Step 5 of 6

Count the rows down

Need minus placed equals open. When those numbers meet, the line decides itself.

The rule of thumb: Need minus placed equals open: a row whose remaining tents exactly fill its open clearings pitches them all; a met count grasses the rest.

The counts are arithmetic, and arithmetic is relentless. For any row or column: tents still needed is the number minus what’s placed, and the open clearings are what’s left to choose from. When needed equals open, every open clearing holds a tent. When placed already meets the number, everything left in the line is grass.

Count after every move, not just when stuck — each tent you pitch changes its row and its column at once, and a line that wasn’t closed a move ago may be closed now. These practice boards can’t be finished without the counting: remove it and the other techniques stall.

Where to look: Lines whose number sits close to their open-clearing count. Recheck the row and the column of every tent you pitch.

Worked example

A real position from a board that needs Count the rows down. Purple: what the reasoning rests on. Dashed: the cells in question. Green: what it proves.

Row 2 (its count is purple) already holds its 1 tent. The dashed cells are its clearings that are still open.

Row 2 already holds its 1 tent — the rest is grass.

Practice it ↓