Cross-referencing: let rows and columns feed each other

The loop

Pick a line and settle everything it can settle. Then look at the lines that cross the squares you just changed. Each new box or cross is a fact about two lines at once, and the second line may have been stuck until now.

The loop is simply: row, column, row, column. A square never stays unknown for lack of cleverness. It stays unknown because the line that could settle it has not yet seen the fact that unlocks it.

A good order

Start with the biggest clues and with lines that already hold several boxes, because they change the most. After each deduction, go to the crossing lines before you pick a new row. Finish a sweep by checking every line once more, since late crosses often rescue a line that was dull on the first pass.

The practice grid below is chosen so that rows alone never finish it, and neither do columns alone. It takes several full sweeps of rows and columns.

The move in three steps

1. Settle one line. Use any technique on a single row or column until it yields nothing more.
2. Switch direction. Move to the lines that cross the squares you just changed.
3. Sweep again. When you run out, check every line once more, because earlier crosses may have changed it.

Worked example: one fact travels

In a five by five grid, row 3 has the clue 5. It fills the whole row at once. Now every column has a box on its third square.

Every column now has a known box on its third square, which is exactly the kind of fact that glue and mercury need. That is the loop: a result in one row becomes a fact in five columns, and each of those can feed a new row.

Common slip. Staying on one row hoping for more. If a line has stopped yielding, leave it and let the crossing lines change it.