At first I "hand-waved" 30.Qf6+ because of 30...Bxf6 and saw that 31.exf6+ is bad but didn't look at all the forcing candidates, namely 31.Rg3+. So this took me WAY too long to solve.

30.Rh7+ doesn't work: 30...Kxh7 31.Qh5+ Bh6. Too slow is 32.Rh3 Qf1+ 33.Kc2 Qd1+ (good enough) 34.Qxd1 Rxd1 35.Kxd1 and white is lost.

30.Qh5. This looks good but is too slow. For example, 30...Qe4+ 31.Ka1 Qg6 defends and threatens to exchange queens. Note that 32.Rg3?? Qxh5 33.Rxh5 Rd1#.

Hiarcs suggests 17...Ne4 18 Qe3 Nd6 after which Black's game may be tenable.

I continue to be amazed and impressed by these chess players' ability to set up positions where a subtle but decisive move ends everything.

or accepted 30...♗xf6 31 ♖g3+ and mate in two more moves.

Here, the thing to notice is that black's king is "walled in" to the g and h files, thanks to his own pieces sealing of f8 and f7, and our Pe5 sealing off f6.

When a king is walled in like that, one thinks of rooks (or rooks and queen) to deliver mate by taking away the remaining squares on which the king is confined.

We already have one rook taking away the h-file, so we just need to take the g-file, which is currently blocked by the bishop. This makes the bishop the target of our attack.

"Looking for forcing moves" may not be enough, as Rc3 is more or less forcing, but also worthless. To me this is both a tactical and positional puzzle. By analyzing the whole of blacks position, instead of jumping to the forced attack we can see he has positional weaknesses across the kingside.

Positionally, the black bishop is overworked by defending the king along the g column, (ineffectually) preventing the text move, and supporting the black queen threat at c1 and other back rank attacks. Also, it has neither contact with other pieces nor natural defenders. How then to move against these weaknesses?