Computing target number from numbers in a set

I'm working on a homework problem that asks me this:

Tiven a finite set of numbers, and a target number, find if the set can be used to calculate the target number using basic math operations (add, sub, mult, div) and using each number in the set exactly once (so I need to exhaust the set). This has to be done with recursion.

So, for example, if I have the set

{1, 2, 3, 4}

and target 10, then I could get to it by using

((3 * 4) - 2)/1 = 10. 

I'm trying to phrase the algorithm in pseudo-code, but so far haven't gotten too far. I'm thinking graphs are the way to go, but would definitely appreciate help on this. thanks.