I've worked in research since 2002. I always solve the problem. I'm the one you go to, after the other teams ran into trouble (I work rather hard to position myself as that).
I take the details of your issue, and offer to come back to you. Then I brainstorm and come back with a proposal. I will probably discuss the problem with several other specialists, one or two at a time.
Ideas occur at a Poisson rate with time spent thinking. I find running helps to focus the time spent thinking.
My most creative problem-solving ideas I've had while peeing. I think it is the interruption.
These screening interviews will rule me out, with high probability. Fine.