Groups and crossingsTough boards

Aligned pair exclusion

Take two squares that see each other and list the ways they could be filled together. A pair that would leave a third square with nothing is ruled out, and a number no surviving pair uses goes.

The pairSquares they both seeLoses a pencil mark

Why it works

The two squares hold two numbers between them. Any pair that takes both of a neighbour's last options is impossible, so only the pairs that leave every neighbour something survive.

How to spot one

Look for two squares that see each other, each with few options, beside two-option squares that see them both. List the pairs; there are fewer than it sounds.

What it gives you

One removal, usually. It comes after the shapes, because it means listing combinations rather than spotting one.

Practise Aligned pair exclusion

Boards that need it, with the owl's hints when you're stuck.

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