Coming from Stack Overflow forum because someone told me to ask here for rigorous proofs: https://stackoverflow.com/questions/60261555/three-sums-problem-space-complexity-why-is-it-on
For a given sequence of N distinct integers and a target sum K. For example:
$-8, -6, 1, 2, 3, 5, 6, 12$
$K = 0$
We want to find out the number of unique triplets summing to the target sum. In this example, the number of permutations will be 3:
$(-8, 2, 6), (-8, 3, 5), (-6, 1, 5)$
So from here, I can see the permutation is definitely less than ${N\choose 3}$, since all numbers are distinct. How do I mathematically find the number of unique triplets summing to a given number?