- #61
nerd_police
- 1
- 0
can we enter a line, then trace along it for a while without having "crossed it twice"
Brain Teaser that is impossibly solvable
- Context: High School
- Thread starter kinnabird5
- Start date
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SUMMARY
The forum discussion revolves around a complex geometric puzzle involving a rectangle divided into smaller rectangles, where participants debate the feasibility of drawing a continuous line through all 16 edges without overlapping. The problem was presented by a user named kinnabird5, who claims it is solvable, while others argue it is mathematically impossible based on Eulerian path principles. Key insights include the necessity of understanding graph theory and the implications of defining "line" versus "continuous curve." Ultimately, the consensus leans towards the problem being unsolvable under strict interpretations of the rules.
PREREQUISITES- Understanding of Eulerian paths in graph theory
- Familiarity with geometric shapes and their properties
- Knowledge of continuous curves versus straight lines
- Basic mathematical reasoning and problem-solving skills
- Research Euler's theorem on graph connectivity and paths
- Explore the Bridges of Königsberg problem for historical context
- Study the definitions and differences between lines and curves in geometry
- Investigate alternative interpretations of geometric puzzles and their solutions
Mathematicians, educators, puzzle enthusiasts, and anyone interested in the intersection of geometry and graph theory will benefit from this discussion.
- #62
Tclack
- 37
- 0
___________
|_____|_____|
|__|_____|__|
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.
|_____|_____|
|__|_____|__|
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.
- #63
Gib Z
Homework Helper
- 3,341
- 7
Yea i was thinking that too, can the line trace a lot the sides abit, then it will be simple.
- #64
Brainteasercool
- 1
- 0
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
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
- #65
cristo
Staff Emeritus
Science Advisor
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Brainteasercool said:
With those rules, the problem has been shown (many times in this thread) to be insoluble.
- #66
bagelboy92
- 1
- 0
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
- #67
cristo
Staff Emeritus
Science Advisor
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bagelboy92 said:
Wow... you really haven't read the earlier posts in this thread have you?
- #68
- #69
- #70
cristo
Staff Emeritus
Science Advisor
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light_bulb said:
Nope... you missed a side. It is impossible!
- #71
light_bulb
- 197
- 0
i have a new one with all lines but it adds up to 17? maybe unsolvable
Last edited:
- #72
tehno
- 375
- 0
I'd second that.cristo said:
- #73
Sting1974
- 1
- 0
Why doesn't someone make a computer program to see if its solvable? might be easier and it could do calculations or attempts hundreds of times faster than us.
- #74
d_leet
- 1,076
- 1
Sting1974 said:
Because that would be entirely pointless, for as it has been said numerous times in this thread it is simply not possible.
- #75
MindCrack
- 1
- 0
This thing is like crack cocaine! I don't know what its called so I just call it Mind Crack. I've been doing this puzzle for about 6 months now and haven't figured it out. It was shown to me by a neighbor who says he's seen the answer but had been done on a computer. Whether that's true or not I do not know. Seeing as he's an alcoholic but still. If anyone has the true answer. Quit hiding it and reveil it! Because I am sure there is otehr people out there that are craving to know the answer!
...Mind Crack
...Mind Crack
- #76
cristo
Staff Emeritus
Science Advisor
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MindCrack said:
Why don't you read the n posts above telling you that this is impossible! There's a proof of this in one of the early replies.
- #77
mhhottie111
- 2
- 0
Icarus said:
i want to see your solution...
- #78
mhhottie111
- 2
- 0
i want to see your soltution to this problem.i have been trying for 2 years and still can not seem to find any answer
- #79
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
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As has been said many, many times before (and proven once), this problem has no solutions. Therefore, it serves no purpose to continue to seek solutions to this problem and hence any discussion on the topic is also useless.mhhottie111 said:
Thread closed.
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