Look through the text "Thinking like a genius" and write down the words and phrases that combine with the word "problem". See Ex. 47, p. 93 in Student's Book. Use a dictionary to add more to it.

to arrive at a solution to a problem (находить решение к проблеме)
to find a solution to a problem (найти решение проблемы)
to look at a problem (смотреть на проблему)
to think through a problem (продумывать проблему)
to cause a problem (вызвать проблему)
to think a problem over (обдумать проблему)
to have a problem (иметь проблему)
to solve a problem (решить проблему)