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Step 3 of 5

No Room

Before a queen goes anywhere, check who it would leave stranded.

In one line: A queen on a cell would wipe out every open cell of some area, so that cell is out.

Pick an open cell and imagine a queen on it. It would rule out its row, its column, its region and the eight cells around it. If that wipes out every open cell of some other row, column or region, that area would have nowhere left for its queen. So the cell can’t hold a queen: ✕ it.

This is a thought experiment, not a guess. You never put the queen down. You prove it can’t go there and move on.

The usual case is a region with two or three open cells left, close together. A cell that touches all of them, or shares a row or column with all of them, would block the whole region.

Where to look: Regions down to two or three open cells. Check the cells around them, and along any row or column they all share.

Worked example

A 6×6 board, some ✕s in, no queens yet. Each step below is the move the step-by-step solver makes from here: the easiest one available.

  1. 1. Where to look

    Row 5 is down to two open cells. Now imagine a queen on row 6, column 3, and check what it would see.

  2. 2. The deduction

    A queen on the marked cell would rule out every open cell of row 5, leaving it no place for its queen.

  3. 3. What it unlocks

    With that ✕ in, row 6 is down to one open cell, so its queen goes on row 6, column 4. That’s a Last Cell, and the No Room step is what opened it up.

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

Practice

Each of these boards gets stuck without No Room. Hints, ✕s and auto-mark all work as usual.