How to tell if the sequence can "sum and/or sub" to $x$ Consider a sequence of length $n$ which elements are integers that were randomly (and uniformly) sampled from $[1,2,3...,x-2,x-1]$. One can wonder whether by addition and subtraction only, is it possible for the sequence to sum up to $x$?
For example let's consider the following sequence where $n=3$ and $x=10$
$[2,7,5]$
This sequence can "sum and/or sub" to $x=10$, as $7-2+5=10$ Please note that the first number can also be used to the negative so that the order of the sequence does not matter. The following sequence of length $n=4$ however cannot "sum and sub" to $x=10$
$[2,7,5,2]$
Given $x$ and $n$, what is the probability that the sequence can "sum and/or sub" to $x$?
Let's denote this probability $P(x,n)$. For $n=0$, $n=1$ and $n=2$, it is relatively easy. $P(x,0)=P(x,1)=0$ and $P(x,2)=\frac{1}{x-1}$ but it gets harder with larger values of $n$.

There are $2^{n}$ possible ways to make a sequence. With repitition, there are infinite number of sequences that work and an infinite number of sequences that don't. Partitions would probably help you out, as they can get you how many ways you can add up to a specific number. For subtraction, you will have to improvise, usually by finding how much you are over and then using a partition for that result, and inverting its sign.
Either way, this isn't going to be easy.
