Let's imagine you want to get a number $A$ from a set of number $M$. You might use only +/- between the numbers and your job is to determine, whether it's possible to get the result $A$ or not.
So let's say $A = 12$ and $M =\{ 3,4,5 \} $ then the solution is $3+4+5 = 12$. $-3-4-5 = -12$ so $-12 <= A <= 12$.
The number of possible ways is $2^n$ where $n$ is number of elements in $M$. I also know that if there is odd number of odd numbers, $A$ must be odd and the GCD of $M$ must be also denominator of $A$ and so on. But in case I'm given $100$ numbers, it's not possible to check every possible way.
With two numbers, like $M = \{ 3, 4 \} $, solving it for let's say $A = 1$ might be as simple as solving two variable equations:
$$x^2 + y^2 = 25$$
$$x + y = 1.$$
But with $3$ or more numbers, it's just two equations and many variables. Is there a way to determine, if $A$ is among those possibilities ?