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Yup, there are just so many routes and they all lead to mate.
At least you got the idea to sac the rook. In the game, my opponent didn't even block with the pieces to delay the inevitable but went Kb2, so sacrificing the rook on a2 comes with a check... Next rook replaces it, and then queen delivered mate in the corner
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Blocking would have been good because with Kb2 I can automatically see the mate. With the blocking, even though they lose material, I couldn't see the forced mate as that's still 7 moves out. There's a chance I would have misplayed
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Technically white can block with rook check with the queen, too, on a4. White will obvs lose but it'll take a bit longer navigating to the exact mate
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I wasn't able to find the full winning line, but I got this far, and confirmed that my instincts were correct
What I wasn't sure was what white would do next, but checking with the engine it just appears that white's position is just horrible in general, and there are many forced mates from there.