How do I solve messy problems with many variables?

You can analyze most problems now, so your method works. The ones that still defeat you are the ambiguous, many variable kind, and those are hard for a specific reason. There is no clean starting point, and every piece seems to depend on every other piece. The trap is trying to solve the whole tangle at once, in your head. Even strong analysts cannot hold that many moving parts together. What they do instead is break it down. Pin the pieces you are sure of, isolate the one or two variables that matter most, and let the rest wait. A messy problem becomes a set of smaller, cleaner ones. Next time one of these lands, resist the urge to crack it whole. Write down what you actually know, name the biggest unknown, and solve just for that. Then move to the next. Ambiguity feels like a wall because it is shapeless. Your job is to give it a shape, one variable at a time, until it becomes something you can actually reason about.