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What the hell is this problem?

it is an endgame puzzle, not a lemonade dispenser

Seriously, though - that is the correct solution. Black does not have a perpetual check, and White will eventually queen his b-pawn
The key (which I only realised after getting the puzzle wrong) is to recognize that Black can never capture ...fxg3, because that would allow Rxg4+. So the Black pawns are simply not threatening anything.
@biscuitfiend You could not be more wrong. Rg4+ is a blunder, although rather tempting. The point is that b7 fg3 Rg4+ Kf7 followed by Rb2 might "talk some people out" of playing 1.b7.

However, b7 fg3 b8Q Ra1+ Rb1 just wins. Simple as that.
Yeah, and I would have played 2.Rb1?? on 1...fxg3 :-/

But the engine plays 1...Ra1+ :->
@KALEDZEDAJIMAMSLINU And I suppose after 1.b7 Ra1+ 2.Kf2 Ra2+ 3.Ke1 Re2+ 4.Kf1 fxg3 you would change your mind about me being wrong? :)

Of course 4.Kf1 is not forced but that seems rather beside the point. In this variation 5.Rxg4+ is the only move which doesn't lose immediately. Without this move available, the Black pawns would at least give White something to think about; with it, White has nothing to worry about, ever.
"Of course 4.Kf1 is not forced but that seems rather beside the point."

Absolutely not beside the point. Your point is "yeah, everything wins, so let's play the worst move on board where b8=Q does not work".

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