Looking on the internet deeply has found these results:

solution to the problem is the most popular phrase on the web.

solution for the problem 1346,000 results on the web	solution to the problem 15,130,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
Jun 25, 2015 ... If you need to avoid repetition of 'to', you can say solution for the problem. Although the construction solution of the problem wouldn't be my first ... Mar 2, 2011 ... I will agree with both RGB and JasperLoy that if I heard "a solution for the problem" I wouldn't think it was necessarily incorrect, it just doesn't ... May 7, 2011 ... You almost always hear "solution to the problem" and sometimes "solution for the problem" — but almost never do you hear "of" in that context. What is the best solution for the problem of gerrymandering? "In the process of setting electoral districts, gerrymandering is a practice that attempts to establish a ...	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

solution for the problem

1346,000 results on the web

solution to the problem

15,130,000 results on the web

More popular!

Jun 25, 2015 ... If you need to avoid repetition of 'to', you can say solution for the problem. Although the construction solution of the problem wouldn't be my first ...
Mar 2, 2011 ... I will agree with both RGB and JasperLoy that if I heard "a solution for the problem" I wouldn't think it was necessarily incorrect, it just doesn't ...
May 7, 2011 ... You almost always hear "solution to the problem" and sometimes "solution for the problem" — but almost never do you hear "of" in that context.
What is the best solution for the problem of gerrymandering? "In the process of setting electoral districts, gerrymandering is a practice that attempts to establish a ...

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.