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.