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Step 2 of 5

Region Squeeze

A region that fits in one row takes that row’s queen with it.

In one line: A region fits inside one row or column (or a line inside one region), so the rest of it is out.

Look at a region’s open cells. If they all sit in one row, the region’s queen is somewhere in that row, and a row only gets one queen. So the row is spoken for: every cell of it outside the region gets a ✕.

You don’t need to know which cell the queen takes, only which row it’s in. The same goes for columns, and it works in reverse too: if a row’s open cells all sit inside one region, the rest of that region gets ✕s.

Where to look: Thin regions: a strip lying along a row or standing in a column. Also regions that earlier ✕s have trimmed down. They often end up in one line even if they didn’t start in one.

Worked example

A 6×6 board, right at the start. Each step below is the move the step-by-step solver makes from here: the easiest one available.

  1. 1. Where to look

    The gray region has two open cells, and every one of them is in column 1.

  2. 2. The deduction

    Every open cell of the gray region sits in column 1, so column 1’s queen has to be the gray region’s, and no other cell in column 1 can hold a queen.

  3. 3. What it unlocks

    With those ✕s in, the purple region is down to one open cell, so its queen goes on row 2, column 2. That’s a Last Cell, and the Region Squeeze 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 Region Squeeze. Hints, ✕s and auto-mark all work as usual.