By difficulty
Expert puzzles
The hard end of the database. Solutions here regularly begin with a move that gives away material for a positional reason, or with a quiet move that does nothing visible. Most players never solve these reliably, and that is what the rating means.
How to spot it
Trust the position rather than the material count. If the opponent's king is exposed or their pieces are badly placed, the answer is usually the move that keeps them that way, whatever it costs. Then calculate it properly, because at this level the refutation is real if there is one.
The positions
Easiest first. Every one is from a real game, and the rating under each board is what it costs the players who have tried it on lichess.
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1. White to play Play it out →Answer
18.Qg7+ Kxg7 19.Nf5+ Kg8 20.Nh6#
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2. White to play Play it out →Answer
37.Rxb7+ Rxb7 38.Nc6+ Ka8 39.Rf8+ Rb8 40.Rxb8#
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3. White to play Play it out →Answer
18.exf6 Bxc4 19.Nf7+ Kg8 20.Nxd8
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4. Black to play Play it out →Answer
26...h6 27.Qg3 Qxe5
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5. Black to play Play it out →Answer
25...Ne1+ 26.Kf1 Qg2+ 27.Kxe1 Qxf2#
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6. Black to play Play it out →Answer
33...Rg2+ 34.Kxe3 Qd3+ 35.cxd3 Rxd3#
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7. Black to play Play it out →Answer
20...Ne2+ 21.Kh1 Nxc1
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8. Black to play Play it out →Answer
28...Rb1+ 29.Kxb1 Qb5+ 30.Kc1 Bb2+ 31.Kd1 Nc3+ 32.Kd2 Qe2#
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9. White to play Play it out →Answer
41.Rf3+ Kh4 42.Rh2+ Kg5 43.Rf5+ Kh6 44.Be8+ Kg7 45.Rg5+ Kf6 46.Rg6#
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10. White to play Play it out →Answer
10.axb4 Qxa1 11.Nc3
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11. White to play Play it out →Answer
21.Qh8+ Kf7 22.Qh7+ Ke8 23.Qxg6+ Rf7 24.Rh7 Nf8 25.Qxf7+
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12. White to play Play it out →Answer
35.gxh5 gxh5 36.Kg3 Kf5 37.fxg5 Kxg5 38.h4+ Kf5 39.Kf3
Reading about a pattern is the easy half. Motify finds the positions where you missed one, by running your own lichess and Chess.com games through Stockfish, and puts each of them behind two or three puzzles on the same idea so you meet it having just found it three times. See how Motify works.
Positions from the lichess puzzle database, released under CC0.