Tactics
The royal fork
A fork that hits the king and the queen together. It is the most valuable version of the tactic because the reply is not a choice: check has to be answered, and the queen is still attacked when it has been. Usually a knight, occasionally a queen or a bishop, and almost always the end of the game.
How to spot it
Whenever an enemy king and queen sit within reach of each other, treat it as a standing weakness rather than a coincidence, and keep asking which square sees both. Sacrifices to *create* the geometry are worth calculating: giving up a rook to force the queen onto a forkable square is a good trade.
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
45...e1=N+ 46.Kf1 Nxd3
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2. Black to play Play it out →Answer
65...g1=N+ 66.Ke3 Nxf3 67.Kxf3 Kg1
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3. Black to play Play it out →Answer
35...Rxg4+ 36.Qxg4 Qxg4+
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4. White to play Play it out →Answer
34.Nb6+ Kb8 35.Nxd7+
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5. Black to play Play it out →Answer
18...Nf3+ 19.Ke2 Nxg5
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6. Black to play Play it out →Answer
28...Ne4+ 29.Kxe3 Nxd6
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7. Black to play Play it out →Answer
34...Bb4+ 35.Qxb4 Qxb4+
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8. Black to play Play it out →Answer
18...Nxf3+ 19.Bxf3 Qxd2 20.Bxd2 Bxf3
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9. White to play Play it out →Answer
47.Qxg8+ Qxg8 48.Nf6+ Kh8 49.Rxg8#
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10. Black to play Play it out →Answer
31...Bxf3+ 32.Qxf3 h3+ 33.Kf1 Qxf3
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11. White to play Play it out →Answer
25.Nxf6+ Kh8 26.Qxh6+ Bxh6 27.Rh7#
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12. White to play Play it out →Answer
31.Nxf6+ Rxf6 32.Qxe8+
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.