Line Weave: a matching row can still disagree with its columns
A five-by-five teaching puzzle makes a row’s local success visibly different from a board-wide solution, with a complete clue set you can reason through.
Worked examples use the Standard board unless a different size is stated. Hard and Expert may change the board dimensions or amount of information to track.
Read a highlighted clue as a local statement
Line Weave highlights a clue when the currently filled runs in that line match its numbers. That is useful feedback about the row or column you just changed. It does not mean the chosen squares are individually certified correct, because each also belongs to a crossing line that must be satisfied.
A row with clue 1 can highlight after you fill almost any one of its squares. The row has the required single run, but its columns may restrict that run to one particular position. Finishing a puzzle therefore means coordinating both directions, rather than collecting highlighted row labels as separate achievements.
Use a complete five-by-five teaching puzzle
Consider a separate example whose row clues, from top to bottom, are: 1; 3; 5; 3; 1. Its columns have exactly the same sequence from left to right. Each clue is a single run. The middle row must be entirely filled because its run of five occupies all five available squares.
The middle column must likewise be entirely filled. Now examine the first column, whose clue is 1. Its middle square is already filled by the completed middle row, so every other square in that column must be empty. The same reasoning applies to the last column. Those empty edge squares constrain the shorter runs elsewhere.
Find a row that looks right in the wrong place
Imagine that you had filled the top-left square while working only on the first row’s clue of 1. That row would appear locally complete. Once the centre row is filled, however, the first column contains filled squares in rows 1 and 3 with a gap between them. Its runs would be 1, 1, contradicting the column’s single clue of 1.
Clearing the top-left mark fixes that particular contradiction; it does not complete the first row. The filled middle column now shows where the first row’s one-square run belongs: column 3. This move is justified by both directions together, rather than by a preference for a symmetrical-looking outline.
Finish by checking ordered runs in both directions
The second row’s run of three cannot use its crossed-out edge squares, so it occupies columns 2 through 4. The fourth row follows the same constraints. Together with the top and bottom single squares in column 3, the completed rows are 00100 / 01110 / 11111 / 01110 / 00100, where 1 denotes filled and 0 denotes empty.
Verify each column independently instead of stopping at the completed rows. They produce the stated clue sequence too. Crosses can make that verification easier to follow, but unused empty squares may remain unmarked when all runs agree. On larger Hard and Expert boards, use the same habit at a smaller scale: after finishing one line, revisit the crossing clues affected by its marks. Undo reverses an experiment without declaring any line permanently solved. Changing one square can affect two clue highlights, so inspect both after an experiment.
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