Today I encountered this puzzle: https://lichess.org/training/Q941O
The solution is really non-obvious to me, even after looking at the engine lines.
Let me walk you through my thought process:
My first step for trying to solve puzzles is to come up with candidate moves. In this case I came up with:
1. Nf6
2. Rxf7
3. Rf6
The first case can be ruled out almost instantly because after Nf6 Kg7 there is just no threat. The second Case is also no good because after Rxf7 Rxf7 Qxf7 there is Qg7 which holds everything together for Black. This leaves Rf6. The most natural continuation that I see is Qxd5. Here my instinct is to play either Rxh6 or Qxh6 both have no forced checkmating sequence. After Qxh6 Kg8 white is supposed to play Rbf1 a natural looking move but at this point I can't really calculate the lines anymore, because there are so many possibilities. My gut feeling says white should be better, but black still has the material advantage. In case of Rxh6 Kg7 further checks lead to the King escaping. Here it is also essential to play Rf1 to stop the King from escaping.
The bottom line is: I guess I just didn't see the quiet move Rbf1 in the middle of calculation. Is there a Trick to seeing those kinds of moves? In hindsight it looks like a natural move in a game, but inside a puzzle this move seems really hard to spot. Has anybody any tips?
It is experience.
It is also logic: when you cannot checkmate with two pieces, then bring a third.
Many great attacking games have quiet moves between sacrifices.
The material advantage has no meaning as long as the king gets checkmated.
As you solve some more difficult puzzles, the solution quite often involves moving your seemingly worse piece into the action. Piece development is not just an opening paradigm
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