Many puzzles can be solved by considering only one row or column at a time. Certain cells in that row/column can be inferred to be filled or empty. The effect of completing those cells on other rows/columns is then considered. This is repeated until the puzzle is complete.
Below are some methods that can be applied to single rows/columns.
See A1. Word Meanings for the meanings of italicised words
In the examples below the colours have the following meanings:
Grey - unsolved
Solid blue -filled
Solid yellow - empty
Translucent red - leftmost possibility of block
Translucent blue - rightmost possibility of block
Purple - overlap of leftmost and rightmost possibilities - cells that can be inferred as filled
If the freedom in a region is less than the length of one or more of the blocks known to be confined to that region then (length - freedom) cells in the centre of the range of that block must be filled. These are the cells where the block overlaps with itself when placed at the two extremes of its range.
result ...
result ...
When a block has been associated with a particular range of filled cells, then those cells that out of range of any block can be marked as empty. This most often applies to the first and last blocks.
If a known filled cell occurs at or near the edge of a region, within range of the first block in that region, then further cells may be filled in. This can be employed in either direction.
If the unassigned space between two empty cells is smaller than any unassigned block then that space can be filled with empty cells.
The same logic can sometimes allow blocks to be allocated to specific regions, which may allow some cells to be filled in using the "fixed cells" or "edge effects" logic shown above
If there is a group of filled cells that is longer than a certain block, that block cannot overlap (or adjoin) these cells and this limits the range of that block. This may allow cells to be filled.
If there is a single cell gap between two filled cells and filling it would result in a block longer than any possible block, then the gap can be marked empty. If the blocks on either side can be identified then they can then be completed.