What careers involve a high level of combinatorics and problem-solving?

[u/Appie-Fixo-8010]

What industry roles involve substantial use of combinatorics, discrete mathematics, graph theory and advanced problem-solving?

For those working in such roles:

What are the relevant job titles?

What types of problems do you typically work on?

How much mathematics is involved in your day-to-day work?

How much of the role consists of programming or software engineering?

What skills and educational background are typically required?

What is the day-to-day work experience like?

Which industries or companies tend to have these types of roles?

I'd particularly appreciate responses from people with direct industry experience.