Non academic career for maths graduate
Looking at the job market, they don't advertise for people 'who like solving problems'


I think you've already found the perfect way to advertise yourself! There are a lot of companies interested in people like yourself. Now, I'm not a mathematician, and I don't know the full details of your background, but it seems to me like there's plenty of problem solving going on in optimization situations. Since you say your background is in applied mathematics, there may be some overlap with econometrics, too.

And also: don't hesitate to contact companies who are searching for computer scientists if you like the vacancy. Ask them if they would be interested in interviewing someone with your skills palette, it never hurts to ask.