Systematic ways to approach more difficult problems As I’m done solving easy puzzles (1000–1500), I decided to try some 1700 puzzles, but I’m finding it very hard to solve them as there are no obvious checks, captures and threats. Also, most of the times, the solution are about 5–7 moves. So, I figured that maybe a complete different approach is needed to solve these problems.
r1b2r1k/p1p3pp/2pp1q2/8/N1Q2n2/1P1N4/P1P2PPP/3RR2K b - - 0 1

For example for this one, I don’t even know where to begin. I solved easier problems by finding all the checks, captures and threats, and the solution used to come within few seconds, but now things are not that easy. So is there a systematic approach?
for example this one below,don't even know where to begin.Earlier the
way I solved problems was finding all the checks,captures and threats
and the solution used to come within few seconds but now things are
not that easy

&quot;Finding all the checks,captures and threats&quot; looks like a great way to solve the puzzle you've posted. There are no immediate checks but there are some good candidate captures and threats.
[fen &quot;r1b2r1k/p1p3pp/2pp1q2/8/N1Q2n2/1P1N4/P1P2PPP/3RR2K b - - 0 1&quot;]

1... Nxd3 2. Qxd3 Qxf2? 3. Rf1! (1...Be6? 2. Qxf4! Qxf4 3. Nxf4 Rxf4 4. Rxe6)(1...Nxg2 2. Kxg2 Bh3+ 3. Kxh3 Qf3+ 4. Kh4 g5+ 5. Kxg5 Rf5+ 6. Kh6 Qh5++)


Nxd3 is a capture which looks like it might win the f pawn and create back rank mating threats but white looks to be fine after recapturing with the c pawn when the white queen is still threatening the c6 pawn. If white recaptures with the queen then the f pawn is poisoned! It is met by the embarrassing Rf1. So, that doesn't work
The white queen is a little bit short of moves, but the threat Be6 is met by Qxf4 and at the end of the exchanges the bishop on e6 is hanging, so that doesn't work either. Finally -
The capture Nxg2 is a really promising looking sacrifice which is well and truly poisoned. Kxg2 is met by Bh3 and then Qf3+ with mate to follow soon. If white doesn't move the e1 rook then black is just winning a pawn and exchange plus the white king is very exposed. If white does move the e1 rook then Qf3 with the threat of Bh3 is going to be devastating.

So, &quot;checks, captures, threats&quot; does work. You just have to keep the analysis going for more than 2 or 3 moves and find two piece sacrifices as you hunt the king. The fun part of tactics!