alachabre: The first quick glance tempts me to throw the rook against the pawn mass in the center, and force the King into an uncomfortable dance with the White queen and knight.
26. Rxd6+ exd6
27. Qh5+ Kf8, this seems to be best for Black, Ke7 allows further intrusion by the queen, and a draw by perpetual check is in the cards. However, the move as played seems to put an end to my rook sac dreams. The next candidate becomes the natural
26. Nf6+ Ke7, a nice diagonal has been opened for the queen with the knight move.
27. Qb7+ Kxf6, it's hard to see that this is going anywhere, and given that Black has other defensive choices here, I don't want to spend too much time analyzing the line.
Given the strong checkmate threats against the White king (Qb1, Qc3), White must act forcefully and carefully. This suggests another check by the knight (Rd7+ Kxf6 seems a dead end), but neither square looks very appetizing. But let's see what happens.
28. Nd5+ Kxd6
29. Nb4+ grabs the Black queen, but
28. ... exd5, no time for a waiting move by the queen now (Qxd5 Qc3#), so what now? The obvious
29. Qxh3?? Qxd1 is out. So a dead end, it seems.
28. Ng8+ Rhxg8
29. Qxh3 Ra8 doesn't look good for White, except NOW my rook sac leads to mate:
30. Rxe6++ Kxe6
31. Qd6#, an epaulette mate.
So maybe the rook sac is in the winning variation somewhere. But not yet, because:
29. ... Qc3+ leads to exchanges that seem to leave Black a little better because of pawn structure, as well as material edge.
I've looked at 28. Nh7, shutting off escape squares, but that fails against Rxh7. 28. Rd7+ Kxe5 doesn't look terribly great. So I guess I'm stuck. Now I'm left with only one move that doesn't lose the knight or allow checkmate, 28. Nh5. This renews a threat of Qxa3, and keeps the heat off the White king for a little while longer. It also takes away e6 as an escape square, mmm, and g7 too, so back rank mate threats are still on the table. Qb7 is still a threat, albeit apparently easily defended.
Ok, I have to look at this position more deeply, and I need a board to do it. The Black knight doesn't have an escape square (why does it seem like this puzzle is starting out one move too soon?), so it must be defended.
27. Nd5+ Ke7
28. Nh7 b4
29. Qb7+, White has to proceed carefully now, because Qc3# is hovering over the king.
29. ... Rc7?
30. Rd7+ etc., the Black position falls apart here.
29. ... Ke8 (Kf8? Rd8+ and mate soon), and now my original rook sac idea is back:
30. Rxe6+ fxe6
31. Qd7+ Kf8
32. Qg7+ Ke8
So 28. ... b4 is out, and it would appear the Black knight is lost. The analysis is getting very deep and long, and I haven't looked at a critical variation yet.
26. Nd5+ Ke8
27. Nh5 as before, with the same benefits? The double threat of Rd8+ leading to mate, and Qxa3. Yes. So it seems I've found a beneficial continuation, but I couldn't do it strictly by visualization; I set up various positions on a board, and it took me a very long time to work through it. But that's the whole point of practice and study, I suppose. There's more work to be done on whether Black can save the a3 knight or not, but I'll do that later and won't bore the board with the details.