# How long would it take to bruteforce?

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.

• What is your problem? Commented Apr 11, 2020 at 10:38
• Updated the question. Commented Apr 11, 2020 at 10:42
• How many of the combinations are valid solutions? If it's just a few like $10^{100}$ among the $\approx 10^{400}$ then forget about brute force. Commented Apr 11, 2020 at 10:48
• My current theory is that there will be only one valid solution. Commented Apr 11, 2020 at 12:29
• What are the constraints? Commented Apr 11, 2020 at 17:57

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.