Here is a mate-in-4 I have been trying to solve:
[FEN "2r4r/b5pp/q3pp2/8/4QBk1/8/3R1PPK/4R3 w - - 0 1"]
(white mates in 4). I have been looking at it for about half an hour but not solved it. My question is: what can I do to improve my ability to solve problems like this?
(please don't just give the solution, I can easily find that by computer, but you can't use computers in a game).
Here is what I have tried so far.
Enumerating attacks and checks.
- White checks: Qf5+, Qg6+, Qf3+, Qxe6+, B-anywhere+, f3+
- White captures: Qxh7
- Black checks: none
- Black captures: Bxf2
Enumerating other ideas:
- Black can play Bxf2 or Qf1 which will cause havoc for a move , so probably the solution is checks on every move; at least the first two
- White has to be careful not to let BK run to g6 as then it can move to f7 escaping mate in 4
- In several variations below, Kh5 escapes with ...g5 or other pawn cover, so I am looking for tricks involving sacrificing rook to break that pawn cover.
Tree of analysis (have omitted some sub-variations that mate for brevity)
Be3+ Kh5; Rd5+ g5; ??? Bc7+ (or other B moves) Kh5; Rd5+ g5; ???? g4+ Kh4; ???? Qf3+ Kf5; Qh5+ (otherwise Kg6) g5; g4+ Kxf4; ???? Qf5+ or Qg6+ or Qxh7 don't go anywhere Qe6+ Kxf4; Re4+ Kg5; Rg4+ Kh6; ???? f3+ Kh5; g4+ Kh4; ???? Rd5+ g5; g4+ Kh6; ???? Rd3 Qxd3; Qxd3 Kxf4; no mate Re3 Bxe3; Bxe3 can't be better than 1.Be3 Rd5 exd5 Be3+: doesnt work g3: doesn't seem to do anything, Black can wait
Now I have looked at all the checks and some other interesting moves, none of them work, and so to solve the problem online I'd be reduced to just guessing random moves (and then probably being stumped on the resulting mate-in-3 for a while, as if I could solve that easily then I would have realized the first move by now).
But in a real game that is not possible; so where do I go from here?
Is there always a "key idea" to look for (and if so, how do I look) or sometimes do you just have to be able to brute force every possible move no matter how unlikely? I can't even think of any more candidates I haven't checked.