If Hogwarts spits back an error if you try to add a non-integer number of house points, and if you can explain the busy beaver function to Hogwarts, you now have an oracle which answers n∣BB(k) for arbitrary k,n∈Z+: just state ”BB(k)n points to Ravenclaw!”. You can do this for other problems which reduce to divisibility tests (so, any decision problem f which you can somehow get Hogwarts to compute; if f(x)=1, 2∤f(x)).
Homework: find a way to safely take over the world using this power, and no other magic.
I’d be worried about integer overflow with that protocol. If it can understand BB and division, you can probably just ask for the remainder directly and observe the change.
If Hogwarts spits back an error if you try to add a non-integer number of house points, and if you can explain the busy beaver function to Hogwarts, you now have an oracle which answers n∣BB(k) for arbitrary k,n∈Z+: just state ”BB(k)n points to Ravenclaw!”. You can do this for other problems which reduce to divisibility tests (so, any decision problem f which you can somehow get Hogwarts to compute; if f(x)=1, 2∤f(x)).
Homework: find a way to safely take over the world using this power, and no other magic.
I’d be worried about integer overflow with that protocol. If it can understand BB and division, you can probably just ask for the remainder directly and observe the change.