Step 5 of 5

Triple Squeeze

Three regions, three rows. This one takes counting.

In one line: Three regions fit inside three rows or columns (or the reverse), so the rest of those lines is out.

The same squeeze, one size up. If three regions’ open cells all fit inside the same three rows, those regions take all three of those rows’ queens, and every other cell in the three rows gets a ✕. Columns work the same way, and so does the reverse (three rows whose open cells sit inside three regions).

It’s easy to miss because no single region, and no pair, fits on its own. Each region can spread across two or three of the rows. Only the count, three regions inside three rows, gives it away.

Where to look: When nothing else works, pick a band of three rows or columns and list the regions that sit entirely inside it. If there are exactly three, you’ve found one. Bands along the edges are a good place to start.

Worked example

A 8×8 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. Where to look

Take the red region (three open cells), the yellow region (two open cells) and the pink region (three open cells). Between them, those three regions have open cells only in rows 6, 7 and 8.

2. The deduction

The red, yellow and pink regions only have open cells in rows 6, 7 and 8, so those three regions use up all three of those queens, and no other cell in rows 6, 7 and 8 can hold a queen.

3. What it unlocks

With those ✕s in, the gray region is down to one open cell, so its queen goes on row 5, column 6. That’s a Last Cell, and the Triple 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 Triple Squeeze. Hints, ✕s and auto-mark all work as usual.