The way in which computer algebra systems, such as Maple, have made the study of physical problems of some considerable complexity accessible to mathematicians and scientists with modest computational skills is illustrated by solving the multiple pendulum problem. A solution is obtained for four pendulums with no restriction on the size of the angles through which they move, and for as many as a hundred pendulums if the angles remain sufficiently small. An attractive and informative graphical display of the motion in animated form can be obtained from the solution, and the effect of varying the initial conditions can be investigated visually. (Contains 8 figures.)