Are you sure that all lines give 34 ? (I tried some things but 34 seems too big)
I just used some logic and strategy and excel.
If you give it a try you immediately see that ll of the big numbers have to be shared by the rows so they must be in the center and all of the little numbers have to be on the outside. Once I realized that it only took a few minutes.
I suppose you could also assign variables to each point on the star and write out equations which all add to 24. Then there is a really cool matrix method that would give you the answers in a snap though I can't remember how to do it at the moment.
I know that paultwang (an old contributor to this forum knows how to do it. you could pm him and see if he answers.