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Faulty puzzle

Here it is: lichess.org/training/tk65c

(EDIT: After 55. f6 Bc3) instead of the given solution 56. f7, 56. Kf5 also seems to work (which I played). Engine thinks it is a draw first, but after playing a few moves the eval goes up (a bunch of only-moves apparently). For example 56...Kxh3 57.Kg6 Be5 58.f7 Bd6 59.Kxh6 Kg4 60.Kg7 wins according to the browser engine. I don't have the apparently required computing power at my disposal, so it'd be great if someone could check if Kf5 is indeed winning. In any case, to calculate all that is quite inhuman. Also there should be a button to report a bad puzzle, even though it is the first faulty one I encountered on here!
And another one!
lichess.org/training/twcoW

After 48. Kxg4 Bd8 49. Kf5 Kc5 50. g4 Kd6, given solution is 51. b4. But g5 wins as well! (guess what, I played that) If 51... Bxg5 52. Kxg5 Kxe6, the tablebase gives a mate in 30 after Kf4. The other lines instead of Bxg5 win on narrow paths, but they do win... so it happened to me twice in 3 days, that's pretty unlucky. I assume that in generating these puzzles, there is no tablebase involved..? Because browser stockfish only gives a stable +1.5 after 53. Kf4. Maybe you want to change that...? :)

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