By difficulty
Intermediate puzzles
Three moves deep, and the first move often looks wrong. This is the band where sacrifices start being the answer and where the habit of checking your opponent's best reply rather than their likeliest one starts paying for itself.
How to spot it
When the forcing moves run out without a win, look at what your opponent is defending and with what. The answer at this level is very often a deflection, and the move that finds it is the one that attacks a defender rather than a target.
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
27...Nf3+ 28.Kh1 Qe1+ 29.Qg1 Qxg1#
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2. White to play Play it out →Answer
13.e5 Nbd7 14.exf6
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3. White to play Play it out →Answer
7.Bc3 Qd5 8.exf6
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4. White to play Play it out →Answer
18.Nf6+ Kh8 19.Nxh5
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5. Black to play Play it out →Answer
11...Qxe5 12.Nxe5 Bxd1
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6. White to play Play it out →Answer
27.Rxc3 dxc3 28.Rxd6
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7. White to play Play it out →Answer
11.Bxe5 Qxe5 12.Qxe5+ Bxe5 13.Re1 f6 14.f4 Kf7 15.fxe5
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8. White to play Play it out →Answer
10.Bf3 g5 11.Qh5+ Bf7 12.Qxf7+ Kxf7 13.Bxg2
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9. White to play Play it out →Answer
28.Rxf7+ Kxf7 29.Qxe5
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10. White to play Play it out →Answer
22.Qh7#
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11. White to play Play it out →Answer
25.Qh4+ Rh5 26.Qxh5#
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12. White to play Play it out →Answer
21.Nh6+ Kh8 22.Nxf5
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.