Asymmetric Newton's Cradle

Is there a way to calculate the result?

Lagrangian Mechanics is the exact subject you seek and is typically taught in an intermediate mechanics college junior course. You learn how to deal with some interesting things like double pendulums, or beads on strings... on trains, or systems of springs. The weird stuff that you think of in introductory physics 1 but would have no clue how to even approach, that type of stuff.

And this problem type doesn't have multiple solutions as long as it's well posed and you're careful about your q's and such.