Tactics
The attack on f7
At the start of a game f7 and f2 are defended by the king and by nothing else. Every quick disaster in the opening runs through one of those squares, which is why a bishop on c4 and a knight coming to g5 is the most common attacking setup in beginners' chess and stays dangerous long after.
How to spot it
Count the defenders of f7 before you count anything else. If the answer is only the king, look at every piece you have that can reach it and at what happens after the king takes: a king on f7 in an open position is usually lost, whatever the material count says afterwards.
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
9.Qxf7#
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2. White to play Play it out →Answer
13.Qxf7#
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3. White to play Play it out →Answer
10.Bxf7+ Kd8 11.Ne6#
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4. White to play Play it out →Answer
8.Bxf7#
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5. Black to play Play it out →Answer
20...Bxf2+ 21.Kd2 Qe3#
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6. White to play Play it out →Answer
9.Bxf7+ Ke7 10.Bg5#
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7. White to play Play it out →Answer
16.Bxf7+ Qxf7 17.Rxe5+
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8. White to play Play it out →Answer
8.Nxf7 Qe7 9.Nxh8
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9. Black to play Play it out →Answer
9...Nxf2 10.Qd2 Nxh1
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10. White to play Play it out →Answer
7.Nxf7 Kxf7 8.Bxg6+ hxg6 9.Qxd8
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11. White to play Play it out →Answer
8.Nxf7 Kxf7 9.Bxe6+
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12. White to play Play it out →Answer
12.Bxf7+ Kxf7 13.Nxg5+ Kg8 14.Qe6+ Bf7 15.Qxf7#
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.