By difficulty
Hard puzzles
Longer lines, quieter first moves, and defences that hold if you calculate them carelessly. At this level the puzzle is often not about winning material but about a position where the material comes later and cannot be avoided.
How to spot it
Calculate to the end of the line rather than to the point where you are happy. The most common failure here is stopping one move early, at a position that looks winning and has a defensive resource in it. Find their best answer to every move, including the ones you think are forced.
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
39.fxg5+ hxg5 40.h5
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2. Black to play Play it out →Answer
18...Rxd4 19.Qxd4 Bc5 20.Rf2 Bxd4
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3. Black to play Play it out →Answer
19...Bc5 20.Rxe8+ Rxe8 21.Ne4 Rxe4
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4. White to play Play it out →Answer
39.Rf8+ Kxf8 40.Qf7#
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5. White to play Play it out →Answer
32.Qxh5+ Kxh5 33.Rh3#
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6. White to play Play it out →Answer
10.Bxf7+ Nxf7 11.Ne6 Nde5 12.Nxd8
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7. Black to play Play it out →Answer
16...Nc6 17.Qa3 Ra8 18.Qxa8 Rxa8
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8. Black to play Play it out →Answer
26...Nxc7 27.Rxg5 Rxe1+
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9. Black to play Play it out →Answer
27...Rab8 28.Qxb8 Nxb8
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10. Black to play Play it out →Answer
27...Qf1+ 28.Rxf1 Ne2+ 29.Kh1 Rxf1#
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11. White to play Play it out →Answer
16.Re8+ Kg7 17.Rg8+ Rxg8 18.fxg8=Q#
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12. White to play Play it out →Answer
15.Bxd5 Bxh4 16.Bxb7
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.