Atleast almost...

A few nights ago i was just browsing through keywords in the google keyword tool. until i found something nice. A keyword that had a 25$ cpc. I check the competition and it was pretty hard. The keyword was a solution to a problem. So i checked how many people googled for the problem right, because that's what most people do, they google what their problem is because they do not know yet what the solution will be. The problem keyword was a 3 word keyword and had a niche micro niche result: 2000 exact local searches + around 1000 local searches for very similar keywords. What did i see to my surprise? there was almost NO competition on these keywords. First page in SERP were filled with very long url's, forum posts, some blog posts etc. almost none with pr. The allintitle and allinurl were both below 300!

I registered the exact keyword domain, put a 400 words article on it and within 48 hours i was on page two in google. With a few backlinks and 2 more articles i expect to hit the top 3 in ±2 weeks.

Now my question is: Is it possible to rank for the keyword of the problem but write the article about the solution,so my adsense ads will target the high paying solution keyword?

I put the keyword of the problem in the url, meta, h1. thats it. The high paying solution keyword is in the meta, h1, h2 and in the text.

Will this work?

absolutely. as far as you your content i relevant to your site theme,u should be ok with going after such kw.