Coincidentally I was just solving (a variant of) this problem today. The approach I took is taking the list of numbers and recursively replacing each pair (x, y) with x+y (replace + with any operation), until one element remains.

You can separate the process by transforming the list of numbers into a binary tree and applying the operators at the nodes. You then consider all possible binary trees and all combinations of operators.

Bonus: by sorting the input values, you can consider half of the trees, because the operations either commute (x+y = y+x) or don't make sense to reverse in the integers (4/2 vs. 2/4).