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4 wrong Puzzles

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1. lichess.org/training/RZYuG:
Winning line:

55. Qf6+ Ke8
56. Qxg6+

But 56. Qxe6+ also seems to win according to the lichess tablebase.

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2. lichess.org/training/dku9r:
Winning line:

18. Bh3+ Kg6
19. Qh5+ Kxh5
20. Bf5+ Bh2
21. Rxh2#

Here 18. Qg4+ is definetly much harder to spot but it's also a winning move (Mate in 10).

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3. lichess.org/training/ynV4e:
Winning line:

59. ... Kg3
60. Rc2 Rg8

Here 60. ... Re8+ also wins according to the engine and the lichess tablebase.

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4. lichess.org/training/J4UtK:
Winning line:

42. ... Qd2+
43. Kb3 Qd5+
44. c4 Qxe6

42. ... Qe2+ has almost the same evaluation as 42. ... Qd2+.

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For most chess positions, if there is a mate in four, there are very likely to be longer checkmating sequences, that are by definition inferior. Just like in real chess games.

A mate in one puzzle is not incorrect because there is also a mate in 23. The mate in 23 solution is incorrect because it's not a mate in one!
So your complaint is that you don't care about the length of the solution as long as it achieves the same result. It seems to me like that would create a less useful training tool, so I'm not very sympathetic to that view.
So chess is generally about checkmating the other king. So does it matter whether i go for a mate in three or a mate in four move? Well probably not because both moves do guarantee me a victory. If you spot a mate sequence in a game then you don't look for another mate you just play the move that wins.
@Splorer i definetly understand why for example a +9 move where you win a rook is better than a +2 move where you have a positional advantage. But not considering the length of the solution there is better and no worse mate. But why does the length matter when you win the game on the spot?
@KeithDenning I agree with you that in your scenario the mate in one is superior. But this is a mate in 4 and mate in 10. And considering that the computer just plays some ridiculous moves to prolong the game which nobody would ever play, I do think that both solutions are correct answers because the mate in 10 is hard to see but in fact spottable.
#7 Well, for a computer, the length wouldn't really matter. For humans, the length represents opportunities to make incorrect moves. Preferring lines with fewer opportunities to make incorrect moves, when all else is equal, should lead to more wins over many games. For examples of humans making incorrect moves, just check the games in my profile.

That said, maybe there is room for "runner-up" solutions in puzzles, where you neither gain nor lose points as long as the move you make is among a list of moves that are still eventually winning.
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