How to solve mate-in-N problems

Question

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).

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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.

Answer 1

Assuming this is a chess problem, then you want to start by looking at things that show up as problem themes, more than as game themes. There are a few salient features of the position:

• White's queen-bishop battery; it seems very likely that discovered checks from the bishop are likely to be a mating resource.
• The white bishop being on a line with the king, thus leaving it vulnerable to a pin from either the Ba7 or the Qa6.
• The open h-file, and in particular the possibility of a king-rook battery to deliver mate.
• More remotely, the possibilities for interference between the black pieces (e.g., bishop/rook interference on c5).

Given these, I would investigate the possibility of a move like Rh1; this offers up the threat of 2. Be3+ Kh5 3. Kg1 mate and forces black to defend immediately. The most natural defenses are via the aforementioned pinning moves, 1...Bb8 and 1...Qd6, so I'd start looking there.

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Assuming, OTOH, that the problem is a tactics puzzle more than a 'chess problem' problem, then I'll just point out that your analysis missed one particular bishop check, and you should consider the question of where the bishop can go that covers key squares in the vicinity of the king; not just for a mating net, but also as possible 'drop points' for the queen.

Answer 2

The other two answers give you a several good hints to solve the problem in your question, so I won't deal with that specifically. As for the heart of your question "What can I do to improve my ability to solve problems like this?", I might be able to offer a little help.

The first thing to note is that there is no way to really improve except to continue solving mate problems. The important thing here is that you will both learn (and continually improve on) a process that you can use to solve any position that you believe might contain a mate somewhere, and more importantly that you will be repeatedly exposed to different tactical and mating 'patterns' within each problem.

A good way of doing this is to work iteratively from the shorter puzzles to larger ones. Some people like to take pride in being able to solve puzzles with a large number of moves, but restrict themselves to the simpler varieties so as to avoid damaging their ego. In reality, there are many problems that are mates in 2 or 3 that can take a decent amount of concentration to properly solve, so there's no shame in looking at the shorter ones.

As a resource for doing this I recommend a book similar to Laszlo Polgár's Chess: 5334 Problems, Combinations and Games (ISBN 1579125549), which begins with several hundred Mate-in-1 puzzles before ramping up to mates in 2 and 3. The here is that you get a reasonable grounding in all of the basic patterns that occur in one-move mates, then two, three and so on. Even just solving the first section of this can benefit if you haven't done any serious training in this area before.

This is not exactly the sexiest way of improving your vision, as it does require some work, but it is also less demanding than it sounds, and should be something that sticks with you throughout your playing career.

Answer 3

I start off by looking at the king positions. White's King is well protected; Black's is not. Notice all the spots the Black K cannot go. Aim to take away all the safe spots.

If we chase the Black K around, what's the worst that can happen? That it escapes through the hole on f7. Preventing this is the entire point of the problem. The White Q is blocking that hole so I would not be inclined to move it. Then I looked at various discovered checks with the B. I saw Bh6+ but didn't see a lot more after that.

Then I noticed the Black K is in danger from the White pawns. So what happens if we let the pawns do the heavy lifting? Try that.

The Black Q and B shut down the White Rooks by controlling d3, d4, e2, and e3. How can we bring some heavy wood into the game? It would probably be helpful if we we able to place a R on d4, e4, or e5.

So, without giving the solution, that's my initial approach.

Answer 4

Basically it is "trial and error"!

Chess is all about analysis, and doing it in a proper way! That means not wasting time with things that go no where! This is the main difference between beginner and master level.

Especially for mate tactics what can help you to find your way through is to be acquainted with the most common mate patterns, which are pretty much clear in Mate in 1 or 2 positions, but not that much in Mate in 3 and 4 where the mate pattern needs to be built for the mate to happen. It could mean removing a defender, or reducing the scape area for the king placing a piece in a better position, etc... until you can apply the mate!

For your problem try to see what happens after Rh1... =]]

Here are some of the most common mate patterns. So what would be the mate pattern for your problem?

The more chess pattern positions, not only mates but also pins, fork, interference, etc... you have, the more quickly you will make good analysis of positions. You can achieve this by solving tactics in a daily manner. The habit to solve a minimum of 20 tactics a day has helped me to improve a lot in my chess lately.

I hope this might be of some help!

Answer 5

I think when you are looking for a mate, the answer lies in blocking out the escape route of opponent's King, in this case Kg6 is clearly something that white does not want. And since white Queen is the only piece that can guard that square you must look at other pieces for a tactical mate. Clearly the second thing then is trapping black King on h-file, which can only be done with white moving Rh1, which essentially are three moves: moving the pawn because you want to then move your king away from h-file and moving the rook. And since its a mate in four, the fourth move will definitely be a check.