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Last Cell

Every row, column and region needs a queen. When one is down to a single open cell, the thinking is done.

In one line: A row, column or region has only one open cell left, so the queen goes there.

A cell is open until something rules it out: a queen in its row, column or region, a queen touching it, or a ✕ you’ve proved. Count the open cells of any row, column or region. When the count reaches one, that cell holds its queen.

Last Cell is the only move that places queens. Every other technique just adds ✕s, and those ✕s matter because they bring some area down to one cell. So after any deduction, ask again: what did that just squeeze down to one?

A new queen clears a lot at once: its row, its column, its region and the eight cells around it. That usually leaves another area with one cell, and the next queen follows.

Where to look: Wherever your last queen landed. Its fallout is where the next Last Cell usually is. On a fresh board, start with the smallest regions.

Worked example

A 6×6 board, 1 queen in. Each step below is the move the step-by-step solver makes from here: the easiest one available.

  1. 1. Where to look

    The blue region started with four cells. The queens and ✕s so far have ruled out three of them. Count what’s left.

  2. 2. The deduction

    The blue region has only one open cell left, so its queen must go there.

  3. 3. What it unlocks

    The new queen rules out its row, its column, its region and the cells touching it. That leaves the green region with one open cell: another Last Cell, at row 2, column 3.

Outlined: where to look. Green queen or red ✕: what that step proves. Gray ✕: already ruled out.

Practice

Each of these boards gets stuck without Last Cell. Hints, ✕s and auto-mark all work as usual.