I spent a little time on 19.Bxf6 and even more on 19.Nd6+ but thought 19.Bxf6 was much easier. 19...Rxf6 (19...gxf6 or 19...Qxf6 20.Qxd7#) 20.Qxd7+ Kf8 21.Qd3 stops the back rank threat. 19.Nd6+ seemed much more complex and uncertain, though I spent some time trying to work out the details and didn't like what I saw.

19. Nd6+ Ke7
20. Nc8+ Rfxc8 (Raxc8 21. Qxd7#, or Ke8 21. Qe5+ Kd8 22. Qe7+ and the f rook is toast) 21. Qxd7+ Kf8 ultimately goes nowhere.

Bxf6 looks promising, but Patriot's analysis is at least as good as anything I could come up with.

Then I looked at 19.Qxd7+, and I still had to pause to let my visualization skills (such as they are) convince me that I had all the squares covered by the knight and bishop (now that the black knight was not blocking my bishop).

"almost" : black ♔ still has a square to escape : e7.

black ♔ can escape to e7 because black ♘f6 "cuts" the action of white ♗g5...

How can we get rid of this annoying black ♘f6 ?

Through a sacrifice of deviation : 19 ♕xd7! ♘x♕d7 20 ♘d6+++ mate

The first mistake was 10...Nf2+? allowing 11. Rxf2 , since 10...cxd5 = would have held nicely.

So we don't think "it's a monday, let's look for queen sacrifices". Instead, let's look for moves that we might actually consider in some draughty church hall sitting on uncomfortable plastic chairs.

We have black's king in the centre, but we are a rook down. And that means we must attack.

The d1 rook would love to attack via e1, but that pesky black queen is in the way. Bxf6 doesn't seem to go anywhere. Ditto queen moves (for now).

And that just leaves Nd6+. Hmm - this is more interesting. The knight not only gives check, it also covers the f7 escape square. Black has only one move Ke7. Can we hit the king again? No, not really. Re1 still does not work. But wouldn't it be great if the Nf6 was off the board? Then the Bg5 would cover the black escape squares near the king.

How can we get rid of the Nf6? Bxf6 doesn't work, because Rxf6 gives the king another flight square that we cannot cover. How else can we get rid of the knight?

It is only then that we think about the queen sacrifice. This deflects the knight, so the Bg5 can combine with Nd6 to give mate.

A quick blunder check ... can black wriggle out? Nope, both moves are forced.

You and me both, brother.

I found that looking specifically at the color of flight squares, finding the square(s) where a N covers them, and then calculating the (parity of the) number of moves required by a N to get to the square(s), sometimes gives useful hints for N mates.

I think it was Averbakh who wrote that when he looked at each position in his games, he first looked for a way to sacrifice his queen.

My reality: Look at board. See Qxb7... take!

Surely he jests you say: ah, alas no. yesterday I played four games; lost them all. In two I just lost pieces through one ply oversight; in one I played a suboptimal move (after 20 seconds of thought in a critical position) which (in gong over the game after) was a sure winning position (absent another one ply oversight) and in the fourth I actually told my opponenet my winning move,when I thought it was no longer available, except that it was still avalable and he defended.