This problem can be expressed mathematically as

s = { sum(y) = n | y in P(x) }
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where x is the bag (list) of elements, n is the number the elements in the bag should sum up to, P is the "power bag" operator, and s is the set of solutions. (Bags allow duplicate elements, in sets all elements are unique.)

That is, all you need to figure out is how to write a "power bag" function, and luckily for you several people have done that already. Try searching CPAN for "power set" for Perl versions.

lodin