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This is interesting and it makes me really want to see the 5 4000+ puzzles...

I am not sure that the 5 specific puzzles maxed out at the 4000 also represent the very best, most fun, and most insightful. Sometimes the reason a puzzle comes up as an extreme outlier is somewhat obtuse, and we are more inclined to remove the puzzle after we see how users interact with it.

For example https://www.chess.com/puzzles/problem/568140 is mostly rated 4000 because ...Qe1+ is so compelling that it pulls in even excellent players, while there's an easy material pickup on the board.

But there are exceptional puzzles throughout the 3000s, like 3500-rated https://www.chess.com/puzzles/problem/769056 , which absolutely anyone can follow, but few can solve on the first try.

why is Qe1+ compelling? It pushes the king to greater safety and activates the rook. If the correct move is e3, then I think that the problem with a 4000 rated puzzle is that the prior is so strong that players feel like they can ignore the obvious moves. You should try just resetting the rating of that puzzle and see it ends up in a different spot.

We sometimes do that. I'm resetting that puzzle down to 1480.

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