Brain Teaser that is impossibly solvable

[Matter]

would a spiral work!?

 

[koroljov]

Found!

I found it. First try worked. (See attachment).

edit:
You're right, I missed one.

 

[Zorodius]

I found it. First try worked. (See attachment).

Missed a spot, there. You did not cross the segment directly to the left of the center of the figure.

You will always "miss a spot", because there exist no solutions to this problem, aside from the "thinking outside the box" answers like poking holes in the paper and so on.

 

[Galileo]

There are five rooms. The wall between two given rooms must be crossed by the line.
So you have to get from one room to the next.
Give every room a vertex and connect the vertices when there is a wall between them.
This will give you the following graph (see graph.bmp).

Then the upper two rooms (vertices) must have two more lines going out, and so do the two rooms and the bottom left and bottom right.
The room in the bottom center has one more line going out.
The graph will look graph1.bmp.

Since the line must be drawn without removing your pencil from the paper, the entire graph must be connected.
However you connect the loose ends, there will be 3 odd vertices, so there is no solution to the problem.

 

[CrankFan]

I've heard of a similar problem to this one, which had no solution and was supposedly given to grade school students for extra credit. As if that isn't enough of a coincidence just like this version of the story it was rumored to have been solved by one student, so you "know" a solution has to exist!

I suspect that stories of this kind are intentional hoaxes which persist as a kind of elementary math folklore.

 

[Ethereal]

I've heard of a similar problem to this one, which had no solution and was supposedly given to grade school students for extra credit. As if that isn't enough of a coincidence just like this version of the story it was rumored to have been solved by one student, so you "know" a solution has to exist!

I suspect that stories of this kind are intentional hoaxes which persist as a kind of elementary math folklore.

That's a good one! I bet the same thing happened with all those famous conjectures which were supposedly proven by mathematicians in the past, but whose proofs were lost. Fermat comes to mind...

 

[Matter]

Is this it?

How do I post an attachment!? This is driving me maaaaad Never mind I got it!

 

[Galileo]

Dude, you missed a spot.

It can't be done!

 

[Gokul43201]

It is not possible to do this : this is an old problem known as the Bridges of Konigsberg, and was solved by Euler, nearly 300 years ago.

PROOF : There are 3 rooms with an odd number of walls. If you start inside a room with an odd number of walls, and walk through each wall once (you're a ghost), you will end up outside the room. Conversely, if you started outside, then after walking through the last wall, you will end up inside - and can't leave because you've walked through all the walls. This means that one end of your journey must always be inside an odd walled room - either the beginning or the end. Unfortunately, a journey (or a line or curve or whatever you choose to call it) has only 2 ends. But the house has 3 odd-walled rooms, and you can't have a journey with 3 ends, so it's not possible.

THE END

...unless you cheat, by traveling through vertices, (or drawing the figure on a torus), or using a really thick marker, or some other such childish ploy.

 

[Matter]

where?

Dude, you missed a spot.

It can't be done!

There are 5 rectangels with 4 walls each! 6 of these walls are shared or common walls . I went through each wall of each rectangel once ! so where did I miss one!

 

[Matter]

There are 5 rectangels with 4 walls each! 6 of these walls are shared or common walls . I went through each wall of each rectangel once ! so where did I miss one!

don't answer that I see it! Dang! I hate not having a solution!#"!

 

[Galileo]

bladibladibladibla

EDIT: Whoops. I`ve been screwing with that picture so long you posted your message in the meantime.

 

[discomb]

aaaaahhhhhhhhh.

after reading all that, I feel soooooo much better.

before, i was like this:



and now, i am like this:



cheers everybody, and particularly to Mr. Euler and his chums

 

[Myclicheisbetter]

If you approach the puzzle in three dimensions you can easily do it, in fact it only takes about 5 seconds, and the mind set of a jackass. I can attach it if you want, but I'm sure you understand what I'm getting at.

 

[Gokul43201]

Yes, the problem is insoluble only on the plane or the homotopy class of a sphere.

It has a solution, for instance, on the torus.

 

[kerryfan]

Is this the solution?

I was given this problem as a brain teaser and am wondering if I've found the solution (see attachment) or if there is a solution besides cheating, use a marker, etc. This has been driving me nuts, please help if you know the answer.
Thanks

 

[cogito²]

I was given this problem as a brain teaser and am wondering if I've found the solution (see attachment) or if there is a solution besides cheating, use a marker, etc. This has been driving me nuts, please help if you know the answer.
Thanks

If going through a corner counts as going through all three then yes this is a solution. If that is not allowed then there is no solution as has been shown like 10 times throughout this thread. It depends on what conditions you put on the problem. So you decide: is that a solution?

 

[BTruesdell07]

make it really small then draw through it with a thick marker covering the entire puzzle. You go through every line only once.

 

[Sisco424]

Hi,
I've been lookin for the answer to this on the internet because one of my teachers was offering a small cash reward to whoever could solve it and i now know that it is possible because my friend printed a picture of it completed off the net but i just got a quick glance and he took it away thinkin that we was going to steal his answer, i just want to figure it out cause its driving me crazy so if someone finds the answer tell me. It is definately possible

 

[BigStelly]

This has been seen to be impossible for several centuries ever since Euhler proved it was. This comes from the bridges of Konisberg and for centuries nobody figured out a way to cross all the bridges once and only once without crossing back over their path, Because its impossible.

 

[Data]

Sisco424, you will impress your teacher more if you take a book on Graph Theory out of the library, learn about the question, and prove that it is impossible in front of your class :)

If you want a bunch of "completed solutions" then just look through this thread: All of them either cheat or miss a side.

There is a very good reason for this.

 

[animejunkie1100]

I have worked on it for like a year almost and still can't find the answer please help!

 

[d_leet]

I have worked on it for like a year almost and still can't find the answer please help!

This is because, as many people have mentioned in this thread, that it is impossible and has been proven impossible.

 

[-Job-]

You can convert the problem to the attached graph.
The problem can be solved only if you can find a path that goes through every edge exactly once. Such a path is called a Euler path, or Euler tour. Euler showed that a graph can only contain such a path if either all or all but two nodes have an even degree. The graph corresponding to this problem has 4 nodes of odd degree and two of even degree, so it can't contain a Euler tour.

 

[ValenceE]

Hello to all !,

Guys, if we accept the fact that any corner is the junction of as many sides as are connected, then there’s a way to solve this puzzle. Actually there’s probably more than one way, but here’s what one of them looks like.

It also has a neat shape to it…


VE

edited to replace .jpg file by .bmp

 

[nerd_police]

can we enter a line, then trace along it for a while without having "crossed it twice"

 

[Tclack]

___________
|_____|_____|
|__|_____|__|

This is basically what the image looks like, and yes it is impossible. If you look, you'll see any rectangle has either 4 or 5 sides (even or odd). Now if you were to start inside an odd one, you eventually would have to end up on the outside and if there were two odd box's it would be fine but there are three... it's hard to explain, but it's impossible. I actually devised a way to find out whether or not a puzzle like this is impossible or possible. First add up all the rectangles with even "doorways" and odd ones. Cancel every even with every even, and every odd with every odd. I found that's it's not possible if you end up with an odd. It's possible: if they all cancel out, if you have a remaining even. However there is a special case if you end up with 1 even and 1 odd; If you have an odd amount of odds (3, 5, 7...) then it's not possible, But it is for 1.

As I read over that, it's a little difficult to understand, read it carefully.

So if we look at the original we see that we have 3 odds and 2 evens:
o oo ee . The paired ones cancel out so we have an o remaining. If you look back at my list, a remaining odd is...Not Possible, hence the puzzle is unsolvable.

Note: I haven't showed this mathematically, I made puzzle types a bunch of times and tried them, the ones that weren't possible and the ones that were possible had the same properties, that's what this is based upon. You can try it yourself.

 

[Gib Z]

Yea i was thinking that too, can the line trace a lot the sides abit, then it will be simple.

 

[Brainteasercool]

the rules
you can go over a line one time
you can't go along a line
you can start in the middle or outside
you can have a straight line or a curved line
you can't cut or go through corners

 

[cristo]

the rules
you can go over a line one time
you can't go along a line
you can start in the middle or outside
you can have a straight line or a curved line
you can't cut or go through corners

With those rules, the problem has been shown (many times in this thread) to be insoluble.

 

[bagelboy92]

this seems to be impossible because first of all there is an even number of lines to cross for one line to go through and second of all i have made a NOTEBOOK of individual papers that have front and back non repetitive attempts...i lie to you not this is impossible...i have lost time trying to figure this out on a state high school test that determines if i pass high school! (Breathing hard like a maniac while saying that) ... ... yes I am okay but i tell you with confidence for all who read this that it is impossible

 

[cristo]

this seems to be impossible because first of all there is an even number of lines to cross for one line to go through and second of all i have made a NOTEBOOK of individual papers that have front and back non repetitive attempts...i lie to you not this is impossible...i have lost time trying to figure this out on a state high school test that determines if i pass high school! (Breathing hard like a maniac while saying that) ... ... yes I am okay but i tell you with confidence for all who read this that it is impossible

Wow... you really haven't read the earlier posts in this thread have you?

 

[light_bulb]

fun, will insert another quarter :(

 

[light_bulb]

i think this one is right?

 

[cristo]

i think this one is right?

Nope... you missed a side. It is impossible!