I sat down for 2 minutes and wrote a brute-force solution that ran the 10k scenario in 400ms in python. Hint: you only need two loops.
you may not necessarily be timing what you think you are timing
Well, yes, there are all sorts of tricks, including the use of a solver :)
In my earlier post, read "brute-force" as "full enumeration". The comment was about dev's intuitions re: the time required to fully enumerate a space; ie when is it worth thinking about anything other than the stupidest solution possible.