Edge solving
Runs have the least room to move at the edges of the grid, which makes the borders and corners the easiest places to force squares. Edge solving is the habit of always checking what the outermost rows and columns give you before hunting in the middle. This guide shows the two moves that come up most, and how to keep working inward. It assumes you're comfortable with runs, clues, and the overlap method.
Anchor a run to a filled edge
The strongest edge move: when the very first square of a line is known to be filled — often from a crossing clue in the perpendicular direction — the first run has nowhere to slide. It can't hang off the edge of the grid, so it must begin exactly there. Fill the whole first run from the edge, then mark the square immediately after it empty, because every run needs a gap behind it.
In the example below, the line's clue starts with 3 and the edge square is already filled. The run is pinned to squares 1-3, and square 4 is forced empty — three filled squares and one empty from a single known cell.
Filled edge anchors the first run
Given the edge square is filled and the first clue is 3: squares 1-3 are filled and square 4 (✕) must be empty.
An empty edge shrinks the line
The opposite is just as useful. When the edge square is known empty, that square is effectively removed from play, and the line becomes shorter by one. A run that gave you nothing on the full line can suddenly overlap once the line shrinks. This is edge solving and the overlap method working together.
Here, a run of 4 on a 6-wide line normally forces just two squares (2×4 − 6). But once the edge is known empty, the run lives in the remaining 5-square window — and 4 in 5 forces three squares, pushed inward from the border.
Empty edge + overlap
Given the edge square is empty (✕): the run of 4 now lives in a 5-square window, so it forces 3 squares inward — more than it would on the full line.
Corners are constrained twice
A corner square sits at the edge of both a row and a column, so it answers to two clues at once. That double constraint means corners resolve early: often the first square of a corner's row is forced by the row's clue and the column's clue independently, and whichever settles first hands the other line a filled or empty edge to anchor from. Whenever you're stuck, scan the four corners — they're the most over-determined squares on the board.
Work inward from the border
Edge solving isn't a one-time move; it's a direction. Every square an edge forces becomes a clue for the line one step inward. Fill the outer ring where you can, mark its empties, then treat the next row or column in as a fresh, slightly-more-constrained edge. Puzzles that look blank in the center are usually solved from the outside in.