Problem Solving

I have a computation problem!

So, here it is….

I have a beginning matrix that consists of 35,000 rows and 120 columns (sample of smaller version below).


A B C D E F Sum Helped
1 10 14 3 5 3 1 sum # of columns w/ # < 6
2 6 7 14 11 11 15
3 6 12 1 1 0 0
4 1 2 3 4 14 15
5 12 0 1 0 10 14
6 3 10 15 13 0 13
7 5 6 8 8 11 0
8 6 15 10 0 10 2
9 7 1 8 6 13 12
10 9 5 12 14 6 4

Definitions:
Sum – Sum of cells for a combination of 30 columns
Helped – The number of columns with a value that is less than 6 within the combination of 30 columns
Cell Values – Random values between 0 and 15
Successful or Best Combination – The combination that has the greatest value in the “Helped” Column.


First, I already know that the number of combinations for 120 is REALLY big!


So, in my sample problem above lets use the combination of 4. Is there a way that one could eliminate combinations without actually running the combination? Or is there a “simple” way that one could determine the best combination?


Solutions??????