Hello, dear chess friends!
Last puzzle was seemingly very hard. But it required more chess analytics than any concrete lines. Black knight was able to stop pawn only on a7. For this purpose it has 3 squares b5, c6 and c8. c6 is never allowed to it; but squares b5 and c8 are available through the whole puzzle. So, White needs to take both of them under control. How to get this. First, White pushed BK away from pawn a6 but it's only a part of solution. BN leaves on b5 as far as we don't attack it with our N. But if we do this from c3 or d4 it moves to d6-c8 and BK comes back to attack pawn a6 from a5 or b5. In such way he gets another kind of fortress - Nc8 stops pawn; BK attacks pawn and in such way defends Nc8. So, we need something different. What it could be? After a while we realize that we can push BN from c7! In such way we also solve a problem of pawn a6 and WK is free to push N from c8. That's it!
There are many possible solutions. White can maneouver for hours before he does his winning plan. I just show one of possible lines (seemingly the shortest but maybe I missed something).
Next position is much easier but at the same time it's more spectacular - White should make a draw. Good luck!
Solution is here: http://blog.chess.com/view/daily-puzzles-36