But you used the accelerometer for movement control, right?
And the other puzzle games are point'n'click.
Like, currently I'm making t35tbot mainly for the iPhone (I'm already using the appropriate resolution, but that's not important).
I have onscreen controls. Check out Archibald's Adventure on the AppStore. You'll know what I mean.
If you need a more popular example, there's the best graphics game on the App Store: N.O.V.A, a halo clone. It also uses an onscreen joystick with a couple of buttons you have to press/use simoultaneously.