I wanna try too, I lived in Germany 1 year during a school exchange and I think I actually memorized the majority (but not every single) state.
1. Baden-Wuttenberg, Stuttgard
2. Bayern, München
4. Bradenburg + ???
9. Niedersachsen, Hannover
10. Nordheim-Westfalen, Bochum? Essen? Dortmund? Dusseldorf?
13. Sachsen, Dresden
15. Don't remember the name exactly, I know it has Holstein or something and the capital is Kiel
How did I do it?