Why handle multiple runs matters
Reliable solvers cycle through proven operations instead of searching for a lucky square. In this lesson, the goal is to preserve run order and the required separators between groups. The standard is strict: a cell is filled or crossed only when every legal placement consistent with the visible clues agrees.
Keep the row clues and column clues active at the same time. A move justified in one direction changes the legal spaces in the other direction, which is why complete solving method becomes reliable only when you rescan the crossings.
- Name the clue or confirmed cell that supports the move.
- Distinguish a forced placement from one possible placement.
- Update crossing lines immediately after a confirmed mark.
Worked picture-logic example
Read the five-cell example before touching it. Add the run lengths and reserve one mandatory gap between same-color runs. Then compare the earliest and latest legal placements. Cells shared by every placement are safe fills; cells excluded by every placement are safe X marks.
The picture is not evidence by itself. Treat the emerging shape as a reward and a final error signal, while the numeric clues remain the proof for each individual cell.
A repeatable method
First, scan for exact fits and completed lines. Second, calculate overlap on the longest remaining run. Third, use confirmed X marks to split the line into segments and reject any segment shorter than its assigned run. Fourth, inspect every crossing changed by those decisions.
If no line changes, do not guess. Recount the clues, verify separators around completed runs, and choose the line with the least unused space. On larger boards, keep the same order while working one visible region at a time.
- Exact fit: clue space equals available segment space.
- Overlap: fill only the intersection of all placements.
- Fence: add X immediately before and after a completed run.
- Cross-check: rescan every perpendicular line touched by the move.
Mistakes to catch and a practice check
The most common error is extending a run because the emerging picture looks plausible. Another is forgetting that two separate same-color runs require at least one empty cell. A third is leaving a completed line unmarked, which hides useful constraints from its crossings.
Before moving on, point to one safe fill and one safe X in the example and say why each is forced. Then complete a 15×15 puzzle and use Check Answer only after every row and column clue appears satisfied. If a check fails, repair the first inconsistent line instead of clearing the whole board.