Can I have my own activation key input in my free app for app store?

I have created a local educational game for my own country. It is for kids in my country to learn our local native language. I have created the IPA file and tested on my iPad and iPhone devices and works great. I have programmed it in a way that when first installed, it would be as a trial version and the game can be played only partially. Some alphabet letters are skipped for instance. And if the user likes my game, I have created an activation menu within the game, just a simple serial number generator so that locals can contact me for activation key.

My question is, will this game be allowed to be published in the app store as a free download app? Or is having such in app activation code and restriction be violating any apple rules? If anyone can clear this out for me that would be great. Any help and responce would be greatly appreciated.

Best regards

Affan