Can this shape be traced in a single line without lifting my pencil of the paper? Recently, a friend of mine gave me this challenge to trace this object in one line, without lifting a finger of the paper, and without tracing a line more than once, saying it was possible. 
P.S, the curvy squares at the end are actually ment to be semi-circles
Every time I try to do it myself, I always get so close with only one line left. I know this type of problems is generally solved using graph-theory (Not saying that this is necessarily solvable) , so any help is appreciated!
 A: Not possible, by Euler: There are four vertices of odd-degree.  In the best case, you will be missing a line connecting two of the corners.
A: What you're wondering is if there is something called a Eulerian Path in this graph. An Eulerian Path is a sequence of edges in the graph, with consecutive edges incident in the graph, and this sequence of edges contains each edge of the graph exactly once. You can prove that a graph has an Eulerian path if it is connected and has at most two vertices of odd degree. If all the vertices are of even degree, then there actually exists an Eulerian circuit, a path that ends where it starts.
A: It is possible, to trace any figure, by tracing back along the same line again!  If you add the condition that you can go along a side only once, then it is not possible.
At each vertex, you must (i) begin tracing, (ii) end tracing, or (iii) pass through.   If you pass through you must enter along one line and exit along another, you use two edges. If a vertex has an odd number of lines emanating from it, the path must either start or end at that vertex.  This figure has all four vertices with an odd number (5) of lines. But you must say "using each side only once".  Without that any figure can be drawn.
A: The proof of whether it is or is not possible is in the line junctions. There can be only two junctions with an odd number of lines forming the junctions. The trace will start at one odd-line junction and end at the other.
