4×4

This small puzzle is a great opportunity to learn how to analyze properly when approaching a chess problem.

Let’s begin by noticing something simple but important: the ♚ is currently blocked from every direction — and that’s usually a good starting point when you’re aiming for a checkmate position.

It’s also useful to note what we don’t care much about (to get used to ignoring misleading directions 🙂).
For example: there’s a threatened ♜ here — but that doesn’t help White. This isn’t a long endgame where we try to gain advantage by trading pieces.
There’s also a threatened ♖ — but that’s not a reason to rush and “save” it. On the contrary, in artistic problems, sacrificing valuable pieces often makes the solution more elegant.
_{(OK, Still, we don’t dismiss ideas too quickly — so let’s check: what if the ♗ captures the ♜?
If the ♚ takes back, then ♖e8 is mate — but any other Black move is enough to delay defeat.
What about moving the ♖ from e6 to safety? After such a move, even with Black’s full cooperation, there’s no mate on the second move.)}

Now, let’s try imagining a similar but checkmate position:
If only the ♖ currently on h2 were on the left half of the 8th rank — that would be mate! And it could even get there in just two moves. That same mate would still work even if all other White pieces disappeared (except the ♔, of course).

So… did we just find the solution?

Before explaining why not, let’s learn another neat thinking trick used in such puzzles:
If we trust the composer, there must be one unique solution — only one first move that works.

If we try to bring the ♖ from h2 to the left side of the 8th rank, there are three possible starting squares that look equally good (a2, b2, or c2).
But since three different “solutions” can’t exist, we’ll have to keep thinking.

What actually saves Black from this simple plan (and also saves the puzzle from being boring — admit you’d be disappointed by such ending😉)?
The answer is a black ♟ move that opens an escape square for the ♚.

So now we notice that any ♟ advance can be problematic for White.
That means we might look for a sequence where a ♟ moves forward — and still, there’s a mate after that.
For instance: ♖f2 (or ♖h5), then ♟f5, and finally ♖xf5#.
But we’ve already learned that Black isn’t supposed to cooperate.

So what’s left?

Here’s one more powerful idea that expert solvers often use to crack tough mate-in-two problems:
find a strong default move for Black — a move you can assume he’ll play, to test your candidate ideas.
Such a move helps eliminate many wrong lines quickly — and often points straight toward the winning key.

In this position, that move is advancing the ♟ from g7, freeing the ♚ to move there.
After that move, there’s no mate in two!
So the key must prevent that move — and that’s how we finally arrive at the winning idea.

From there, you can explore each Black move and enjoy the beauty of the composition.