A full line deduction finds a row or column whose clues use every available square. When the run lengths plus their mandatory gaps equal the line length, there is only one arrangement. You can fill every run and mark every separator without guessing. This is a useful first scan before tackling partial overlaps.
Add runs and mandatory separators
For a line with one positive clue, count the run length. For several positive clues, add all run lengths and one separator between each neighboring pair. Three runs need two mandatory separators; there is no mandatory empty square before the first run or after the last.
In a line of length L with k positive clues, the minimum required space is the sum of the clues plus k − 1. If this equals L, the line is an exact fit. If it is smaller, there is spare space and this full-line rule alone does not fix every square. If it exceeds L, check that you read the clues and line length correctly.
A five-cell row with clues 2, 2
This original example is a complete teaching line, not a fragment of today’s Daily puzzle. Two groups of two must fit inside five cells.
Clues: 2, 2 · Length: 5
- Add the filled runs: 2 + 2 = 4 cells.
- Count separators: two runs need one empty cell between them.
- Add the total: 4 + 1 = 5, exactly the row length.
- Fill cells 1 and 2, mark cell 3 empty, then fill cells 4 and 5.
- Recheck the five crossing columns. Each new cell constrains its column too.
An extra empty cell at either edge would leave too little room for the two runs. Moving the middle gap would break one of the runs. The equality forces both the filled cells and the separator.
Other exact fits
A five-cell line with clue 5 is filled from end to end. A seven-cell line with clues 1, 2, 2 fits as filled, empty, filled, filled, empty, filled, filled: five filled cells plus two separators use all seven positions. A zero clue is the separate all-empty case; do not treat it as a positive run in the formula.
Distinguish full lines from overlaps
Clue 3 in a five-cell line does not fill the entire row: the run can occupy cells 1–3, 2–4 or 3–5. Only cell 3 is common to all placements. That is an overlap deduction, not an exact fit. Do not fill the two edge cells just because the clue is large.
For multiple runs with spare space, the extra empty squares can appear at the edges or between runs. You need crossing information or other line reasoning to narrow their positions. Keep unknown cells distinct from confirmed empty marks.
Use completed lines to make progress
Scan rows and columns for exact fits before making detailed notes. Resolve those lines, then switch axes: a filled square or empty separator may determine part of a crossing line. Repeat until no new certain moves appear.
An empty mark divides the available space, but assigning clues to each side still needs proof. A five-cell open segment does not automatically receive clues 2, 2 just because those numbers appear somewhere in the row. Use the full-line calculation inside a segment only after establishing which complete runs belong there and that their boundaries are valid.
On Puzzuno, use Fill for proven filled squares and Mark Empty for proven gaps. Unknown empty cells are not marked automatically. The Nonogram How to Play guide explains these modes and how completion is checked.
Common mistakes
- Leaving out separators. Clues 2, 2 describe two groups, not one group of four.
- Adding compulsory gaps at both ends. Runs may touch the line edges.
- Marking all unused-looking cells empty before locating the runs. Spare space is not yet a proven gap.
- Applying the formula to a partial segment without establishing its clue assignment.
- Assuming a completed row settles every crossing column. Each column must satisfy its own full clue sequence.
Frequently asked questions
Does the rule work for columns?
Yes. Read their clues from top to bottom and use the column’s height instead of the row’s width.
What if the total is one cell short?
There is one extra empty cell to distribute. The line is not an exact fit. You may still find overlaps, but this rule does not establish the entire arrangement.
Does this depend on a unique puzzle solution?
No. The line’s arithmetic forces its arrangement in every solution consistent with those clues. It does not certify that the whole puzzle is unique.
Try an exact-fit scan
Start Nonogram and compare each line’s minimum required space with its length. Explain the gaps as well as the fills. Visit Daily Challenges for a shared puzzle; no current Daily solution is included here.