somebody PLEASE help me solve this puzzle

[Sound Wave]

over the years, i have occassionally tried to solve this puzzle. i can't figure it out and it is driving me nuts. today i ran into the person who originally showed me this puzzle. he swears there is an answer to it.

he gave me a hint. he said that to start in the upper left hand section. he said that there is only one solution for it (although, i would assume there are two... a mirror image of each other)

anyways, the object is to draw a continuous line. the line has to pass through every segment once and only once.



for example:


PLEASE someone solve it for me so i can put this puzzle behind me. i give up!!!!!

[rockNroll]

Let it go There is no solution. Your friend probably knows this.

[Apex]

I'll need to give it a try.

[ScraitT]

Edit nvm...I just realized I messed up :-x

Ok, I gave up and tried to look it up online. A LOT of people claim it's possible, but no one had an answer. Then a LOT of people used math to prove it impossible.

The only reasonable explanation I found was that this puzzle started out a LONG time ago as "complete this puzzle with out lifting your pencil. You can not pass through a line segment twice." The solution had to do something with folding the paper while you drew the line, making it a 3d puzzle and not a 2d puzzle as it seems.

On the other hand, this puzzle is supposidly at the bottom of the Petrona Towers in Kuala Lumpur. It's made of wood and has a string..so there's obviously no folding that. I don't know if it's actually there or something someone made up.

[Sound Wave]

well, the person who showed us was my private christian middle school teacher. i don't think he would lie to me about that. he showed us that puzzle back in 1982. saw him at a restaurant yesterday. but yeah. he holds that there is a solution.

but thanks guys for trying anyways. i was thinking it has to be one of those "think out of the box" sort of puzzles.

[Custom Seat Creations]

oh man. now I'm gonna spend hours trying this one.

[g21-30]

The real difficulty here is that an assumption is made, creating an unwritten rule. This unwritten rule, this self imposed limitation forces the problem solver to focus on the problem, NOT THE SOLUTION. By recognizing the problem (NOT FOCUSING ON IT) - a long line cannot enter and leave each space enough times without making an illegal crossing- we can find the solution. The solution is this: use a very wide marker or brush and cross the entire box in one diagonal line. All stated conditions are met, the problem is circumvented and the solution is found. Clearly this is not the intended answer, but it is indisputable

[coffeecandy]

i think i figured it out....

[ScraitT]

Originally Posted by g21-30

The real difficulty here is that an assumption is made, creating an unwritten rule. This unwritten rule, this self imposed limitation forces the problem solver to focus on the problem, NOT THE SOLUTION. By recognizing the problem (NOT FOCUSING ON IT) - a long line cannot enter and leave each space enough times without making an illegal crossing- we can find the solution. The solution is this: use a very wide marker or brush and cross the entire box in one diagonal line. All stated conditions are met, the problem is circumvented and the solution is found. Clearly this is not the intended answer, but it is indisputable

You copied that from somewhere I remember reading it while looking for an answer.
What you didn't copy was the reply to that, which is just as valid. A wide marker would essentially make a plane, not a line. A line by definition has no width.
To make that a somewhat valid solution you would have to draw the entire thing with a large marker so that all lines in the problem have the same width value.
It is thinking outside the box, but I don't think that it's right.

[ScraitT]

The only solution I could think of is the following.

Consider the direction.

the object is to draw a continuous line. the line has to pass through every segment once and only once.

Depending on how you interpret the shape, there could be different number of line segments. If all the horizontal lines are single segments rather than multiple segments you could have the following.



Given that, drawing a line through THOSE segments becomes a simple task...




That may or may not be a real solution, but it's thinking outside the box.

[Greg_E]

You might look at an alternative definition of "through" each segment It might be possible to draw a line through the vertex of several lines, thus touching each once and only once yet touching two or three lines at the single point. Or you are meant to draw the line in the plane coming out of the paper, looping in and out to make the continuous line.

[zeroth]

Isn't this a solution?



I guess they could make it difficult by adding stipulations like "you can't cross over your line", but I didn't see anyone mention that...

[zeroth]

Actually here is a solution that meets the added stipulation that "you can't cross over your line":

[P1NDLESK1N]

I don't get it.

edit: Oh wait now I get it.

[zeroth]

Originally Posted by ScraitT

The only solution I could think of is the following.

Consider the direction.

the object is to draw a continuous line. the line has to pass through every segment once and only once.

Depending on how you interpret the shape, there could be different number of line segments. If all the horizontal lines are single segments rather than multiple segments you could have the following.

I agree with Tyler, how you interpret the shape, there could be a different number of line segments. In the solutions I posted, I assumed each straight continuous line was one segment. But you could interpret each segment as ending at each intersection, as shown here:


I gave it some thought and came to the conclusion that if you do interpret the segments as above, crossing each segment one time only without lifting your pencil (other than the cheat method like using a really thick pencil) is impossible.

Here is my reasoning (warning: weird logic ahead!):

Consider the drawing in terms of enclosed regions, identified by unique letters.


Notice that regions A, B, and D are bounded by 5 segments, whereas regions C and E are bounded by 4 segments. Let's look at each region individually and consider where the pencil mark has to start and end.

In regions C and E, because there are an even number of segments, if the pencil starts inside, it has to end inside (first crossing take it out, second brings it in, third takes it out, fourth brings it in). Conversely, if the pencil starts outside, it has to end outside (first crossing brings it in, second takes it out, third brings it in, fourth takes it out).


What does this mean? The pencil either has to start and end in one of these regions, or start and end outside.

In regions A, B, and D, because there are an odd number of segments, if the pencil starts inside, it has to end outside. Conversely, if the pencil starts outside, it has to end inside. Look at this illustration.


What does this mean? The pencil either has to start in one of these regions, or end in it. Well, herein lies the problem. There are THREE of these regions. The pencil can start in A and end in B, but what about D? Or it can start in D and end in B, but what about A? This is why it's impossible: There are more than two regions made of odd numbered segments.

You could ask how I'm able to ignore all but one region when doing the above analysis. See, I'm not actually saying the pencil won't move in and out of another region when it moves out and in to one region, just that I'm ignoring all except one region when doing the analysis. Then I'm hitting rewind and drawing everything again, but looking at a different region. So from each region's point of view, it doesn't matter whether I'm going out into another region or out into empty space.

Someone who's good at logic/geometry, please chime in and either back me up tell me why I'm wrong!

Edit: In Gary's original post, the line started outside of all the regions, and ended inside region D. So regions A and B were violated (Gary noticed this: the segment bordering regions A and B was not crossed).

[Flashmonkey]

Oh sweet jesus I hate these things....

Is this one of those puzzles that you assume is a 2 dimensional puzzle, but is in actual fact, a 3 dimensional puzzle? I've gotten zinged with a few of those and have turned bitter ever since. If this is the case, then fold that sucker in half and draw a line at your leisure

[cifex]

Google.....making people on the interweb seem smarter since 1998.

[g21-30]

Originally Posted by ScraitT

You copied that from somewhere I remember reading it while looking for an answer.
What you didn't copy was the reply to that, which is just as valid. A wide marker would essentially make a plane, not a line. A line by definition has no width.
To make that a somewhat valid solution you would have to draw the entire thing with a large marker so that all lines in the problem have the same width value.
It is thinking outside the box, but I don't think that it's right.

You're absolutely correct! Why reinvent the wheel? If you're going to walk thru a mine field, do you want to make your own path? Or, follow someone who did it successfully?

That's why we post DIY's so those who are afraid to tackle different mods can see how easy or not they are.

Good luck in your quest!

[Sound Wave]

thanks for all the help people. i am pretty convinced now that:

1) there is some stupid thing to make this work. ie... folding the paper, fat line (i swear that better not be it)
and
2) that it is impossible by conventional means

i did try googling it, but my search words are not hitting it. i enjoy puzzles to a point, but this one seriously pisses me off.

[Sound Wave]

i just googled "line puzzle" (duh....) and i got a few hits. seems like they didn't have luck either.

as the person said on the other site, after struggling with this thing off and on for 28 years, i just want some closure.

i was REALLY hoping when i saw my teacher the other day that he would either tell me that it was impossible or what the answer was. but as i said, he insisted there was an answer. it has to be something really dumb.

[noche_caliente]

he probably doesn't know

[Samer]

I have the definitive answer, It is not possible.

But I CAN PROVE THIS. Acutally, Euler has proven this. If you don't know, Euler was a Swiss Mathematician. He was by all accounts the most prolific Mathematician in history, and by most accounts, the greatest Mathematician ever.

It is actually quite simple. Each of the boxes can be treated as an island. Euler showed that starting from one of the islands, you'd have to leave and come back an even number of times, except perhaps for the starting and ending nodes. In this case, the top two boxes have an odd number of bridges and the bottom middle one also has an odd number of bridges, which means an Euler walk is impossible. Case closed in 1735! Thanks Euler!

http://en.wikipedia.org/wiki/Seven_B..._of_Königsberg

[LazinCajun]

This is way off topic, but is there anything that Euler didn't do first? :P

[zeroth]

Originally Posted by Samer

I have the definitive answer, It is not possible.

But I CAN PROVE THIS. Acutally, Euler has proven this. If you don't know, Euler was a Swiss Mathematician. He was by all accounts the most prolific Mathematician in history, and by most accounts, the greatest Mathematician ever.

It is actually quite simple. Each of the boxes can be treated as an island. Euler showed that starting from one of the islands, you'd have to leave and come back an even number of times, except perhaps for the starting and ending nodes. In this case, the top two boxes have an odd number of bridges and the bottom middle one also has an odd number of bridges, which means an Euler walk is impossible. Case closed in 1735! Thanks Euler!

http://en.wikipedia.org/wiki/Seven_B..._of_Königsberg

Cool -- Lenny Euler and I think alike! (That's exactly the same reasoning I used in my proof above!!)

[bob706]

http://www.tummyfluff.co.uk/puzzles/lines.htm

[beowuff]

See this puzzle is a thought experiment. There IS a solution if you consider the lines to NOT end at the intersections. (No where did I see any rule saying that they did...)

More important to the person asking the question is how you think about the problem. Not weather or not you solve it.