Right, I invented the jrockway function which is defined as f(2, 2, 2, 2) = 7 so I made 7. Maybe the rule is "someone else has to invent the function", but I invented that so you can use it. (Please make me a the__alchemist function.)
Maybe the rule should be that the function has to be invented before the inventor has knowledge of this game. But now I'm just going through /usr/bin looking for binaries where the 2222th byte is 0x7.
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!
Maybe the rule should be that the function has to be invented before the inventor has knowledge of this game. But now I'm just going through /usr/bin looking for binaries where the 2222th byte is 0x7.