# Need help with this puzzle

1. Dec 1, 2004

### Galaxy

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 copy.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: Dec 1, 2004
2. Dec 1, 2004

### nnnnnnnn

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 cant be done under certain conditions and this puzzle fit the conditions...

3. Dec 1, 2004

### NoTime

You could draw this on a Mobius strip.
That would fix the problem.

4. Dec 1, 2004

### Gokul43201

Staff Emeritus
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.

5. Dec 2, 2004

### NoTime

Isn't the Mobius surface considered to be a plane?
A toroid or sphere, two solutions in the thread you refered to, would not be.

6. Dec 2, 2004

### Gokul43201

Staff Emeritus
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)

7. Dec 2, 2004

### NoTime

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.