Step 3 of 5

Corners are decided

A corner cell can only belong to a patch that has that corner as its own.

The rule of thumb: A corner cell has to be the corner of its patch, and usually only one clue can stretch that far.

Every cell needs a patch, and a corner cell is the neediest on the board: whatever covers it must start right there in the corner and stretch inward. So ask which clues could reach all the way to the corner without picking up a second clue on the way. Very often the answer is one clue — and the corner is decided, even while its patch still has shapes to choose from.

These practice boards each reach a moment where exactly one clue can cover a corner, and that clue sits at least two steps away — it had to stretch. The same thinking works along edges, and in the nooks that placed patches leave behind: any cell boxed in on two sides behaves like a corner.

Where to look: All four corners, early. For each one, list the clues that could stretch a rectangle there without swallowing another clue.

Worked example

A real position from a board built around Corners are decided. Purple: what the reasoning rests on. Dashed: the patch in question. Green: what it proves.

Row 1, column 1 (purple) is a corner, so whatever covers it must start in the corner and stretch inward. Only the clue at row 2, column 2 — 8, tall rectangle — can reach it without swallowing another clue or crossing a placed patch. The dashed patch is the one way it can.

So the corner belongs to that clue. It had 2 ways to go, but only this one reaches the corner, so the corner settled the patch too.

Practice it ↓