Tactics
The quiet move
A move with no check, no capture and no obvious threat, which wins anyway. These are the hardest puzzles there are, because every habit that makes you good at tactics, look at checks, look at captures, points away from the answer.
How to spot it
Quiet moves turn up when the opponent has no useful move of their own, so start by asking what they are threatening. If the answer is nothing, you have time, and the move to look for is the one that takes away their last escape square or adds a second attacker to something they cannot defend twice.
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. Black to play Play it out →Answer
54...e4 55.g6 e3 56.Rxc2+ dxc2 57.g7 e2 58.g8=Q e1=Q#
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2. White to play Play it out →Answer
23.Rg3 g5 24.hxg6
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3. Black to play Play it out →Answer
44...Bf4 45.Ra1 c2
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4. Black to play Play it out →Answer
57...b2 58.Rb6 Bb4 59.h7 b1=Q+
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5. White to play Play it out →Answer
17.Ne4 dxe4 18.Bxe3
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6. Black to play Play it out →Answer
46...Nd4 47.Rd6 Ne2+ 48.Kd1 c2+ 49.Kxe2 c1=Q
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7. White to play Play it out →Answer
33.Rc1 Re8 34.Qe7
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8. Black to play Play it out →Answer
22...Rc6 23.Bc7 Ra6+ 24.Ba5 Rxa5#
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9. White to play Play it out →Answer
25.Qh6 Rg8 26.Rh3 Rxg2+ 27.Kxg2
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10. Black to play Play it out →Answer
38...g4 39.f5+ Kg5 40.f6 Kxf6
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11. Black to play Play it out →Answer
53...h4 54.f5+ Kxf5
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12. White to play Play it out →Answer
23.Rh3 Be8 24.Qg7+ Rxg7 25.Nxf6+ Bh5 26.Rxh5+ Rh7 27.Rxh7#
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.