Yeah, you're probably right - at first I thought it would be fine if it was a free app, but that probably still wouldn't fly.
I wonder if we could get away with just leaving out the logo but keeping the name "Magical Motoring Ball". Looks like from the picture of the box that there's a (TM) or something in superscript after the name though.
If you did the project as a non-profit i.e using it to promote anything other then mini and would not be able to sell ad space on the app you would be ok. Now the reality of building a native app is that it's expensive. Even though this is a simplistic application your still looking at 25k if you can find yourself a Euro programmer 55k if you go with a stateside firm. On that note it would be pretty awesome though !
fwiw, it does appear there are already Magic 8 Ball apps available in the App Store for iOS devices - I just didn't look through long enough to see if any of them give you the ability to input your own answers. Nor do I know whether any of them can be skinned with a UJ like it appears the Android app can do.
