Second Troitzky line, where knight and pawn could be located? I am trying to understand where the pieces should be located for the second Troitzky line (checkmate 2 knights vs a pawn in 50 moves limit) and fail to get it. So from wikipedia:


  Black's pawn is blocked by a white knight on or behind one of the
  dots, White can force a win within fifty moves. If the pawn can be
  blocked on or behind one of the Xs, White can force a win within fifty
  moves more than 99 percent of the time.




The problem is that I still can not understand where the pawn and a blocking knight could be located.

Just to resolve ambiguity: I do not need to know how should white force a mate, I just need to understand which positions are possible to win with 50 moves rule. For example, are these positions a theoretical win?

[FEN "8/8/2p1N2k/8/2N5/5K2/8/8 w - - 0 1"]


,

[FEN "8/8/8/1N2pk2/1N6/8/8/4K3 w - - 0 1"]


,

[FEN "8/N7/6k1/7p/8/8/8/1K5N w - - 0 1"]
This has been already solved by Helmut Conrady, his elegant 15-page solution is available here.
It is filled with diagrams and examples as you wanted.
Let me know if you have any questions regarding the diagrams or explanations given.
EDIT: In reply to the edited version of the question and the three positions added:
For the position to be winnable under 50 moves, there are two simple conditions:

Either the black pawn is blocked by the knight on the 5th ranked
Or the pawn is blocked on either b6/b7 squares or on g6/g7 squares.

This means:

First position Winning for white in 50 moves because the pawn on c6 isn't advanced enough and is already blockaded, so no hope for black.
Second position Draw because white cannot win it under the 50 moves limit, as no matter what he tries in the current position, the pawn will get the chance to go past the 5th rank. White isn't in time to block the pawn, two examples:

First:
[Title &quot;pawn will advance to 4th&quot;]
[StartFlipped &quot;0&quot;]
[FEN &quot;8/8/8/1N2pk2/1N6/8/8/4K3 w - - 0 1&quot;]

1.Nd6+ Kf4 2.Nd5+ Kf3 3.Nf5 e4

Second:
[Title &quot;pawn will advance to 4th&quot;]
[StartFlipped &quot;0&quot;]
[FEN &quot;8/8/8/1N2pk2/1N6/8/8/4K3 w - - 0 1&quot;]

1.Nd6+ Ke6 2.Ne4 Kf5 3.Ng3+ Kf4 4.Kf2 e4


Third position: Draw: easy enough to see that white can't stop the immediate advance of the pawn past the 5th, so white cannot win under 50 moves.

In order to conclude, although if one of the conditions is fulfilled white will have a theoretical win under 50 moves, but that is only possible if no tempo is lost usually, so techniques like triangulation are continuously applied, as shown in the examples of the link.