Dizzy Squares: free puzzle app game for iphone, ipad

Dizzy Squares is a very simple puzzle. Rotate any 3x3 square grid to match the pattern on the bottom.

There are 10 levels and I'm stuck on level 6. And they only get harder!

I'm wondering: can any permutation of random colored tiles be solved?

Did I mention that Dizzy Squares is a free puzzle app?
http://dizzysquares.com/