Tactics
The sacrifice
Giving up material for something worth more than material: a king dragged into the open, a line opened, a defender removed, mate. A real sacrifice is a calculation and not a mood. The positions below are the ones where the calculation ends well, which is the only kind that belongs in a puzzle.
How to spot it
Sacrifices become findable when you stop asking what is safe and start asking what is forcing. List every check and every capture, including the ones that lose a piece, and look at what the position is one move later. The clue is almost always an enemy king with few squares and few defenders near it.
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
16.Qxc6+ bxc6 17.Ba6#
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2. Black to play Play it out →Answer
35...Nxg3+ 36.hxg3 Rh5+ 37.Bh3 Rxh3#
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3. White to play Play it out →Answer
14.Qxc6+ bxc6 15.Ba6#
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4. Black to play Play it out →Answer
29...Qb1+ 30.Rxb1 Nc2#
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5. Black to play Play it out →Answer
30...Qxf2+ 31.Rxf2 Rc1+ 32.Rf1 Bc5+ 33.Re3 Bxe3+ 34.Kh1 Rxf1#
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6. Black to play Play it out →Answer
12...Qxc3+ 13.bxc3 Ba3#
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7. Black to play Play it out →Answer
28...Qxb1+ 29.Nxb1 Rc1+ 30.Bxc1 Rd1#
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8. Black to play Play it out →Answer
27...Bxg5 28.Qxg5 Qxh3 29.gxh3 Nf3+ 30.Kg2 Nxg5
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9. Black to play Play it out →Answer
22...Rxg3 23.hxg3 Rc6 24.Rf4 g5 25.Rh4 gxh4
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10. Black to play Play it out →Answer
14...Qxg1+ 15.Rxg1 Bg4#
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11. Black to play Play it out →Answer
17...Qe3+ 18.fxe3 Bh4+ 19.g3 Bxg3#
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12. White to play Play it out →Answer
30.Nf6 Nh6 31.Qg8+ Nxg8 32.Nf7#
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.