The phrase "a different sort of problem" is correct and usable in written English.
You can use it when discussing an issue that is distinct from others previously mentioned or considered.
Example: "While we have addressed the budget concerns, we now face a different sort of problem regarding team dynamics."
Alternatives: "a different kind of issue" or "a unique challenge".
But this is a different sort of problem.
Each presents a different sort of problem: or at least Russia and Ukraine do.
Another start-up, Fandor, a subscription service for independent films, had a different sort of problem.
Intentional transmitters, like mobile phones, two-way pagers and walkie-talkies, present a different sort of problem.
Representative Ron Paul came quite close to beating Mrs. Bachmann, but faces a different sort of problem.
Now the city faces a different sort of problem: Along the way, it became one of the most expensive places in America to live.
The Eva Solo box had a different sort of humidity problem: the stylish floppy flap didn't close tightly, and was so large that when opened it completely released the moisture.
But last week, people were talking about a different sort of structural problem: whether there would there be room enough inside if both Matisyahu, the reggae rapper, and Sway Machinery, a cantorial blues band, performed before a midnight prayer service that marks the beginning of a week of penitence leading up to the High Holy Days.
But policymakers now face a different sort of inflation problem: determining which of many competing indices is giving the best picture of prices in America.The most popular measure, the consumer price index (CPI), is a representative basket of goods and services drawn from a survey of the spending habits of 12,200 households.
This is a different sort of agreement problem.
Last week, a boycott finally happened, at Grambling State University, a historically black college in Louisiana, but the football players brought attention to an entirely different sort of problem: budget cuts that have hurt the entire university.
