The three body problem though is famous for having no solution in terms of basic functions. I think for your planets model you must have been making different assumptions than in the article.
In system dynamic you can divide a problem in simple (with a finite number of solution) and complex (with an infinite, fractal shaped, number of solution).
If the problem is "complicated" (a lot of strange, ugly, non analytic equation)but simple you can roughly cut the solution space by hand, assuming a small number of solution.
If the problem is complex all you can do is looking for cycle and equilibrium point using your intuition about the system or being lucky and find a strage attractor (chaotic behavior) slightly moving the parameter.
So, yes, I was to quick writing my reply, you can definitely model the n-body problem, exactly solve it is another beast, check a solution however is still relatively easy...
