Solve the Infamous Puzzle: One Continuous Line Challenge | Step-by-Step Guide

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Discussion Overview

The discussion revolves around a puzzle that requires drawing a continuous line through every segment without retracing or crossing itself. Participants explore the feasibility of solving this puzzle under various conditions, including the use of different surfaces such as a Mobius strip.

Discussion Character

  • Debate/contested
  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant claims that the puzzle is impossible to solve on a plane, citing graph theory as a basis for this assertion.
  • Another participant suggests that drawing the line on a Mobius strip could provide a solution to the problem.
  • A different participant references a previous thread that discusses the impossibility of the puzzle on a plane, mentioning that cheating methods exist but do not count as valid solutions.
  • There is a discussion about the nature of the Mobius strip, with one participant questioning whether it can be considered a plane.
  • Participants discuss the Euler characteristic of the Mobius strip compared to that of a plane, indicating a mathematical distinction between the two surfaces.
  • One participant raises a question about the relationship of the Mobius strip to a cylinder and whether dimensional changes affect the properties discussed.

Areas of Agreement / Disagreement

Participants express differing views on the solvability of the puzzle, with some asserting it is impossible on a plane while others propose alternative surfaces like the Mobius strip. The discussion remains unresolved regarding the implications of these surfaces on the puzzle's solution.

Contextual Notes

There are unresolved mathematical distinctions regarding the properties of different surfaces, such as the Mobius strip and the plane, which may affect the discussion of the puzzle's solvability.

Galaxy
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Hi everyone. I've been stumped trying to figure this one out for the past week, I think some may have seen it before. It looks like this:

*EDIT* The picture I attempted to draw didn't post right, I'll have one up soon.

*EDIT 2* Here we go:
http://members.lycos.co.uk/evilx22/hpbimg/Untitled-1%20copy.jpg

What you have to do is draw one continuous line through every line segment on the puzzle, without going through one twice and the line can never cross itself. I'm hoping some have seen this before, so any help would be appreciated.
 
Last edited:
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Its impossible... you can prove it with graph theory.

This was posted previously and there was a link to a site that had a general proof that it can't be done under certain conditions and this puzzle fit the conditions...
 
You could draw this on a Mobius strip.
That would fix the problem.
 
There's an infuriatingly long thread dedicated to this problem here

The short answer is that it is impossible to do this, if the picture is drawn on a plane, unless you cheat by going through a corner or using a giant marker, or some such thing. The proof is found in post #5 (by NateTG) in the above linked thread.
 
Gokul43201 said:
if the picture is drawn on a plane.
Isn't the Mobius surface considered to be a plane?
A toroid or sphere, two solutions in the thread you referred to, would not be.
 
NoTime said:
Isn't the Mobius surface considered to be a plane?

No, a mobius strip is not homeomorhic to a (projective) plane.

(Additional Info : the mobius strip has an Euler Characteristic = 0, while this is 1 for a plane)
 
Gokul43201 said:
No, a mobius strip is not homeomorhic to a (projective) plane.

(Additional Info : the mobius strip has an Euler Characteristic = 0, while this is 1 for a plane)
Interesting.
So it would be related to a cylinder somehow?
Does this remain true if the dimensionality changes?
I vaguely recall something special about this as well as klein bottle for N other than 3.
 

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