How to design an algorithm to calculate countdown style maths number puzzle

Question

I have always wanted to do this but every time I start thinking about the problem it blows my mind because of its exponential nature.

The problem solver I want to be

Answer 1

I wrote a slightly simpler version:

1. for every combination of 2 (distinct) elements from the list and combine them using +,-,*,/ (note that since a>b then only a-b is needed and only a/b if a%b=0)
2. if combination is target then record solution
3. recursively call on the reduced lists