Question 134686
I won't rob of the fun in solving this one. But here are a few ideas for you to consider.

1)When working with a "massive' problem, rather than try to solve it directly, attempt to make a similar smaller problem and solve that. Always looking for patterns in the solution that can be generalized. If you can find a pattern, then just extend that pattern to the big problem.

For instance, try a set using 20 instead of 120 and see what you find


2) Consider factoring each number into it's prime factors and then merging what you find in step 1 with what see doing this.

Good luck and enjoy!