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RE: Chess problem 53 / Schachaufgabe 53
I think the most promising drawing plan is to get rid of the king side pawns and just have the black king camp out between c7 b8 squares. One possible sequence:
f3, ...
regardless of what white does next, that g2 pawn is going away.
..., gxf3
gxf3, Bxf3
Kb6, Bb7
Kc7,
From here black can just give away his g7 pawn somehow. Afterwards have the black king shuffle between c7 and b8. White won't be able to make any progress since black king can't be kicked out of the corner. If white's king ever gets too close like d7, d6, c6 etc. that's stalemate.
Like @juanmi96 you had the correct idea that white actually cannot win with king, bishop and pawn against king and pawn in this special position. Well done!