Corresponding squares

Advanced · 14 min

Pairs of squares for the two kings: whoever must move from a pair gives way. Find them and keep the move.

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The idea

Paired king squares: whoever must move from a pair gives way.

White’s king on b5 and Black’s on f3 are a step from a pair.
Kc5 loses: Ke4 leaves White to move in the pair.
Kc6 keeps c5 in reserve, so White reaches the pair with Black to move.

In a game: In a locked pawn ending, ask which king will have to give way, and spend a tempo to make it his.

How the lesson begins

Pawns on d4 and d5 block each other, so only the kings can move. A king that wins the other side’s pawn usually wins the game.

White’s king on c5 attacks the pawn on d5. Black’s king on e4 attacks the pawn on d4. Neither pawn can be taken, because the other king guards it. These two squares go together: they correspond.

Corresponding squares, step 1: White to move — White to move

It is White’s move, and White loses. Every king move leaves the pawn on d4 unguarded, and c4 is not allowed, because Black’s pawn on d5 controls it. Black’s king takes on d4.

So the player who must move from this pair gives way. That is what makes two squares correspond: when one king steps onto its square, the other king wants to answer on the partner square, so that the first king has to move away again.

Corresponding squares, step 2: White to move — White to move

Give the move to Black and the same thing happens to Black. All five of Black’s king moves leave the pawn on d5 unguarded, and White’s king takes it. It is the same pair of squares, and the side to move loses.

Corresponding squares, step 3: Black to move — Black to move

The pair also exists on the other side of the pawns: White’s king on e5 and Black’s king on c4. White to move loses here too.

Corresponding squares, step 4: White to move — White to move

A question

The same squares, but now it is Black’s move. Who wins?

Corresponding squares, step 5: Black to move — Black to move

White: Black has to leave the d5 pawn unguarded
Nobody: the position is a draw
Black, because Black’s king is next to White’s pawn

Show the answer

White: Black has to leave the d5 pawn unguarded.

Right. The side to move is the side in trouble, whichever colour it is.

In numbers

In the puzzle bank

795 puzzles in GreyChess’s bank practise it. Half of them are rated between 1,187 and 2,420.

The piece that makes the first move of the answer: king 57%, pawn 32%, rook 5%, bishop 3%, knight 2%, queen 1%, in puzzles from the Lichess puzzle database.