i agree also. I am speaking as an England native. I appreciate one answers a question and solves a problem but in English conversation I prefer to find answers to problems. I doubt many of my colleagues would use the word solutions either.
"Je vais trouver une solution aux problèmes" , seems to be wrong. Nevertheless there is no difference in pronounciation between "au problème" and "aux problèmes". So I think both should be accepted, no ?