Edge & Endpoint Deduction
Beginner technique
Edge deduction exploits the boundaries of a line — the left/top edge and right/bottom edge — to constrain runs that are close to those boundaries. It's particularly useful when a filled cell appears near a corner of the grid.
The left-edge rule
If the first unknown cell in a line is filled (or if the first cell is filled), that filled cell must belong to the first clue run. You can therefore extend the run rightward up to the clue's length, and mark the cell immediately after the run as empty.
Example: Line starts with a filled cell. Clue is 3 2. The first run is length 3, so cells 1–3 must all be filled, and cell 4 must be empty.
The right-edge rule
Symmetrically, if the last cell in a line is filled, it must belong to the last clue run. Extend leftward by the run's length and mark the preceding cell empty.
When the first run is fully determined
If you can determine the exact extent of the first (or last) run — either because it starts at the edge or because an empty cell caps it — remove that run from the clue and solve the remaining line recursively with the remaining clues.
Boundary interaction with overlap
Edge deduction combines naturally with simple overlap: if overlap places a filled cell adjacent to the grid edge, the edge rule can immediately determine the full extent of that run.
Common application
Look for rows or columns where the first clue run is large relative to the line. A clue of 8 1 in a 12-cell row has so little slack for the first run (4 slack total, but once you account for the separator and second run, the first run's slack is only 1) that overlap combined with edge rules will fill most of it immediately.