A valid line pattern is one complete filled/empty arrangement of a row or column that satisfies its clues and every currently confirmed cell state.
When simpler techniques stop producing deductions, reasoning over the surviving patterns gives a complete way to ask what the line still allows.
Example: filter a 2 2 line down to two patterns
Take a seven-cell line with clues 2 2. Suppose cell 3 is filled and cell 5 is empty:
??■?×??
Only two complete patterns satisfy all of those constraints:
.##..##
..##.##
Compare the two patterns cell by cell:
- cell 3 is filled in both;
- cells 6 and 7 are filled in both;
- cells 1 and 5 are empty in both;
- cells 2 and 4 differ.
Therefore cells 3, 6, and 7 are forced filled; cells 1 and 5 are forced empty; cells 2 and 4 remain unknown.
Forced cells are agreement across all valid patterns
This gives a precise definition:
a cell is forced when every valid line pattern gives it the same state.
If every pattern fills the cell, mark it filled.
If every pattern leaves it empty, mark it X.
If at least one pattern fills it and another leaves it empty, the line alone does not yet decide that cell.
How to construct valid patterns by hand
You rarely need to write every pattern for a large line. But the mental process is useful:
- place clue blocks in the required order;
- keep at least one empty cell between consecutive monochrome blocks;
- reject placements that cross confirmed X marks;
- reject placements that fail to cover confirmed filled cells;
- reject placements that leave a confirmed filled fragment uncovered by any clue block;
- compare what remains.
This is the general model behind exact fit, overlap, block reach, segment assignment, and placement bounds.
Simpler techniques are shortcuts over the same possibility space
Many familiar deductions can be understood as efficient ways to avoid explicit enumeration:
- exact fit → only one valid pattern;
- overlap → a block covers the same cells across its legal placements;
- unreachable cells → no valid pattern fills those cells;
- placement bounds → compact representation of where each ordered block can appear.
Pattern reasoning unifies them without replacing the faster techniques.
Why valid patterns matter on difficult lines
Extreme left/right placements can miss some deductions in complex partially solved lines. A full pattern check considers every arrangement compatible with the current state, not just two extremes.
Computer solvers often use specialized algorithms to obtain the same result without literally storing every pattern, because the number of combinations can grow quickly.
Worked example: four survivors still force six cell states
Take a 10-cell line with clues 3 2, with cell 2 filled, cell 5 empty, and cell 9 filled:
?■??×???■?
Only four complete patterns survive:
###....##.
###.....##
.###...##.
.###....##
Comparing them shows:
- cells 2, 3, and 9 are filled in all four;
- cells 5, 6, and 7 are empty in all four;
- cells 1, 4, 8, and 10 remain variable.
This is a useful reminder that a line does not need to be close to a single final arrangement before pattern comparison becomes valuable. Several possibilities can survive while still agreeing on many cells.
Pattern families can be more useful than individual patterns
On a large line, explicit enumeration may be impractical. You can often group patterns by a meaningful choice instead:
- which segment owns a clue;
- whether two fragments join or split;
- whether a block starts before or after an X-separated boundary;
- which of two clue identities covers a filled fragment.
Then compare the consequences shared by the entire family.
If every pattern in every surviving family fills a cell, the cell is forced. You do not need to write down thousands of arrangements one by one.
This family-based view is the bridge from complete one-line reasoning to multi-line case analysis.
Zero patterns is a diagnostic state
Pattern analysis does not only find forced cells. It can prove that the current line state is impossible.
If filtering leaves zero valid patterns, at least one confirmed mark feeding that line is wrong, or—inside a temporary branch—the tested assumption has created a contradiction.
That distinction matters:
- zero patterns on the real board → trace and repair an earlier unsupported mark;
- zero patterns inside a provisional branch → the branch is impossible and can be rejected.
Pattern counts can shrink suddenly
A crossing-line deduction may change one cell from unknown to X. That single mark can invalidate many line patterns at once.
After filtering, cells that previously varied may become identical across every surviving pattern, creating new forced states. Those states then affect perpendicular lines.
This is the bridge from line-pattern analysis to constraint propagation.
Step-by-step pattern reasoning
- focus on one unresolved line;
- generate or mentally test all clue-valid placements consistent with known cells;
- discard every pattern that violates even one confirmed state;
- compare the surviving patterns cell by cell;
- mark cells that agree in all patterns;
- leave cells that differ unresolved;
- propagate the new states across the grid.
Common mistakes
Keeping patterns that satisfy the clues but contradict known cells
A valid pattern must satisfy both the clue sequence and the current line state.
Forcing a cell because “most” patterns agree
Nonograms are deterministic logic puzzles. Majority vote is not proof. Every valid pattern must agree.
Treating two identical-length clues as interchangeable
Patterns preserve clue order and block identity.
Enumerating the whole puzzle instead of one line
This Guide is still line analysis. Whole-grid case reasoning belongs to contradiction and search-like techniques.
What to learn next
Once you understand line patterns, cross-line techniques become easier to formalize: a new cell state filters the valid patterns of the perpendicular line, which may force another cell, and so on.
FAQ
Do I need to list every pattern on paper?
Usually not. The concept is more important than the literal list. On short difficult segments, writing a few possibilities can be useful.
Is a cell forced if 9 out of 10 patterns fill it?
No. One surviving valid pattern with the opposite state is enough to keep that cell unresolved.
Can a line have no valid patterns?
Yes, but in a correctly played valid puzzle that means the current assumed/marked state is inconsistent. That idea becomes central to contradiction reasoning.