down after an even number of turns, and it will always be up after an odd number of turns. So, in any case where the toggle is down and you turn it an odd number of times it is impossible that it will end down▪ (That was the whole point of this exercise.)
What is the answer? You didn't draw the curve. This is totally ridiculous. The title says solution. Am very disappointed in this video. It was very poorly done.
The explanation was complete. The solution is the explanation of why it's impossible. I also gave you the name of how to solve problems like this, Euler Trails, which you can look up.
Depending on how you tackle the problem, you can end up solving the Eulerian Trail problem which is polynomial, and more precisely linear in terms of the number of eges and vertices; or you could also end up with the Hamiltonian Path problem, and this problem is NP-Complete meaning that only exponential solutions are known (and it's very, very, very unlikely that we will ever find a polynomial time solution for that). Now of course this doesn't really matter here because the graph is not too big, but I thought this was an interesting fact to mention.
I've seen this before. And I've wondered why the impossibility proof can't be explained more simply as follows: Consider the drawing a floor plan of rooms. Draw a door in each wall leading to an adjacent room or to the outside. The puzzle now becomes this: Walk through all the doors without going through any door twice. Notice that every time you enter a room you have to leave by a different door, unless you started or finished the trip in that room. So all the rooms except the first and last must have an even number of doors. But there are three rooms with an odd number of doors--five doors each. Hence it can't be done. The proof is equivalent to what was presented in the video, but without the extra steps of drawing the graph with a center point in each room, etc. The graph using the centerpoints of each room is useful in a sense, because it illustrates a correspondence with problems of drawing geometric figures without lifting your pencil. But that equivalence isn't necessary, and I think my version of the proof is easier to see..
At first glance I notice that the top two rectangles each have 5 required crossings, which in words would be: "In-out-in-out-in" ---> both of them require that you stop inside, since you need to stop inside of two different places it's impossible
If the rule is you can't take your pen or pencil off the paper you go through leaving 1 edge inside and your line on the outside, you bend the paper into a roll until the edge of the paper is next to the uncrossed edge and then draw over it, it's continuous from 1 observers perspective
So reading comments, corners count as two, so it's possible you count that (It isn't specified that you can't do that) the other way, is that you use horizontal line, and draw a line over top of all of them, but then you just have to pass through the vertical lines.
Each time you cross a line touching a box you either go from the inside to the outside or from outside in, so for a box with an odd number of lines you will go in and out sequentially an odd number of times and end up either outside if you started inside or inside if you started outside, so for each odd numbered box you will either start or end inside. This picture has 3 5 sided boxes and you can only start in one, and finish in one, meaning at least one of the boxes cannot be started or finished in and therefor cannot be crossed the requisite 5 times. edit: the outside of the boxes is also an area with an odd number of sides touching it(9) so there will actually always be at least 2 sections missing 1 cross over, not to mention if one section has a side not crossed then it must have a section next to it also missing a side.
For all of the people claiming "click bait" and "didn't show a solution", in maths, no solution is an answer. The answer to this problem is null set, and he proved it.
When I was young my 5th grade teacher showed us this "puzzle" and said he'd show us the solution tomorrow. I was absent the next day and no one would tell me what the solution was so I spent the rest of the school year trying to figure it out. I eventually came to the conclusion that was impossible. I figured with the amount of lines you had to cross, 16 vs the amount time I had spent trying to solve it that it was actually statistically improbable that I hadn't solved it yet. In other words, I either had absolutely shit luck, or the thing was impossible.
That's the first step towards the solution. But you never completed the second step: Understanding why it's impossible. Well, until two years ago when you watched this video, I guess.
If it must be done on a two dimensional plane with the requirement to cross through the edges, then it’s impossible. But if the wording says to intersect the lines, it’s really easy. (Think inside the box for that one.) It’s also feasible if you approach the problem using three dimensions. (Like taking a needle and thread to puncture/pass through each edge, then tie the thread outside the piece of paper.)
Found this puzzle a couple of years back and it is in fact impossible if you do it this way, but if you go through corners, where 3 lines connect (in an angle where all 3 are crossed) you aren't abusing the rules but you can still get a solution.
It's just graph theory isn't it ? I counted the number of lines (and not sides) of each boxes and saw 2 boxes have 4 and 3 have 5. Since there can only be 2 boxes with an odd number of lines, this is impossible. (Because we have to enter and exit once every box but the one we begin with and the one we end with, all the boxes but 2 should have an even numbers of sides).
Whenever you go through a wall of a room, you end up at the different side (inside or outside) of the room. If a room has odd number of walls and you go through all of them, you end up at the different side (inside/outside) of that room. There are 3 rooms (named A, B and C) in this puzzle have 5 walls, and you try to go through all of them: If you start inside one of them (say room A), which means you start outside room B and room C, so you must end inside both room B and room C if you plan to go through all walls, which is impossible. If you start outside all of them, then you have end insides all of them, which is also impossible.
Even knowing what Eulerian trails and Eulerian paths (and their distinction) are, and looking at the title of the video, I just couldn't think of a way to convert the picture into a representative graph until you showed it (except you didn't join the 'outside' as a nine-edged vertex). With the underlying graph drawn it can be easily shown how to change the original puzzle such that it _is_ possible to cross every line only once, and then there are quite a number of ways to do this-either by removing a certain line, or splitting a certain line, to respectively remove or add an edge between odd-degree vertices to make them of even-degree. The original problem is itself a graph, and it turns out that its 'dual'-where the faces are the vertices and the vertices are the faces-is the graph needed to solve the puzzle. (I use the properties of Eulerian trails a lot in my work, as I do embroidery and it saves thread to visit every edge only once, and if the Eularian trail does not exist, how to split the design into subgraphs of which it exists.)
To the people complaining that he said Solution in the title and therefore baited you into the video, what did you expect? Did you want him to title it, "This puzzle is impossible"??? The point is to make you want to try and figure it out on your own, if he told us it was impossible in the title, it would take away from the excitement of wanting to solve it or potentially figure out why it cannot be solved.
James the only problem is that it's possible to cross 3 lines at the same time.. if you cross through an intersection. However you will start inside and end up inside or start outside and end up outside.
In fact, there's lots of solution. The problem says that the line may not cross the same line twice. But we're allowed to make the line crosses itself, think about it and u'll find a solution, there are many possible like that.
Read the whole book "Journey threw GENIUS". Euler is mentioned in that book but changed because more books means you need to go down way down and lose to someone for the name.
As long as it's not required to bisect each line you can solve it by crossing at the intersection of 3 lines (the corner) which covers 3 lines with one crossing. Solved.
Adult Hintler It has a solution In 0:47 he could enter the left square and cross the down line then enter again from the outside throw the ledt line then the top line .. and finally the middle line in the picture ☺☺
When I was about 10 or 12 years old, my science teacher showed me this puzzle & told me that Albert Einstein was the only known person in history to solve it on his first try. Looking back, he was probably bullshitting me, but he did his job as a teacher by sparking my interest in math & science. I played with this puzzle over the years & ultimately conceded that it was impossible. If you have determined that it's impossible, you have essentially solved the puzzle. Admitting that something is impossible is like admitting defeat, it's no wonder so many of us get hooked on this & keep trying. Excellent video, thanks for posting.
Logan's Hot Rod & 4X4 This is a great comment. I think I like your teacher.
+singingbanana o-o still trying. I MUST FIND THE SOLUTION
Logan's Hot Rod & 4X4 A basic principle of the scientific method is that if you cant prove that something is impossible then it must be possible. So what you say is true, but only if you have the evidence to prove that it is impossible in fact.
Logan's Hot Rod & 4X4 buts it's proven to be possible just google images- 5 room house puzzle solved
+Nathan St John Shhh, let them have their stirring speeches about admitting defeat, they learned more than you or I with our google cop-out.
We wasted so much time in school trying to figure this out. I am glad UA-cam didn't exist back then - or else I would have wasted my time on something else.
Well, good👍
I’m convinced that Euler is the most productive mathematician, nay, human in the entire goddamn cosmos. He’s so prolific it’s not even a joke to say his work in today’s era would’ve probably earned him more PhD’s then some universities have ever handed out.
Underrated comment
I have the solution.
A marker the size of the puzzle is gonna do the trick.
1 line, all edges touched ONCE.
That is not a line though...
+Matthew Sakamoto Point to point so a line ;) GOOD JOB LALUGAMING
lol
+TheLastDino but a line has no end or beginning, it's not point to point what you see is just part of the line, and it is indefinitely small so it cannot be that thick.
+LaluGaming no that means you will cross the lines infinitely many times, sit down
+LaluGaming Theoretically lines dont have width
This puzzle has plagued me for 25 years since I was shown it as a kid!! Thanks for finally putting my mind at ease
I paused when he said pause to try it out and spent an hour and a half doing it before pressing play again :(
I feel your pain my friend.
+Justin Franklin Lol I starting cussing saying it was impossible, as soon as I pressed play he confirmed my thesis
that's great! this is the most important thing we do, try and fail. everybody that succeed has failed and learned. only idiots ars afraid of trying
Ahaha 'President Trump' calling a man who ACTUALLY has spent alot of thought on a problem an idiot! The irony!!! ='D No, this even surpasses irony. It's in a whole other league! It's some sort of... paradoxal hyper-irony! x'P
edit: *disclaimer*: I'm pretty sure that I wasn't talking to a figment of my imagination and that this mysterious "President Trump" has silently deleted his comment.
+President Trump Nice Person
Yay, I figured it out myself before I continued watching. I drew a square and saw that if you start outside, you can only end outside. Then I drew a 5-sided object and saw that if you start outside you can only end inside. So if your line only has two ends there's no way your picture can have more than two uneven sided objects. I'm glad that there is no super smart way to solve it.
Except there actually is a super smart way to solve it...
What is it
KingInky13 Nope, the diagramm at 2:29 contains all legal moves. It is impossible.
Thank you for actually explaining why it's impossible. I've been watching a lot of videos of puzzles like these and most of them are just reposted by people that don't understand the puzzle at all and it's very unsatisfying.
I thought about this in terms of there being two types of boxes - they either have five sides (odd) or four sides (even). With even-sided boxes if you start your line on the inside of this box it must also finish on the inside when crossing each segment, and likewise if you start on the outside you must finish on the outside. The odd-sided boxes are the opposite - if you start your line outside and odd-sided box, to cross each line you MUST finish on the inside, and vice versa. So to be able to escape from an odd-sided box and continue completing the puzzle, you MUST have to start on the inside of it, but given that there are three odd-sided boxes and you can't start your line inside more than one, it becomes impossible. If there were only two odd-sided boxes it would be ok because you could start inside one and finish inside the other, and you'd just pass through the even-sided ones on the way. When I worked this out I just gave up trying to find the clever solution and watched the rest of the video, only to find out there is no solution :P
People, please!
I see the majority of people don't understand the term impossible.
You've been given rules saying you can only cross through lines.
You've then been told that this is proven to be impossible.
And if it's mathematically proven to be impossible with these rules, then the only way you can think you did it is by doing it wrong.
A lot of you say you can do it by using corners.
Of course you can, but you can also do this by ignoring any other rule. I did it by completely ignoring half of the bricks but that clearly doesn't count. If I said to you, "This is impossible, but try to go through this maze by getting through all the doors while only going through each door once" and I saw you trying to walk through a corner of the wall into the other room because you're that stubborn, I would laugh.
I know how to do it!
1. Get a really really thick marker
2. Draw a huge line through the paper.
.
PivotMapping OMG ur a genius!!!!
Caleb Stremcha fuck u
ya 😂😂
REEEEEEEEEEEE
Solving it involves proving that it's impossible. That is the solution.
+TheGreatRakatan fold the paper you moron
+TheGreatRakatan Its not impossible
it has been done
+Jalvlie sorry I was using different rules to solve the puzzle, I was using each black line as 1 wall: not multiple
It is impossible, using some of Euler's maths and theories you can prove its impossible
+Nathan de Pater Lol, oh this is gonna be good. Please explain oh master of planes.
roses are red,
violets are blue,
if you think you did it,
you screwed a rule.
roses are red,
violets are blue,
this comment is so true it woke king Neptune.
Roses are red
Grass is greener
When I think of you
I play with my wiener
Roses are Red, that much is true! but Violets are Purple, so buddy Fuck you!
Roses are red, violets are blue, god made me pretty, what the hell happened to you!
Last Requiem ^^
Haha at all these people. "Technically I did solve it I just went to another dimension and crossed the corners and went on a line so this is solvable."
k guys, k.
He said cross. Not intersect (sharing a point) but cross. In 2D, they're interchangable (kind of, cross is actually wrong but nobobdy would get confused), but in 3D, a pair of crossing lines is defined as a pair of lines that are not parallell, but also don't share a point. If they're not parallell but they do share a point, they're intersecting. So, if you consider the puzzle to be 3d, it's actually incredibly easy since all you have to do is draw a line that is not parallell to any line in the puzzle and also doesn't share a point with any of them.
i teleported
you sound just like the guy from numberphile...
+AmazingGryphon Cool.
He is one of the numberphile speakers!
LLHLMHfilms lol yeah maybe he went on numberphile once
+AmazingGryphon Once? He is one of the better known ones.
+singingbanana Hi James!
lol I immediately recognize the voice's guy being from the channel Numberphile
My teacher gave us that problem in 3rd grade. I proved it was impossible then after trying the whole year. Wasted notebooks trying before I figured out it was impossible. I don't remember my exact proof but my teacher was really impressed. I went to a really advanced private school if you're curious about the advanced placement of math.
Excellent. And you remember it! That's good teaching.
Rohan Mudumba what is a really advanced private school, and was it a really long year realising this is impossible?
Do you have to press the marker down so hard so it makes the ''RHHHHHHHHHHHHHHHHHHHHHHHHHHHH'' noise?
ikr it gets annoying 😂💯😀
+Fennekchu ghahahha
You guys get easily annoyed, I'm sorry that you had to hear a sound that you dislike lol
Love that sound!
yes
OMG you're that guy from numberphile :0
Phonzo Cisne Yup.
+Phonzo Cisne OMFG
I knew it from the voice!! Then I scrolled down and saw this comment xD
+Phonzo Cisne its very familiar how he said "here" :D
Why are there dislikes?! He explained it and gave a proper video description. Do you people not like his accent?? Sheeese... UA-cam smh
Dislike bots
+Apocalypse For one, there is a wall that a line didn't go through, and two, he/she/you cheated and went through an intersection not an actual wall
He didn’t really prove anything. He just gave a blanket rule without explaining why it’s true.
its because he said he would give solution. so it was kinda click bait
He actually did. It has to be a pair number of lines since you want to go in as many times as you go out, except for the beginning point and the end point
A kid showed this puzzle to me in the 6th grade in 1984. He moved away before I ever found out if it was solvable. Over the years, I have wondered was there an actual solution. Thank You for letting me off the hook, Lol
Since you used the word "cross" and not "intersect" then there is a technicality that makes this puzzle solvable, and that is that we can cross one of the lines (specifically the upper middle vertical line) from end to end just as you would cross a bridge. That, however, is the only way this puzzle can be solved.
Nice one.. I came up with this solution and you are the only other person who has pointed that out in the comment section. Exactly !!. Running along a line or edge is not the same as intersecting it.
So three of the boxes are odd nodes, each having valence=5.
You might notice that the outside region is another odd node, with valence=7.
So there are actually 4 odd nodes, and 2 is the maximum for an Euler trail to be possible. (There must always be an even number of odd nodes, BTW.)
My grandfather showed me this and it kept me puzzled for years. Eventually I I worked out that it was impossible by virtue of the number of individual lines versus entry/exit points you need.
But really it just reminds me of my grandfather, how wonderful he was, and how he always wanted to give me something to think about (or to keep me quiet 😂).
To be really correct about Euler trails, you need to consider a “center point” at the outside of the design, because if you represent this as a graph you would have 6 nodes : one for each rectangles and one for the outside. Therefore you don’t have 3 but 4 nodes with an odd number of edges.
Obviously the answer stays the same : you still need 0 or 2 nodes with odd number of edges to have an Euler trail in the graph.
It could be anywhere between one and four 'centre points' on the outside though I think, which is why he leaves that open on his diagram. I think it does gaurantee at least one more odd node on the outside though, given that there are nine crossings to the outside.
I have found a solution but the UA-cam comment section is too small to contain it
Its easy... figured it out in about 25 secs
Classic Fermat trolling
there is an easy solution. think of this drawing as a 2 dimensionsional entity in a 3 dimensional space. you can go up and down through the paper. problem solved.
Stop it, Pierre!
uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuhhhhhhhhhhhhh no
3 of the rooms have exactly 5 walls. For a path to exist that crosses every wall exactly once, it must, for each of the 3 rooms, enter a times and leave b times. b > a only if your path starts inside the room. So for at least two of the rooms, a > b. There's no way to enter a room 4 times and leave once, or enter a room 5 times without leaving, so it must be that you entered both rooms 3 times and left both rooms twice. Since you entered once without leaving, your path must end in one of them, but also the other, which is impossible. So no path exists.
I love all you guys saying "I Solved it" cause i know u did not :D
He showed a proof that it is immposible.
So, if u solved it, you did somthing wrong!
Best way to check if its solved is to follow the line you drew, and highlight every edge you cross. Most "solutions" either have one edge not highlighted, which would normally not be detected.
It is possible to solve this puzzle, talk of going through corners and following on top of your own line is against the rules! To make it more specific; make a door in each of the walls, you must go through each of the doors only once without taking the pen off the paper. Hint: the answer lies in the phrasing of the rules, the solution is not mathematical. Have fun.
Some of these solutions I am reading are the same as saying 'I Solved the Rubic's Cube by pealing off the stickers and sticking the same color ones on the same side. Duh, it's so easy.
I have been trying to figure this out for 20 years!!!! I just decided to Google it.... only to find out I was wasting my time doodling this in my notebooks all throughout school lol😂
"I solved it by making the puzzle 3D"
"I solved it by crossing the intersections instead of the edges"
And thanks for saying that you broke the rules of the game
It's really funny that this came up in my recommendations today. I was reading about this exact problem last night.
P.S. YES PEOPLE, IT'S THE GUY FROM NUMBERPHILE
FuckYouGooglePlus
true i was about to say that
I am a Chinese and learned it while I was a pupil, really I remember this all my life. In China it is called Olympic Maths and a lot of children learn it in order to be smarter than others. Now I am guaduated my bacholer of science and my major is mathematic. Thank you making me remember that happy childhood
This seemed like a great puzzle, and one I could surely solve...after carefully drawing the puzzle I proceeded to draw out all possible combinations of lines by creating triangles throughout the puzzle (which he basically does). Within ten minutes I realized that this puzzle must be impossible. However, after staring at this piece of paper for an additional hour I realized that the only way you could solve this puzzle was thought the intersections (corners)...I then thought to myself "Hey, maybe I'm not as stupid as I thought! ". Of course, another five minutes later I realized that this was cheating and confirmed that I am indeed stupid. Being unable to solve an impossible puzzle isn't grounds for stupidity...however, realizing a puzzle is impossible within the first 10 minutes, and then staring at the puzzle for another hour stubbornly searching for an "ah ha" moment is bang on stupidity. Sorry Dad, but I'm a dummy.
It's important to note that this, as simple as it looks, is part of a revolutionary math paradigm that Euler did.
I think one of the most remarkable problems is the "Königsberg bridge problem" which inspired Euler to do this kind of things (this is a cite from my geometry book, I do not really know if this is true and whether it is or isn't we can agree it makes for a cool story)
When I was middle school I looked a brick wall in class and out of bordem decided to make a puzzle for myself. This was the puzzle. You have no idea how many years I spent trying to solve it and how many times I drew the damn the thing. I think was still attempting it as a Senior. Now I know I was never going to achieve my goal.
Your approach was wrong.
When you kept failing over and over, you should have stopped trying to brute-force it, and instead analyzed why you keep failing.
That way, you could have figured that it's impossible, and why, instead of wasting your time drawing pointless lines over and over.
I paused the video before the answer and spent the last 3 days writing code modelling the problem and flipping tables wondering why my program wasn't finding any path bigger than 15 crossings. Hm... At least I wont forget what a Euler's Trail is.
Mathematics can be a mean teacher, sometimes haha! (T_T)
Nice solution fam, you really showed it in the vid
Not a click bait at all
Nice observation skills fam, this video is 7 years old. I don't think the uploader will even see your comment. And if he does, he certainly won't care.
BeFondOfJohn Well that's not true. Zero is the absence of things. You see more 0's in a day than basically any other number. You see 0 real murders (I hope), 0 living mountain dew bottles, 0 polar bears. Numbers themselves as in 1 the idea and 8 the idea it's also very real. 0 is just as much an abstract idea as all the other numbers.
BeFondOfJohn Explain when a number isn't a measurment in some way. Numbers are ideas and 0 is the one we interact with most, making it the most real number.
BeFondOfJohn But 0 does exist in measurements. That's pretty basic. I have 0 polar bears. There's 0 inches between me and myself. The ball traveled 0 feet. Now you can't get negative measurements that's true. But you can get a measurment of 0.
Cool demonstration. I recall reading about this. The Königsberg Bridges problem. For years nobody could find a solution or figure out for sure that the solution did not exist. It was Euler who proved that it was impossible in similar fashion that you did. I think it was something like - If you enter an island (box) then you must leave it, so there need to be an even number of bridges (except for start and finish as you stated).
Wait, it took them years to figure this out?
With several people trying?
...I solved this puzzle without help a few years back. My father presented me with the puzzle and I just couldn't find a solution, so I figured it must be impossible. But I wasn't satisfied with just thinking it's probably impossible, so I tried to solve it mathematically. Turns out I was right, it's impossible to solve it the traditional way, for exactly the same reasons that were explained in the video, so that's the solution. I can't believe it took them so long to figure out why this is impossible. O.O
What if somebody take it seriously ,paused the video,tried to solve it for a week having patience,came again to video for solution and he got to know that it was impossible....
I solved it!!
I cheated
***** You're right
you ain't solved shit!! if you had you'd be a million dollars richer!!
Oh hey it's me from 2 years ago
baileyboy125 what's up?
Heya +kieran sia how are you?
I "solved" this problem 45 years ago in 8th grade. My math teacher gave me an "A" for creativity. Every Friday, he gave me a puzzle to solve over the weekend. After 20 weeks or so, he presented me this puzzle. You should have seen his expression when I informed him Monday morning that I 'solved' it. PRICELESS! I adhered to all the rules, crossed through each line only once, and didn't lift my pencil off the paper.
You see, my teacher didn't tell me it was a trap like the Kobayashi Maru.
en.wikipedia.org/wiki/Kobayashi_Maru
The second time I did it (And I though I solved it) I realized that the straight horizontal line counts as 4 lines, then the recangles have 5 lines to be crossed, odd number, that means that you only can end inside of it, but then you have 3 of them, it's like having 3 cages and you need to end in all of them at the same time.
geminix365
Thats bullshit since its impossible to solve.
Let me be clear: I will not rest, and my administration will not rest, until we've solved this puzzle.
I just did it
+Bugboy24MC Liar!!!
+Stefanie Neko start in the middle
+Daniel Bundrick Try to start with just a simple pentagon, exactly... YOU CAN'T FINISH OUTSIDE OF IT, the rectangles are basiclly pentagons, with 2 was already impossible with 3. It's like trying to draw a square with 3 straight lines, Impossible. Btw, I guess you were kidding, have a nice day.
So how are you 2 years without sleep
5 square rooms + outside = 6 rooms
3 rooms with 5 doors
2 with 4
Outside has 9
Basic rules:
Each room is in one of two states > 0=Empty, 1=occupied
On only one room can equal 1 at a time
Am odd number room (5 and 9) will always end opposite of what they started with
Even number rooms (4) end the same as when they start.
Senarioes:
Door#: Start State > Fiinsh State
Starting ng in odd number room:
Odd(5): 1 > 0
Odd(5): 0 > 1
Odd(9): 0 > 1
Even(4): 0 > 0
Even(4): 0 > 0
Ends with 2 rooms occupied, impossible!
Starting in even number room:
(5): 0 > 1
(5): 0 > 1
(9): 0 > 1
(4): 1 > 1
(4): 0 > 0
Ends with 4 rooms occupied, still impossible.
Beautiful.
WHY IS NO ONE NOTICING THIS?
If you were to count each box as having it's own 4 sides and then add them up- the total should be 20 sides- NOT 21.
So this whole diagram requisite is false. Here's why... They're technically asking you to go through the upper part of the middle brick's edge TWICE, when instead it should be considered ONE brick edge (for the top part of the middle brick). The bottom center box is being divided into an imaginary two squares or brick edges, when the lower middle box's upper brick edge should be considered one line, and the center-line that separates the upper two bricks should be considered the line necessary to cross that lower middle box. As is it defies logic and deliberately makes the task impossible, but when looked at the way I described- it's possible... and logical.
No, you misunderstand. Where an edge is bisected by a perpendicular line, as the top edge of the middle-lower brick is, it is considered two lines, and you have to go through each of them once.
I understand that, but the premise is to go through each brick edge- not every line. If it's meant to be every line, then the boxes have nothing to do with it, and they should change the instructions. It shouldn't be both.
Ethromel The premise is to cross each line once and only once. A bisected line = 2 lines, as is explained in the video. The boxes are part of the explanation, not part of the initial objective.
There are no boxes. Just because you see boxes doesn't mean they are there. All I see are lines I need to cross only once.
AwesomepianoTURTLES shh turtle fanatic group they are talking a language that doesnt fit inside google translate, i think its a new species
Doesn't the fact that the bigger squares have unequal entry/exit points mean that it's impossible? You need IN and OUT points and that's 2. Maybe if there was an equal number of the big squares connected it might work but there's 3
+Kusinuppi Exactly
I have come up with two solutions out of about 6 attempts at this. Two solutions that actually work given the description that you and everybody else gave me: cross each line *once*, with one, continuous line. The only thing that is not mentioned, but clearly implied, is that you cannot start and end inside of the house. The two that I came up with involve starting in the top left, and ending in the bottom middle. The possibilities are not limited to those rooms, but those happen to be the solutions I came up with quickly. I even heard another guideline/rule in the scamschool video about this and another number problem: You could even cross the lines if you feel like it. The two solutions that I came up with don't even use this added aid.
I can’t tell if the “Euler’s Trail” paper at the end was computer generated or hand drawn.
can you make more videos on Euler and his proofs like bassal problem, amicable number and other? He was amazing and wonderful mathematician .
I certainly will at some point!
I tried it like 5 times, and in between each I thought about how there were 3 boxes with 5 lines to cross, so it must be impossible, but I kept trying because obviously if you were about to give the solution, it must exist. Then finally, I was so sure it was impossible that I gave up and decided unpause to see your solution.
Quick version: it has more than two odd vertices and thus cannot be solved ;).
I assumed it was because of an odd number of odd vertices
@@parodysam It can be even too but still create an invalid situation only if it's 4 and over.
If you think outside the box you will find a solution for this. The puzzle doesn't say you can't cross the lines at a 0 angle.
But thats not an edge or line. It's angle so you still have to do the other ones also this is mathematically proven to be impossible like how it is mathematically impossible to fly in a place with gravity in a stand still position.
But thats not an edge or line. It's angle so you still have to do the other ones also this is mathematically proven to be impossible like how it is mathematically impossible to fly in a place with gravity in a stand still position.
+Saleh Haddad Then you overlap it instead of crossing it.
+Saleh Haddad The line must curve. Sorry!
Overlapping means infinite intersections, that means you are crossing the line more than once!
Just wanted to offset all the negative comments and say that this is a great puzzle, feels like a more complex Königsberg bridge problem. Also, I find it awesome you're still replying to comments after seven years.
Go through the corners that join multiple lines...
I started in the top left line(not corner) then went down to the bottom corner and up through the inner corners of those first two rectangles on the left, next I went through the top right corner and kept going to make an arch that came back around to the bottom right corner then came up through the middle bottom and through its top right corner to complete the puzzle! :D
Caroline Johanson My god... you're right. I just did it that way and it worked. Nice work thinking outside the box. =3
Thanks! I spent awhile coming up with it though... this puzzle was really frustrating in the begining
Caroline Johanson So when you go through a corner, which line are you crossing then?
both, lol
Jesus Christ you sound too much like Numberphile.
+TheWilliamMaster You do realise that he is in a lot of numberphile videos, right?
+TheWilliamMaster I am the guy from numberphile.
+singingbanana didn't think that you still read the comments on this video lol.
+TheWilliamMaster sounds like Dr James Grime
+Thomas Waller (TiaTnT) YOU DONT SAY!
the rules say that you have to get through so the wall ones by going through a corner you are go through two walls at once
I recognized his voice the moment I started watching the video THE NUMBERPHILE GUY! lol
James grime i think is his name
Are u on numberphile
I am
i recognised your voice immediately
singingbanana I knew it
If you draw a line larger than the rectangle it is considered only going though at one point as it is a single line and only travels in one direction, therefore never goes back to cross again
OK. check it... when I was in the 6 grade we had a sub teacher that gave us this problem and he swore it had a solution. I believed him, why shouldn't I he was a teacher. I spent the next 40 years working this problem and it wasn't until 3 years ago that I mathematically worked it out that it couldn't be solved. I"M STILL PISSED. Tonight, this night I saw this on the tube and my heart raced... I clicked over, never seeing this problem anywhere during my travels over the 40 years.. I thought, what if?? Then I watched the video, the first one, that stops before giving the solution... I WAS pissed again.. then clicked over to this to lay to rest a painful search for a solution and to question everything no matter how credible they may seem..
The story of a lifetime, folks.
+Mike Pratali the solution is to put it on a sphere. draw it on a basketball then do it. with a 3d platform its easily possible
no it isn't
@Mike Pratali - Reading your post, your experience is identical to mine - absolutely to the last detail!!! I was told there was a solution, the teacher wouldn't show us, he left us with the puzzle over a summer holiday. He did say that the solution looked like a 'teddy bear'. I never saw the teacher again so never did get to see a 'solution'. I am sure he couldn't have been that cruel...
There's only one way to solve this: imgur.com/tkhXhwJ
lmao xD
I got it! Pleasse read!!! Start on the top left rectangle . Then draw a line going down in the middle of the long line then take a left going through the left small line.then go down until you have reached the middle of the left side box. Take right and then go down. Then take a right untill you are in the middle of the middle rectangle go up and then take a left after taking the left will be on the bottom left box again go up and take a right going through the other small line but dont stop at the middle this time say about an inch then go down now at this point you should be at the middle rectangle after that take a right and you should be going into the right bottom box go to the middle and then go down now.you should have gone thru the the bottom line of the right bottom box then take a left then go up until you are at the middle take a left which is going thru the right side of the rectangle then go up. Booom! Am I right?
These people commenting that they solved it LOL, please post a screenshot and I'll tell you how you got it wrong thanks :)
I saw one who actually managed to solve it.
Here, I still have the link:
gyazo.com/930b795b6932820f615e11f088f547ef
theuncalledfor yeah thats the only solution :))
prntscr.com/bgkoop
Suknaman you went through the same line multiple times.
where ? :)
next time tell me it is impossible first... before I waste an hour of my life
Not impossible
Well I noticed that this sort of thing can be simplified. If you take just those two top rectangles (and each of the bottom sides are divided into two) or actually just take 2 adjacent pentagons, it appears to be impossible. I believe it's because, going in and out, you take up an even amount of lines, but here there's an odd number of lines, so you are forced to go in a polygon and cannot come out. And yes I didn't finish watching the video
I figured it out!!!! It's not impossible!!!
Yes it is
no
+KittenGaminq then post a video and link it
if I can get my phone to stand up, then okay
+KittenGaminq Why is it that all the people who say they can do it are usually retarded 11 year old Minecrafters?
You were pressing down on that marker so hard when drawing the line it made me cringe lol
it can't just be me that infuriated by the noise of that pen. GET A BALL POINT PEN!
OMG do not do that fkin noise with the markerrrrr!!! Aaaargh!
The solution works took me 3 min to get, it never says u can cross corners and if u cross a corner u will automaticly cross 2 to 3 lines and then it's possible =) it never said cross 1 line at the time =) but if thats the case its impossible
Mind blown
+Matthew L yes and its easy tbh try it out
Robin Lindsten that's total bullshit.
It's a simple case of parity:
If a light-switch, (or toggle,) is down and you turn it the other way, (or toggle it 180° every time,) then it will always be down after an even number of turns, and it will always be up after an odd number of turns. So, in any case where the toggle is down and you turn it an odd number of times it is impossible that it will end down▪
(That was the whole point of this exercise.)
Such an intuitive way to introduce the topic! Great video.
What is the answer? You didn't draw the curve. This is totally ridiculous. The title says solution. Am very disappointed in this video. It was very poorly done.
The explanation was complete. The solution is the explanation of why it's impossible. I also gave you the name of how to solve problems like this, Euler Trails, which you can look up.
Check out my vid it has the actual answer
you used the wrong brick, you silly sod
Its his fault that you cant understand a good and simple explanation, right?
I read your comment in a british accent. idk why :))
Depending on how you tackle the problem, you can end up solving the Eulerian Trail problem which is polynomial, and more precisely linear in terms of the number of eges and vertices; or you could also end up with the Hamiltonian Path problem, and this problem is NP-Complete meaning that only exponential solutions are known (and it's very, very, very unlikely that we will ever find a polynomial time solution for that). Now of course this doesn't really matter here because the graph is not too big, but I thought this was an interesting fact to mention.
I showed this to all of my teachers...i started the year with an A+ for all of my classes. Don't ask how or why, I give the credit to this man here.
I've seen this before. And I've wondered why the impossibility proof can't be explained more simply as follows:
Consider the drawing a floor plan of rooms. Draw a door in each wall leading to an adjacent room or to the outside. The puzzle now becomes this: Walk through all the doors without going through any door twice. Notice that every time you enter a room you have to leave by a different door, unless you started or finished the trip in that room. So all the rooms except the first and last must have an even number of doors. But there are three rooms with an odd number of doors--five doors each. Hence it can't be done.
The proof is equivalent to what was presented in the video, but without the extra steps of drawing the graph with a center point in each room, etc.
The graph using the centerpoints of each room is useful in a sense, because it illustrates a correspondence with problems of drawing geometric figures without lifting your pencil. But that equivalence isn't necessary, and I think my version of the proof is easier to see..
At first glance I notice that the top two rectangles each have 5 required crossings, which in words would be: "In-out-in-out-in"
---> both of them require that you stop inside, since you need to stop inside of two different places it's impossible
If the rule is you can't take your pen or pencil off the paper you go through leaving 1 edge inside and your line on the outside, you bend the paper into a roll until the edge of the paper is next to the uncrossed edge and then draw over it, it's continuous from 1 observers perspective
I've literally been trying this since I was 9 years old and this randomly popped up on UA-cam
So reading comments, corners count as two, so it's possible you count that (It isn't specified that you can't do that) the other way, is that you use horizontal line, and draw a line over top of all of them, but then you just have to pass through the vertical lines.
Each time you cross a line touching a box you either go from the inside to the outside or from outside in, so for a box with an odd number of lines you will go in and out sequentially an odd number of times and end up either outside if you started inside or inside if you started outside, so for each odd numbered box you will either start or end inside. This picture has 3 5 sided boxes and you can only start in one, and finish in one, meaning at least one of the boxes cannot be started or finished in and therefor cannot be crossed the requisite 5 times.
edit: the outside of the boxes is also an area with an odd number of sides touching it(9) so there will actually always be at least 2 sections missing 1 cross over, not to mention if one section has a side not crossed then it must have a section next to it also missing a side.
For all of the people claiming "click bait" and "didn't show a solution", in maths, no solution is an answer. The answer to this problem is null set, and he proved it.
I spent hours trying to solve it and now that know it's impossible I can actually continue on with my life
When I was young my 5th grade teacher showed us this "puzzle" and said he'd show us the solution tomorrow. I was absent the next day and no one would tell me what the solution was so I spent the rest of the school year trying to figure it out. I eventually came to the conclusion that was impossible. I figured with the amount of lines you had to cross, 16 vs the amount time I had spent trying to solve it that it was actually statistically improbable that I hadn't solved it yet. In other words, I either had absolutely shit luck, or the thing was impossible.
That's the first step towards the solution. But you never completed the second step: Understanding why it's impossible.
Well, until two years ago when you watched this video, I guess.
When I was a kid I must have tried to do this several hundred times. Now I’m really pissed to find out that I waisted all that time. Lol
If it must be done on a two dimensional plane with the requirement to cross through the edges, then it’s impossible. But if the wording says to intersect the lines, it’s really easy. (Think inside the box for that one.) It’s also feasible if you approach the problem using three dimensions. (Like taking a needle and thread to puncture/pass through each edge, then tie the thread outside the piece of paper.)
In New Zealand we learn this in Math class as a unit called “Networks”. Great video. :)
Wait, seriously? My school never offered anything like that.
Found this puzzle a couple of years back and it is in fact impossible if you do it this way, but if you go through corners, where 3 lines connect (in an angle where all 3 are crossed) you aren't abusing the rules but you can still get a solution.
It's just graph theory isn't it ?
I counted the number of lines (and not sides) of each boxes and saw 2 boxes have 4 and 3 have 5. Since there can only be 2 boxes with an odd number of lines, this is impossible.
(Because we have to enter and exit once every box but the one we begin with and the one we end with, all the boxes but 2 should have an even numbers of sides).
Whenever you go through a wall of a room, you end up at the different side (inside or outside) of the room.
If a room has odd number of walls and you go through all of them, you end up at the different side (inside/outside) of that room.
There are 3 rooms (named A, B and C) in this puzzle have 5 walls, and you try to go through all of them:
If you start inside one of them (say room A), which means you start outside room B and room C, so you must end inside both room B and room C if you plan to go through all walls, which is impossible.
If you start outside all of them, then you have end insides all of them, which is also impossible.
Even knowing what Eulerian trails and Eulerian paths (and their distinction) are, and looking at the title of the video, I just couldn't think of a way to convert the picture into a representative graph until you showed it (except you didn't join the 'outside' as a nine-edged vertex).
With the underlying graph drawn it can be easily shown how to change the original puzzle such that it _is_ possible to cross every line only once, and then there are quite a number of ways to do this-either by removing a certain line, or splitting a certain line, to respectively remove or add an edge between odd-degree vertices to make them of even-degree. The original problem is itself a graph, and it turns out that its 'dual'-where the faces are the vertices and the vertices are the faces-is the graph needed to solve the puzzle.
(I use the properties of Eulerian trails a lot in my work, as I do embroidery and it saves thread to visit every edge only once, and if the Eularian trail does not exist, how to split the design into subgraphs of which it exists.)
To the people complaining that he said Solution in the title and therefore baited you into the video, what did you expect? Did you want him to title it, "This puzzle is impossible"??? The point is to make you want to try and figure it out on your own, if he told us it was impossible in the title, it would take away from the excitement of wanting to solve it or potentially figure out why it cannot be solved.
James the only problem is that it's possible to cross 3 lines at the same time.. if you cross through an intersection. However you will start inside and end up inside or start outside and end up outside.
In fact, there's lots of solution. The problem says that the line may not cross the same line twice. But we're allowed to make the line crosses itself, think about it and u'll find a solution, there are many possible like that.
This is the only video I can watch on any thing for somereason
Read the whole book "Journey threw GENIUS". Euler is mentioned in that book but changed because more books means you need to go down way down and lose to someone for the name.
On the first try I got within one wall! I was so excited!
Thanks for the puzzle!
Draw a line following the edges,when you draw the last line, make sure to stop it before it touches the others. Then you solve it normally.
As long as it's not required to bisect each line you can solve it by crossing at the intersection of 3 lines (the corner) which covers 3 lines with one crossing. Solved.
You may be a singing banana or a weeping apple, but for me you'll always be the Numberphile guy.
Adult Hintler
It has a solution
In 0:47 he could enter the left square and cross the down line then enter again from the outside throw the ledt line then the top line .. and finally the middle line in the picture ☺☺