1.Rh8+

Skewering the rook on a8 since the rook is untouchable: 1...Kxh8 2.Qh6+ Nh7 3.Qg7#

1...Kf7 2.Ng5+

2...Qxg5

Forced, since 2...Kg7 3.Rxa8 Qxa8 4.Qe7+ (double attack!) Kh6 5.Qxf6:

Analysis Diagram: after 5.Qxf6

...is so clearly won for White.  It is also preferable for Black to the position in the analysis diagram below, after 3...Rxh8.

3.Qb3+

Taking the queen also wins, but not as handily: 3.Qxg5 Rxh8

Analysis Diagram: after 3...Rxh8

Why is this position preferable to the one above it?  Let's see them side-by-side:

Analysis Diagram: after 5.Qxf6

Analysis Diagram: after 3...Rxh8

The position above left is preferable because White has a 2-1 advantage in pieces, which makes his task of promoting a pawn much easier than in the diagram above right, where Black can try to coordinate his two pieces to work together against White.

I'm not saying Black has an advantage in the position on the right, just that White's task is easier in the position on the left.

Now, back to the main line:

3...Kg7 4.Rxa8 Qg4+

Black hopes that White misplays, and allows a queen fork on the long diagonal: 5.Ke3 Qe4+ picks off the loose rook.

5.Kf1

White declines to help Black out, and with an overwhelming material advantage should have little trouble winning this ending.

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