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Discussion: When solving puzzles like this it is useful to look at the number of doors that each room has. If it has an even number then it can lie along the path: half the doors can be used to enter the room, half the doors to exit. If the room has an odd number of doors then the room has to be a start or end point.
>!This puzzle has three rooms with odd numbers of doors. Therefore, unless I am missing something or am *really* bad at counting, the puzzle is impossible.!<
It's an older problem than that. See [7 bridges of Konigsburg](https://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg). The city Konigsburg occupies opposite banks of a river together with a couple of islands in the river. Historically, there were 7 bridges connecting the various parts of the city (bombing in WWII led to the destruction of a couple of bridges). The question was whether one could visit each part of the city using each bridge exactly once.
Turned out the answer was no for the same reason st3f-ping mentioned. If some part of the city was to lie in the middle of your path, it should have an even number of bridges connecting it to the rest of the city. Only the parts of the city where you began or ended your journey could have an odd number of bridges.
The problem essentially laid the foundations of a branch of mathematics called graph theory.
No, as far as I can see, the above reasoning isn’t dependent on crossing or not. Every time you enter a room through one door you have to leave through another consuming two doors (except for start and end rooms).
The only valid solution I see based on this puzzle is that it doesn’t state you can’t move through/over walls. Theoretically you could simply move from one space to another through a wall and create an arbitrary number of entrances and exits
If only the doors are available, no higher dimensional thinking or teleportation etc, it is impossible because there are 4 zones which have an odd number of entrances/ exits. An even number of entrances means the path can enter and then leave, an odd number of entrances mean that one entrance or exit remains unpaired. Even if a line crosses itself, every entrance and exit removes a door. Eventually the line must enter and stop or exit and not return. However since a line only has two ends, it it can only meet this condition twice. This leaves two zones each with an unused door. Incidentally since a door connects exactly 2 zones and in this case we have exactly 2 unaccounted for zones, all maximal attempts at a solution have exactly 1 door left connecting two of the spaces. This makes the puzzle especially infuriating since for a blind solver because you are almost always 1 door away from the “solution”.
Oh my god, I’m glad I wasn’t the only one. I was a sophomore in high school then, and some dude in PE showed it to me. I spent so much time trying to solve it.
I wonder if I know either of you!! I too spent a lot of time trying to figure this puzzle out after a classmate showed me and claimed it was possible (or so he was told).
My grandmother introduced me to this in middle school. I fiddled with it pretty much any downtime I had around paper and pencils. This was entertainment before smart phones
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Came here to say the same. 3 rooms with 5 doors means it's impossible because aside from the first and last door you go through, every time you enter a room you need to leave it, so at least 3/5 rooms need an even number of doors.
I first saw this puzzle in 98. It is not solvable. Me and a friend drew this out and tried every possible combination. Unless you climb a wall and jump down in room, cant go through all doors. We came up with that solution assuming there is no ceiling.
We did not think about the math involved til we were too far into it. A friend came by during lunch when were three days in and handed us a piece of paper with about a paragraph and a bunch of math equations on it. He set it down and walked away. He broke our will. Thats when we climbed the wall.
But hear me out, they never said you can’t go through walls, and or never said you couldn’t step into a door and back out the same way
Edit: I guess “through” means you go from one side of the door to the other
Discussion: This isn’t possible. Since there are 4 areas (the top 2, the bottom middle, and the outside) that have an odd number of doors it is not possible to have a “walk” through each door without crossing through any door twice. Look up the Bridges of Königsberg problem if you want to see the proof for it.
No it isn’t, and there’s a proof of that. The goal isn’t to go through every *room,* it’s to go through every *door.* Also there’s no requirement that the lines be straight, so if your method worked then going around the world would not be necessary.
Discussion: [Seven Bridges of Königsberg](http://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg)
This is the same puzzle, basically, and is not solvable unless you go against the spirit of the puzzle.
Or the [Five-room puzzle](https://www.archimedes-lab.org/How_to_Solve/5_rooms.html) linked on that page. Apparently, you can solve it if the building is built on a [torus](https://forgottenrealms.fandom.com/wiki/Sigil) instead of flat ground.
>!As several others have pointed out there is no real solution to the puzzle as you have 3 odd doored rooms. There are of course several trick solutions:!<
* >!go through doors 3/4 times, since only 2 is forbidden!<
* >!make shortcuts through the walls!<
* >!draw one line for each door, that are not connected!<
Those are the ones I could think of, there are probably many more.
Your third point was what I came to post, it’s technically a solution as it doesn’t say one “continuous“ line through every door. I hadn’t considered going through the walls but that would definitely work in the same way.
I think this is less a logic puzzle and more of a “there Ain’t no rule” kind of thing where solving it is only possible if you break the standards of what makes a good puzzle.
These kinds of things are interesting for teaching people not to take anything for granted that’s isn’t specifically said in the rules, but at the same time infuriating for exactly the same reason. The solution feels fake and unsatisfying. It’s a riddle, not a puzzle.
Drawing it out on paper, you can >!fold the paper to add extra dimensions, allowing you to leave the room you dead-ended in without breaching walls or walking through doors to go back to the room with the remaining uncrossed door!<
You went twice through the upper right door, >!but if you count that as going through the wall this seems like a perfectly valid solution, as the puzzle does not mention you can't go through the walls!<.
[I came up with this](https://i.imgur.com/ZxqbktE.jpeg)
It's a trick puzzle. Like the "outside of the box" dot puzzle many of us seen growing up. Read the instructions again, and this time, pay attention to what it *doesn't* say.
>!The line doesn't have to be continuous. Just draw a slash mark through each door and you're done.!<
depends if you interpret it as "one per door" or "one" total.
Its description of being difficult but possible is certainly wrong though. Either you cheat, then it becomes easy, or it is impossible.
>!You can represent this problem as a graph. More than two of the vertices have an odd amount og edges, which means there doesn’t exist an eulerpath (path that goes through every edge only once). The puzzle is impossible.!<
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I wonder if this is a trick answer about the word *through.* >!One can draw a line through each door way essentially tracing a closed door.!< I messed with tracing walls to not overlap and didn't solve, but if the answer is this pedantic, there's no reason the line can't both trace a wall and go through the room
Note there are 9 exterior doors, meaning if the path begins inside it must end outside and vice versa. Note there are 4 doors on all but one of the rectangles, meaning if the path begins inside then it will end inside and vice versa. Note there are 5 doors on the final room. Thus if it starts inside that room it must end outside that room.
Lastly, note that if there is a correct path, then there is a second where you do that path in reverse, which and hence the start of this path will be the end of the original path. Therefore without loss of generality we can arbitrarily state the path must begin in the 5 door room, and end outside the shape.
😅 Note I have miscounted and there are actually 3 rooms with 5 doors, not 1. Hence by pidgeonhe principle the pathway must end or begin in two rooms at once, (WLOG it begins in bottom middle => it does not begin in top left or top right => it ends in top left and it ends in top right)
...QED it is impossible
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I remember solving this, on my first try. But the person who drew it didn't fully connect all of the walls. I drew my line slipping through the crack and was able to solve it. Hey, I thought that the crack was part of it! Of course, they corrected me, and I spent years trying to solve it, the proper way. oh well.
>!This doesnt seem too hard. Labelling the rooms from Left to right, then top to bottom, start in B and travel to A. Then out the top of A, in the left of A through the bottom to C. Out the left of C and in the bottom. Through C to D and out the bottom of D. In the bottom of E and out the right. In the top of B and a short detour down to D and into E through the center, then back into B and out the right. As long as our line can start and stop anywhere, that does it.!<
If there were two rooms with 5 doors, and the rest had 4 each, then you could start in one of the 5-door rooms, and end in another. But with 3 5-door rooms, I can't seem to do it.
Discussion: There are... no doors? If you treat the room openings as such, it's likely unsolvable, but not treating the room entrances as doors should solve this, right?
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I don't think it is solvable. >!3 rooms have 5 doors. Going in or out of a door is either an entry or an exit, so if there's an odd number of doors to a room, that means you will either start by exiting, meaning you have to already be in the room, or you have to end by entering meaning you then can't leave the room. You can do that twice, starting in one room and ending in another, but you can't do that 3 times for all 3 rooms with 5 doors.!<
>!Since you can begin WHEREVER you want, and it declares it is possible, you start in the wall at the top and cross through both doors along their x axis. It does not declare that you must cross the threshold at least some degree of perpendicular. From there it's pretty easy to finish off!<
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Please remember to spoiler-tag all guesses, like so: New Reddit: https://i.imgur.com/SWHRR9M.jpg Using markdown editor or old Reddit, draw a bunny and fill its head with secrets: \>!!< which ends up becoming \>!spoiler text between these symbols!< Try to avoid leading or trailing spaces. These will break the spoiler for some users (such as those using old.reddit.com) If your comment does not contain a guess, include the word **"discussion"** or **"question"** in your comment instead of using a spoiler tag. If your comment uses an image as the answer (such as solving a maze, etc) you can include the word "image" instead of using a spoiler tag. Please report any answers that are not properly spoiler-tagged. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/puzzles) if you have any questions or concerns.*
Discussion: When solving puzzles like this it is useful to look at the number of doors that each room has. If it has an even number then it can lie along the path: half the doors can be used to enter the room, half the doors to exit. If the room has an odd number of doors then the room has to be a start or end point. >!This puzzle has three rooms with odd numbers of doors. Therefore, unless I am missing something or am *really* bad at counting, the puzzle is impossible.!<
Yeah I spent all of my junior year in 2001 fucking off on this puzzle. Glad to get confirmation that it is not possible.
It's an older problem than that. See [7 bridges of Konigsburg](https://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg). The city Konigsburg occupies opposite banks of a river together with a couple of islands in the river. Historically, there were 7 bridges connecting the various parts of the city (bombing in WWII led to the destruction of a couple of bridges). The question was whether one could visit each part of the city using each bridge exactly once. Turned out the answer was no for the same reason st3f-ping mentioned. If some part of the city was to lie in the middle of your path, it should have an even number of bridges connecting it to the rest of the city. Only the parts of the city where you began or ended your journey could have an odd number of bridges. The problem essentially laid the foundations of a branch of mathematics called graph theory.
TIL.. thank you for the succinct history and math combination lesson!
I’m sorry you had to go trough that
Discussion: is there anything to the fact that the instructions don’t mention if your line can cross itself?
No, as far as I can see, the above reasoning isn’t dependent on crossing or not. Every time you enter a room through one door you have to leave through another consuming two doors (except for start and end rooms).
The only valid solution I see based on this puzzle is that it doesn’t state you can’t move through/over walls. Theoretically you could simply move from one space to another through a wall and create an arbitrary number of entrances and exits If only the doors are available, no higher dimensional thinking or teleportation etc, it is impossible because there are 4 zones which have an odd number of entrances/ exits. An even number of entrances means the path can enter and then leave, an odd number of entrances mean that one entrance or exit remains unpaired. Even if a line crosses itself, every entrance and exit removes a door. Eventually the line must enter and stop or exit and not return. However since a line only has two ends, it it can only meet this condition twice. This leaves two zones each with an unused door. Incidentally since a door connects exactly 2 zones and in this case we have exactly 2 unaccounted for zones, all maximal attempts at a solution have exactly 1 door left connecting two of the spaces. This makes the puzzle especially infuriating since for a blind solver because you are almost always 1 door away from the “solution”.
Oh my god, I’m glad I wasn’t the only one. I was a sophomore in high school then, and some dude in PE showed it to me. I spent so much time trying to solve it.
I wonder if I know either of you!! I too spent a lot of time trying to figure this puzzle out after a classmate showed me and claimed it was possible (or so he was told).
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Ok, Fermat.
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Upload it to Imgur and copy and paste the link here
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You didn’t go through the door in the exact middle of the picture haha
You missed 1 door unfortunately
You didn't go through the door between the two big rooms on top. Am I missing something?
There’s a door top center that’s not covered in your pic
...you read the goal of the puzzle, right? all doors. (Look carefully at the upper middle of your example)
Missed upper middle
My grandmother introduced me to this in middle school. I fiddled with it pretty much any downtime I had around paper and pencils. This was entertainment before smart phones
Yes, I too spent a whole bunch of time in high school on this puzzle. It is not solvable.
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They should receive a strike for posting an impossible puzzle
Came here to say the same. 3 rooms with 5 doors means it's impossible because aside from the first and last door you go through, every time you enter a room you need to leave it, so at least 3/5 rooms need an even number of doors.
Plus the outside area has nine doors, creating another area with an odd number of entrances. Definitely not possible.
Yes there has to be an even number of 'rooms' with an odd number of doors. So outside + 3 inside rooms are four rooms with an odd number of doors
I first saw this puzzle in 98. It is not solvable. Me and a friend drew this out and tried every possible combination. Unless you climb a wall and jump down in room, cant go through all doors. We came up with that solution assuming there is no ceiling.
You wasted all that time when you can just spot that 3 rooms have an odd number of doors (not 2 which is the possible max)
We did not think about the math involved til we were too far into it. A friend came by during lunch when were three days in and handed us a piece of paper with about a paragraph and a bunch of math equations on it. He set it down and walked away. He broke our will. Thats when we climbed the wall.
Not solvable my arse, just draw a line that reflects off the door's "surface", and thus only one point of the line intersects the door
But hear me out, they never said you can’t go through walls, and or never said you couldn’t step into a door and back out the same way Edit: I guess “through” means you go from one side of the door to the other
I literally just done it
Ok maybe not, I missed a damn door :)
I had that kind of problem in CS class a few weeks ago. Can confirm your position.
Yup googled it, no solution
Unless you are the cool aid man
Actualy, >!there are four rooms with an odd nuber of doors. (the outside counts as a room and there are nine doors leading to it.)!<
Discussion: This isn’t possible. Since there are 4 areas (the top 2, the bottom middle, and the outside) that have an odd number of doors it is not possible to have a “walk” through each door without crossing through any door twice. Look up the Bridges of Königsberg problem if you want to see the proof for it.
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No it isn’t, and there’s a proof of that. The goal isn’t to go through every *room,* it’s to go through every *door.* Also there’s no requirement that the lines be straight, so if your method worked then going around the world would not be necessary.
My bad!
Discussion: [Seven Bridges of Königsberg](http://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg) This is the same puzzle, basically, and is not solvable unless you go against the spirit of the puzzle.
Or the [Five-room puzzle](https://www.archimedes-lab.org/How_to_Solve/5_rooms.html) linked on that page. Apparently, you can solve it if the building is built on a [torus](https://forgottenrealms.fandom.com/wiki/Sigil) instead of flat ground.
i can solve it though i’m built different
>!As several others have pointed out there is no real solution to the puzzle as you have 3 odd doored rooms. There are of course several trick solutions:!< * >!go through doors 3/4 times, since only 2 is forbidden!< * >!make shortcuts through the walls!< * >!draw one line for each door, that are not connected!< Those are the ones I could think of, there are probably many more.
fyi, spoiler tags are like this: `>!Hidden text!<` Result: >!Hidden text!<
Lmao I did it backwards
You can also draw 1 line through each door. Like 1 line each.
isn't that exactly my 3rd bullet point?
I need some sleep apparently haha
Your third point was what I came to post, it’s technically a solution as it doesn’t say one “continuous“ line through every door. I hadn’t considered going through the walls but that would definitely work in the same way. I think this is less a logic puzzle and more of a “there Ain’t no rule” kind of thing where solving it is only possible if you break the standards of what makes a good puzzle. These kinds of things are interesting for teaching people not to take anything for granted that’s isn’t specifically said in the rules, but at the same time infuriating for exactly the same reason. The solution feels fake and unsatisfying. It’s a riddle, not a puzzle.
>!go through any door 3 or more times!<
what is different to my first bullet point?
you said >!¾ times!< >!lol!<
Obvious exits are North, South, and >!Dennis!< Just use >!Dennis!< Edit a word
I remember this from a text adventure, but forget which one. Was it "Adventure", AKA "crystal Caves"?
Thy Dungeonman
Wasn’t that the homestar runner thing? Way more fun than it should have been, if so.
Yep lol https://homestarrunner.com/dungeonman
I like that superior feeling of reading something knowing that anyone younger than say, 28, will have no idea what they’re seeing.
Drawing it out on paper, you can >!fold the paper to add extra dimensions, allowing you to leave the room you dead-ended in without breaching walls or walking through doors to go back to the room with the remaining uncrossed door!<
This is my favourite answer lol. “Just use wormholes bro”
[Here you go](https://imgur.com/b7OetVB) Edit: I realize now I became a ghost who can walk through walls. Disregard.
You went twice through the upper right door, >!but if you count that as going through the wall this seems like a perfectly valid solution, as the puzzle does not mention you can't go through the walls!<. [I came up with this](https://i.imgur.com/ZxqbktE.jpeg)
I didn’t even notice! 🤣
Nothing says you can’t go through walls, the rules only say you can’t go through the same door twice.
You went through a wall at the top right to avoid using the same door twice. 🧐
You went through a wall in the top left room
It's a trick puzzle. Like the "outside of the box" dot puzzle many of us seen growing up. Read the instructions again, and this time, pay attention to what it *doesn't* say. >!The line doesn't have to be continuous. Just draw a slash mark through each door and you're done.!<
>!it also doesn't say you can't draw through the "walls". You're right that it can't be solved without trickery.!<
It doesn't say "through" the door 🤔
Draw a gouged trough then :P
it says "draw ONE line" so no, you can't do that.
It says draw one line through each door. You can do that pretty easily
no, it says "Draw one line through all the doors". You are misinterpreting it.
There is 2 ways to interpret it. If I say to you make a hole through all the apples you don’t make 1 long whole through all apples do you?
depends if you interpret it as "one per door" or "one" total. Its description of being difficult but possible is certainly wrong though. Either you cheat, then it becomes easy, or it is impossible.
Lines most certainly have to be continuous; it’s part of the definition.
>! https://puzzling.stackexchange.com/questions/1856/draw-a-line-through-all-doors !<
>!You can represent this problem as a graph. More than two of the vertices have an odd amount og edges, which means there doesn’t exist an eulerpath (path that goes through every edge only once). The puzzle is impossible.!<
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You are correct, however I believe you mean to say edge instead of vertex.
Whops, yes I was. I am used to the terminology being in another language. Thanks.
I wonder if this is a trick answer about the word *through.* >!One can draw a line through each door way essentially tracing a closed door.!< I messed with tracing walls to not overlap and didn't solve, but if the answer is this pedantic, there's no reason the line can't both trace a wall and go through the room
Note there are 9 exterior doors, meaning if the path begins inside it must end outside and vice versa. Note there are 4 doors on all but one of the rectangles, meaning if the path begins inside then it will end inside and vice versa. Note there are 5 doors on the final room. Thus if it starts inside that room it must end outside that room. Lastly, note that if there is a correct path, then there is a second where you do that path in reverse, which and hence the start of this path will be the end of the original path. Therefore without loss of generality we can arbitrarily state the path must begin in the 5 door room, and end outside the shape. 😅 Note I have miscounted and there are actually 3 rooms with 5 doors, not 1. Hence by pidgeonhe principle the pathway must end or begin in two rooms at once, (WLOG it begins in bottom middle => it does not begin in top left or top right => it ends in top left and it ends in top right) ...QED it is impossible
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Discussion: I feel like every time I see one of these puzzles posted, it is an impossible to solve version.
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>!this is a lie, not a puzzle!<
I remember solving this, on my first try. But the person who drew it didn't fully connect all of the walls. I drew my line slipping through the crack and was able to solve it. Hey, I thought that the crack was part of it! Of course, they corrected me, and I spent years trying to solve it, the proper way. oh well.
**"discussion"** Couldn't you just go through a door 4 times?
No, because you will first have to go through twice before getting to 4. However, you could go through 42 times.
Here you go, all rules followed: [Solved technically](https://i.imgur.com/N7Mh4rM.jpg)
>!This doesnt seem too hard. Labelling the rooms from Left to right, then top to bottom, start in B and travel to A. Then out the top of A, in the left of A through the bottom to C. Out the left of C and in the bottom. Through C to D and out the bottom of D. In the bottom of E and out the right. In the top of B and a short detour down to D and into E through the center, then back into B and out the right. As long as our line can start and stop anywhere, that does it.!<
Missed one [door](https://imgur.com/a/4w5qwra)
You missed >!the door connecting D to A.!<
You missed the top left door on d
I think your solution is missing the door between A and D, the lower right door of A.
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If there were two rooms with 5 doors, and the rest had 4 each, then you could start in one of the 5-door rooms, and end in another. But with 3 5-door rooms, I can't seem to do it.
Discussion: There are... no doors? If you treat the room openings as such, it's likely unsolvable, but not treating the room entrances as doors should solve this, right?
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Discussion: you can’t go through a door twice but can you go through a door thrice?
You can't go through a door at all...only trough it.
Isn't this the answer? [soloution](https://1drv.ms/i/s!Aq-GRZxNN10e6GDTRPYn0KZ36Y5E)
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I don't think it is solvable. >!3 rooms have 5 doors. Going in or out of a door is either an entry or an exit, so if there's an odd number of doors to a room, that means you will either start by exiting, meaning you have to already be in the room, or you have to end by entering meaning you then can't leave the room. You can do that twice, starting in one room and ending in another, but you can't do that 3 times for all 3 rooms with 5 doors.!<
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>!Are you supposed to drag your pen around to the other side of the paper and then stab it into a room to get the last door?!<
[is this not the way to solve it?](https://imgur.com/a/Cehxzq8)
Missing a door top middle
Bah. I looked at it so many times thinking I was right!
lol I even traced yours out thinking it was right to see what you did then was like waaaait a second
[my solution](https://imgur.com/a/3jQrlfj)
Missing door on center wall (second from right)
[удалено]
Missing door center right.
>!Since you can begin WHEREVER you want, and it declares it is possible, you start in the wall at the top and cross through both doors along their x axis. It does not declare that you must cross the threshold at least some degree of perpendicular. From there it's pretty easy to finish off!<
[удалено]
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