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[–] Shiva_Cometh 0 points 2 points (+2|-0) ago 

This was taught in my 9th grade geometry class, and then multiple times again in college (discrete math, graph theory, etc.) Look here for more info.

Basically, in order to traverse a connected graph without taking the pencil off the paper, there must be exactly 0 or 2 nodes of odd degree. Graphs that satisfy this are called an Eulerian path. Also if there are nodes with odd degrees, then your path will begin and end with them.

In the video the figure has 4 nodes of odd degree. Therefore you can separate it into two Eulerian paths.

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[–] klusterVug 0 points 1 points (+1|-0) ago 

I think they did teach us something like this in school and it's not possible. When you have stipulations like not retracing your steps, any point with three lines will have the first going to it, then the second one going from it. Logically, you'll need a third going to it, but you have no escape after that. This only works if you have one point that needs three lines, and the third would need to be the finishing stroke. This diagram has four.

If anyone believes I'm wrong, please PM me so we don't ruin the solution, if one exists.

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[–] klusterVug 0 points 4 points (+4|-0) ago 

I just re-watched it and it said "2 unbroken lines." I completed the entire diagram with that rule in place.