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that was easy. nice checkmate
ok... how is white not losing after Kxd8?
Shortly after that I think white runs out of checks, and black is up a mountain of material although it is undeveloped I think he can get enough activated to win.
The first move looks like a blunder to me, and that rook should definately NOT be sacked, and I think whites best option is to go for a perpetual check by moving the queen between f5 g4 & h4, the black kind is exposed enough to be put in perpetual check, but not enoug to checkmate.
This is a good example of how to turn a draw into a loss.
The players who just look at the puzzle and not the comments are now dumber for having listened to you.
I looked for a perpetual, I couldn't find one.
D file is shut down by the rook, no going to the left for the black king. That leaves only to the right.
Move 1 for white = Qh5
Now black has 2 options
1) Qf7 to block... that is just losing, and on the next move so the other move is the only reasonable option
2) Kf8 is what black will do
So we are at 1 = Qh5. Kf8...
on to the next move
now white can move all around between f5 g4 & h4 with his queen attacking the black king from whichever of those squares is right at the time, and the black king should just run around, any attempt to block with the queen on g7 (which is the only piece close enough for the black king to hide behind) leeds to a back rank mate by the white rook and should be avoided.
The black king is in enough danger for white to keep him in check forever, but the black king can survive I think with accurate defense.
There are a lot of checks and things, for what it's wroth this is about as far as I took it before giving up.
Qh5 is check mate im pretty sure