Skip to content
CoronetSuggest an idea (opens in a new tab)

Step 4 of 5

Pair Squeeze

Two regions, two rows, and no room left for anyone else.

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

Find two regions whose open cells all fit inside the same two rows. Each region needs a queen, so both of those rows’ queens go to these two regions. You don’t know which queen is in which row, and you don’t need to: both rows are spoken for, so every cell in them outside the two regions gets a ✕.

Neither region fits in one row on its own, so Region Squeeze can’t see it. It only works when you take the two together. It runs in every direction Region Squeeze does: two regions in two columns, or two rows whose open cells sit inside two regions.

Where to look: Two regions side by side across the same band of two rows or columns, often long thin ones, or two that ✕s have trimmed into the same band.

Worked example

A 7×7 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

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

  2. 2. The deduction

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

  3. 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 3. That’s a Last Cell, and the Pair 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 Pair Squeeze. Hints, ✕s and auto-mark all work as usual.