Wnite to move. How should white proceed?
This is like 40 move long with twists and turns so think carefully!
Typos. I meant 2.....Rh1 is a forced mate after 3.Rd3. At least, it had better be because if it isn't, then everything above is pointless.
This is quite a problem! I have worked on it off and on all evening. I think I have the main idea- win the black rook in exchange for the knight by driving the black king away from the h-file leaving the rook trapped by his own king and pawn and easy prey for the white king. I think the start has to be 1.Kf3 Rh3 2.Kf4 and then there is a major branch point where black plays either 2....Rh1 or 2.....Rh2, but I think 2......Rh2 is a forced mate after 3.Rd3!, but am not completely sure that right now- there is one variation within it I haven't been able to stitch up and will return to it later, but I want to cover what is probably the longest line which is 2......Rh2:
1.Kf3 Rh3 2.Kf4 Rh2 3.Nf5 Kh3 4.Rd3 Kg2 5.Ne3! Kf2
Here, 5......Kh3 is met by 6.Ng4 which is sure a quick mate once the rook is gone. Also, Kg1 is transposed into the main line after 6.Rd1+. Continuing.
6.Rd2 Kg1 7.Rd1 Kf2 8.Rf1 Ke2 9.Kg3! and black must trade the rook for the knight since the rook can't escape.
I will deal with the ending tomorrow, but I already know that it is won- white will freeze the two queenside pawns by attacking the forward one with the rook from the first rank long enough to get the king over to the queen side if the black king goes that way.