Now what if you were allowing conjectures about the rule and someone said “An N*N koan with 2N + 2 black stones will always be green”? 
(I guess in the “arbitrary conjectures” variants we really need to allow a “not sure” response, since it could get tricky even with more natural-sounding conjectures 
)
Edit: @shinuito quickly made this comment outdated by providing a counterexample to the conjecture: