Tactics
The relative pin
A relative pin has something valuable behind the pinned piece rather than the king, so moving it is legal and usually terrible. This is the more interesting of the two, precisely because it can be broken: a defender who is willing to give up what is behind, or who finds a big enough counter-threat, walks out of it.
How to spot it
The same scan as any pin, along your sliders' lines, but the judgement is different. Work out what moving the pinned piece would actually cost them, and then whether it costs them less than leaving it. A relative pin is worth attacking a second time rather than relying on.
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
34.Rxg3 Qxg3 35.Nxg3
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2. White to play Play it out →Answer
29.Nxe6+ Kg8 30.Qxe5
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3. White to play Play it out →Answer
31.Qxc5+ b6 32.Qc7+ Bb7 33.Rxa8+ Kxa8 34.Re8+ Ka7 35.Qb8#
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4. White to play Play it out →Answer
30.Rxg6+ hxg6 31.Qxh8#
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5. Black to play Play it out →Answer
34...Rxc2+ 35.Kxc2 Ba4+ 36.b3 Bxb3+ 37.Kxb3 Qxd1+
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6. Black to play Play it out →Answer
35...Rg8 36.Rc3 Rxg5+
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7. Black to play Play it out →Answer
19...Bxf3 20.Bxf3 Rxg3+ 21.Bg2 Rag8
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8. White to play Play it out →Answer
8.Bxf6 Qxf6 9.d5 exd5 10.exd5 Bd7 11.dxc6
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9. Black to play Play it out →Answer
32...Qxg6+ 33.Qg5 Rxe6 34.Qxg6 Rxg6+
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10. White to play Play it out →Answer
14.Qxe5 Kf7 15.Qxc5
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11. Black to play Play it out →Answer
30...Qxe4 31.fxe4 Bxd4
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12. White to play Play it out →Answer
24.Ng5 fxg5 25.Rxg5
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.