Let's say I have a fixed list of numbers:
$2, 3, 1, 2$
and I can reduce every number from $n$ to $0$, for instance: $1,3,1,2$ or $0,3,0,1$ etc.
I am looking for all combinations of this sort, where I receive zero when applying $\oplus$ XOR to it. For example: $$1 \oplus 2 \oplus 1 \oplus 2 = 0$$
Is there a way to compute all possibilities? Just trying out every combination seems very naive.