LinePuzzle (one word) comes from a Korean company called Welcome. The idea is to start at a point, and then trace a path over all the lines without retracing your path. 
There are 300 levels.  I've done about a third of them. A few weeks ago I woke up in the middle of the night and decided to crank these out.
It's basic topology.  The key: start at a point that has an odd number of lines. Then end at a point that also has an odd number of lines.  If the figure has more than 2 odd numbererd points, then it's impossible.

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