Let karparov(2222) be defined as the number of whole seconds that have elapsed since this message was posted. You cover all naturals this way! But you're all m

Let karparov(2222) be defined as the number of whole seconds that have elapsed since this message was posted. You cover all naturals this way! But you're all missing the point. A winning "solution" to this game is whatever the reader accepts as a legal solution which at the same time is as creative as possible. That's necessarily subjective, but that's fine. Anybody is free to argue that it's a stupid game if these are the rules, and those folks just don't need to play and can let everybody else have some fun!