Tricky Spool Riddle SOLUTION - ft Anne Wojcicki

Isn't this more of a geometry problem and not a physics problem? When you pull the rope, the center of the spool needs to move in order to go back to equilibrium. So we know it moves. If we assume the spool moves in the opposite direction the rope is being pulled, then the center of the spool must unravel at the same rate as the rope is pulled. This is also the same rate of change of distance between the spool and the hand pulling it. However, we quickly see that the situation is impossible because the outer circumference of the spool is greater than that of the wound rope, which means the spool must move at a greater speed than the rate of change for the distance between the hand and the rope. Thus, the only scenario left is that the spool rolls toward the person's hand. 
In contrast, when the rope is at an angle, the speed the spool rolls does not have to be the same as the rate of change in length between the hand and the spool because the angle the rope is pulled at can change. 
I have no clue if this makes any sense w/o pictures...