Question: Can K+N mate K+P?
Answer: Yes and no.
Explanation: Well, we all pretty much know that K+N vs K is a draw. Now, if we give the underprivileged lone king a pawn to help out, surely K+N can't make K+P. Of course not ... UNLESS the player with the K+P decides to participate in a helpmate. True. If the player with K+P will cooperate, there are scenarios in which the K+N can win by mating the K+P. No, you say? Let's take a look at just one scenario, contrived of course. But then, that's what helpmate is all about.
White to move, promote and get mated!
So, why do we waste even a moment on this silly little example? Here's one possible answer. Let's say we're at the starting position and White's clock runs out in. What should the result be?
The FIDE Rulebook states, in part, in Section 9.6: "A game is drawn when a position is reached from which a checkmate cannot occur by any possible series of legal moves."
In our position, clearly a checkmate CAN occur by a remarkable series of legal moves, implying that said position is NOT a theoretical draw (where a theoretical draw is one that cannot result in mate). Given that, then the position is live, so-to-speak. And both sides have chances of winning. Thus, the superior side (K+P) cannot be awarded a draw by an automaton (i.e., chess server algorithm). Does this therefore mean that the K+N should be awarded the win on time? Sure seems like it.
In an OTB game with a human arbiter (e.g., a TD), the side with K+P could demand the draw and get it, I'd imagine. But with only an automaton as judge, jury and executioner, maybe not.
What's the correct resolution here? Weigh in, if you wish.