I don't understand this lesson ending

Lesson is Advanced / Choosing the best move / Making a plan Right at the end, you're left with the king and a knight against a king and passed pawn. "Your plan is complete! White's knight will keep close watch on the critical b1 square, when Black cannot force a promotion without allowing the knight to sacrifice itself for the pawn". I don't get this. What's stopping the king from marching to a5, then b4, kicking the knight off? And if Nd5+ then onto a3, and the pawn can advance to promotion without the knight being able to catch it? If the Nd1, guarding the c2 square, then the king can advance on the a file to a1, then b1 and c1, again kicking the knight and moving the pawn to b2? If then Nc3 again, guarding the b1 promotion square, then king simply moves to c2, kicking the knight to a square from which preventing promotion is inevitable? What am I missing? It's bugging me.

What is the position of every piece and who's turn to move?

Black pieces - King on .......White pieces- King on......

I'll put something here, I don't if you'll be able to open it, or just go in the analysis mode and introduce the moves.

[Site "Chess.com"] [Result "1/2-1/2"] [SetUp "1"] [FEN "2K5/8/1k6/8/8/1pN5/8/8 b - - 0 1"] 1... Kc5 2. Nb1 Kc4 3. Na3+ Kc3 4. Nb1+ Kb2 5. Nd2 Kc2 6. Nxb3 Kxb3 1/2-1/2

The point is that, nothing "stops' the black king to get close. It's just that no matter where he comes from or what moves black makes, the knight either moves in front if the plan, giving check, either attacks the pawn that is blocked by the king, thus ending in a draw. În analysis mode you'll see the eval bar (the black and white bar that evaluetes the advantage) is indicating it's a draw, and it sugests the best moves, which you can try

If you need more clarification, message me privatly, so I get notified and answer you quicker. Heva a great day.

Ok I understand now. I followed your line, also tried a different line which looked more promising for promotion (see image), since white can neither move to b1 nor check the Black king, but I overlooked the fact that White can now simply start moving the king, forcing the Black king to move between a2 and either a1 or a3, until the White king is close enough to stop the move to a3, which results in a draw by repetition (Ka1, Ka2...). Thanks for the clarification.

Sorry, in fact a3 forces a draw anyway, with Nc3+ picking up the pawn next. So Ka1 is the only possible move.

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