<The best try is

36...Rf6

but now white finishes black off with

37 Rh8+ Kf7 38 Rf8#>

3/3

Not that hard, but actually seeing the Arabian mating net is rather complex on sight.

34.Qxh7+!
White announces mate in five.

34....Kxh7
--a--Kf8 35.Qh8#

35.Rh5+

35....Kg8

36.Ng6
Threatens mate on h8. Black can only interpose the Queen, but strangely enough this does create one little trap for White.

36....Qg2+

37.Rxg2
Keeping the protection.
--a--Kxg2? Rf6
Leaving the Knight undefended. Nonetheless, in that position, White regained the Queen and wins much material with Nxe7+.

37....Rf6
Losing least material whilst postponing mate.

38.Rh8+

38....Kf7

39.Rf8#
1-0

Instead, I went with good (but not AS good) 34.Qh6, threatening to create a Q+R battery with Rh5, or (if nothing else) taking Qxd6 creating a dangerous passed pawn.

These threats, plus having the knight to come in at g6 looked like a winning attack to me. There are a number of ways black might respond, but I didn't see any that kept him out of trouble.

For instance:
34...g6 35.Rxg6! hxg6 36.Nxg6 (threat:N(x)e7#)

34...Kf8 35.Qxh7 Ke8 36.Ng6

If it makes you feel better, <YouRang>, I looked hard at the sophisticated 34.e5 and then in desperation at 34.Qh6. After a few minutes, I thought to myself, yeah, 34.Qh6 probably wins, but this is Wednesday, not Friday. Finally, I went back to basics: checks, captures, and threats.

I saw 34.Qxh7+, of course, and erased my first two candidates out of sheer embarrassment.

Oh, I realize 34.Qh6 isn't as good as forced mate, but I rate it much better that a 'slight advantage'. In fact, I'd call it winning.

If black plays 34...Qf2 as you suggest, it does prevent Rh5, but it also removes a defender of g7, forcing both black rooks to guard g7).

That's where 35.Qxd6! comes in, which (1) threatens to win a rook with 36.Qd8+, and (2) creates deadly connected passers. After the queen returns to h6 (37.Qh6), these pawns will march and create havoc for the black rooks, starting with 38.e5 (threat:e6 winning the trapped Rf7).

I found 34.Qxh7+, because I love tactics based on little P pushes. I know they rarely provide the final tactical stroke, however, so when 34.Qh6 did not work, I decided I was being far too fancy. I recalled the best advice I ever had from a teacher (an evening school art teacher, Xiao), which was, "Whenever you get into trouble, go back to basics."

Memory aside, I think there are two ways to work out combinations like this one - check all the forcing moves or look for weaknesses to exploit.

The forcing moves are fairly easy to spot. Rxg7 leads nowhere as the g7 square is protected four times. So then we look at the forced sequence 34. Qxh7+ Kxh7 35. Rh5+ Kg8. Now if a protected rook could land on h8 it would be mate. How can we engineer this? Let's look at Ng6, when there is nothing that white can do to prevent Rh8 followed (after Rf6) by Rf8.

That is when we notice the helping hand offered by the pawn on d5, which stops the king from escaping via e6.

So much for examining forcing lines. Could we work out the solution by looking at the features in the position? Black's problems are a weak h7 (only defended by the king) and dreadful congestion along the seventh rank. The black queen and bishop are out of play. White's trumps are the doubled rooks on the g file (although this point is well defended) and the advanced queen and knight. That ought to suggest an attack on h7, which does indeeed turn out to be the answer.

Is this trolling? It looks like it.

You fail to see the beauty of this puzzle if you're serious about what you said.

A good rule indeed, although in my case, it didn't really apply because I figured that 34.Qh6 DID work. :-)

Toga II 1.3.1 gives

[ply 15/63, time 04:52, value +3.41]

34.<Qh6> Qd4 35.Qxd6 Re8 36.e5 Kh8 37.e6 Bxe6 38.dxe6 Qxd6 39.exf7 Rf8 40.Rxg7 Qd8 41.Rg8+ Rxg8 42.fxg8Q+ Qxg8 43.Rxg8+ Kxg8 44.Ng2 Kf8 45.Nxf4 Ke7 46.Kg2 Kd6 47.Nd3 a5 48.f4 a4

Bad news: this puzzle needs way more than 15 plies. Slide down the proposed lines a couple moves, then back, and you should see a completely diferent best move 34 for black. Repeat, and yet another move surfaces. And this branching happens a lot, and then the engine starts dumping hash, so the analysis starts running in circles. I had to add this game to my engine-killer collection.