Problem 63 Answer

Notice that the two points on the bottom are both the junction of three different line segments. The two points above these two are the junction of five line segments. As you draw the path each point you enter you must also exit, except the beginning and ending points. Thus line segments are added to any given point two at a time. So for any figure you draw, without lifting the pen from the paper, must have an even number of line segments leaving each point, except the beginning and ending point. Given the beginning and ending point, you are allowed two grace points that may have an odd number of segments. However the figure in this problem has four points with an odd number of segments, thus it is impossible.

Michael Shackleford, A.S.A.