I need to find a solution to/for this problem.
Can to and for be used interchangeably here? Is one of them just plain wrong?
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- I need to find a solution to this problem
- I need to find a solution for this problem
- I need to find a remedy for this problem
All three sentences are correct, although the second is less common. Usually, one will find that to is the preposition of choice for the word solution. However, for is preferred in certain cases, and I give two examples to illustrate this:
A bunch of students are working on a physics problem set in the common room. C and J are done with questions 1 through 4 and are currently working on 5. A just finished solving question 4 and wants to check her work with C and J: "Hey guys, could you show me your solution for number four? I'm not sure I did it correctly."
Joe had just bought a fridge for a dollar from an old lady down the road. Still unable to believe his luck, he wasted no time in setting it up in the corner of the hovel he shared with his brother, Alex. Only after plugging in the fridge did Joe realize that the door wouldn't close properly. He repeatedly slammed the door shut only to have it slowly creak open each time to his chagrin. "Hey, bro," Alex finally said, "calm down. Calm down!" He pulled out a crowbar. "There's a quick solution for this."
I would use 'to' exclusively. The problem has a solution, the solution belongs to the problem. I will find a solution to the problem for my boss, because that's what he pays me to do.
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 sound as good to me.
As a native English speaker I regard to and for as interchangeable in the sentence you quoted. I would probably use for more often, but I wouldn't regard to as wrong.
Update: I searched the British National Corpus (BNC) at Brigham Young University (BYU). BYU-BNC found 1165 examples of "solution to" but only 208 examples of "solution for".