Phase 1: Meet the problem.

A sign problem disguised as a counting problem

You're given a list of non-negative numbers and a target. Put a + or in front of each one so the signed sum equals the target. Question: how many different sign assignments work?

Example: nums = 11111, target = 3. You could try +1 +1 +1 +1 −1 = 3. That's one. Are there others? How would you find them all?

Start by trying — flip signs, check if the sum matches, keep track of what works.