I'm working on solving a problem I've been playing with for a while. Fundamentally it involves picking a feasible solution from a solution space of (225 choose

I'm working on solving a problem I've been playing with for a while. Fundamentally it involves picking a feasible solution from a solution space of (225 choose 45) possible solutions. That number is obviously too big to brute force randomly, but I was able to get very close to a solution by hand, and so it feels like there ought to be an algorithm to generate a solution. (It doesn't feel like a problem where the solution wouldn't be polynomial time.) It feels like some kind of branching with aggressive pruning would deliver a solution but I have much I need to learn first to actually develop it.