I'm trying to reduce the solution space by excluding the wrong cases.
The original problem: 4851 choose 693 = 1.70E+862
Right now the possible combinations are (with n choose k):
1680 choose 420 = 4.36E+408
I'd attempt the bruteforce with a notebook, so it is not a powerhouse. I wonder if it is possible to find the solution now or should I try and reduce the available options further.
Update: The problem is the following: I've got a set of graph nodes and some constraints. The goal is to connect the most nodes without violating the conditions.
Assume it takes 1 nano second to construct a candidate and to check whether it is the solution. Then divide the number of all candidates by $2.25 \cdot10^{27}$ to get the time it takes to check all of them, where the unit is "age of the universe". Thus it takes around $$2 \cdot 10^{381} \text{ times the age of our universe}$$to brute-force check all possibilities.