Reading the edges

When you open a fresh nonogram, the eye wants to land in the middle of the grid where the numbers are most interesting. Resist this. The cells worth looking at first are along the edges — top, bottom, left, right — because the edges constrain runs in a way the interior doesn't.

The reason is straightforward. A run of filled cells has two ends, and each end has to either touch a grid edge or sit next to an empty cell. The grid edge is, in effect, a free empty cell adjacent to the run. So a row that starts with a clue of 4 can either start at the leftmost cell — in which case cells 1 through 4 are filled — or start one or more cells in, in which case the leftmost cell is empty. You can't always tell which, but you can usually tell something.

Three patterns to look for, in order:

The first is a clue that fills a whole edge. A row of length 10 with clue 10 (or with a clue list summing to 10 plus the gaps required) is fully determined. So is a row of length 5 with clue 5. Sweep these first — they're free.

The second is a corner with a long opening clue. A row whose first clue is a 7 in a row of length 10 forces cells 4, 5, 6, and 7 by the overlap argument from line-solving fundamentals. If you also know cell 1 is empty (which often follows from the column clue at column 1), the run is pinned to start at cell 2 or later, and the rightmost cell of the run becomes more determined. Edges compound with their perpendicular neighbours.

The third is a single-clue row or column with a clue larger than half the line. Any clue greater than half the line length forces some cells in the middle, regardless of where the run sits. On a 10-line a single clue of 6 forces the middle four; a single clue of 9 forces eight of them, leaving just two cells of ambiguity at the start and end. These half-line-or-greater clues are the highest yield deductions in any nonogram and they often gather on the edges where lines pass through long single runs.

A useful sweep, before you settle in: read every clue list in order, top edge to bottom edge, left edge to right edge. For each, ask whether the line is fully determined, whether the leftmost or rightmost run reaches into the middle, and whether the largest single clue forces overlap. You'll typically come out of that sweep with a third of the grid resolved before you've made a single deductive move.