Queen and king mate

The key idea

The queen locks in without giving check; the king finishes. And before every queen move, one check: does the enemy king have any square left? If it has none and it isn't check, that's stalemate.

Example 1 · Locking in without checks

The queen sets up a knight's move away from the enemy king and keeps taking away board, without giving a single check.

1. Qc3 Look at the queen's position relative to the king: a knight's move away. From there it cuts off ranks, files and diagonals all at once, without giving check. This placement does all the work.
2. Kd6 The king gives ground. It could move around its cage, but getting closer to the queen doesn't help: the cage is still the same.
3. Qc4 The queen repeats the trick: a knight's move away again. Every move like this shrinks the cage by a rank.
4. Kd7 Retreats again. It doesn't matter which square of its cage it goes to: you repeat the method.
5. Qc5 Third time. No rush and no checks: checks here would only get in the way.
6. Kd8 The king is already stepping on the last rank.
7. Qc6 And here THE QUEEN STOPS. The enemy king is on the edge: if you keep shrinking, you stalemate it. From now on, not one more queen move until your king arrives.
8. Ke7 The enemy king wanders through the two squares it has left.
9. Kd2 Phase two: the white king comes in. The queen holds the cage and the king crosses the board calmly. No rush: the position isn't going anywhere.

Example 2 · The finish (and the stalemate trap)

The white king has arrived. Notice the final detail: the queen mates right next to the enemy king, protected by yours.

1. Qg7+ Now yes: with your king alongside, the check pushes the enemy king to the last rank.
2. Kd8 Forced to the edge.
3. Kd6 Your king takes its post, one square from the enemy king. Stalemate check: the black king can go to e8 and c8 — it can breathe. Good, it still has moves.
4. Ke8 It moves through the squares it has left.
5. Qe7# Mate! The queen sits right next to the enemy king with yours defending it. This is the safe finish: queen adjacent and protected. If instead the queen had kept stripping squares from a distance, stalemate was one move away from ruining your game.

Practice

Your turn. The enemy king is already on the edge and your king is halfway there. Push with the queen, bring your king closer, and finish without stalemating.

1. Good: check on the last rank to hold the king in place while yours finishes arriving. Kd6 and Qg7 also win, even faster, but need a different continuation. To continue this line, play Qg8+.
2. Another push: the king goes back to the edge. Notice it still has squares — no stalemate at all. Qf7+ and Qh7+ win just as quickly, but need a different continuation. To continue this line, play Qg7+.
3. Your king takes its post facing the enemy king. The queen holds, the king comes along: everything's ready. This isn't a queen move now: bring your king one square closer, right opposite the enemy king.
4. Mate! On e7 or g8, the queen delivers the final blow and your king completes the mating net. And at no point did you strip the last square without check: zero stalemate scares. There are two mating finishes: Qe7# and Qg8#. Choose either one; your king protects the net.

Queen mate mastered, and the stalemate trap well learned. Half of the 'inexplicable' draws in this endgame come from exactly that: now you know how to dodge it.