▢Strategy · Nonogram
Solve Nonogram with logic, not guessing
Four constraint-propagation rules solve every 5×5 Nonogram without guesswork: the overlap rule, edge constraints, immediate X-marking, and iterative propagation.
The overlap rule
This is the foundation of every Nonogram solve. Apply it once to every row and column before doing anything else. Even on a 5×5, the overlap rule usually fills 30-50% of the board immediately.
The rule generalizes to multi-clue rows: a row of 5 with clues “2 1” needs at least 4 cells (2 + gap + 1), so the guaranteed overlap is 4×2-5 = 3 cells across the placement variations.
Edge constraints
The simplest constraints are the strongest:
- Clue equals row length: every cell filled.
- Clue equals 0: every cell empty (mark all with X).
- Clue starts with a filled cell at edge: if you know a filled cell is at position 1, and the first clue is 3, then positions 1-3 are all filled.
X-out empties immediately
The Mark toggle exists because the human brain forgets. If you've determined a cell must be empty, X it now. Otherwise you'll second-guess later and burn a mistake on it.
X-marks aren't a hint or a crutch — they're a notation system. Players who don't use them solve slower and make more mistakes.
Constraint propagation
Each filled or X-marked cell constrains the intersecting row and column. After filling overlap-rule cells, cycle through rows and columns again — newly-constrained rows often reveal more cells that the first pass missed.
Most 5×5 Nonograms solve in 2-3 propagation passes. If you're on pass 4 and stuck, re-check whether you missed an overlap-rule application somewhere.
A Nonogram never requires a guess. If you're guessing, you're missing a constraint somewhere.
— PuzzleDaily editorial
FAQ
What's the most important Nonogram rule?
The overlap rule: if a single clue requires N filled cells in a row of M cells, the middle 2N-M cells must always be filled regardless of position. For a row of 5 with a clue of 4, cells 2, 3, 4 are guaranteed filled (4+4-5=3 guaranteed). This rule is the foundation of every other Nonogram technique.
When should I use the Mark mode?
As soon as you know a cell must be empty. The Mark (X) prevents you from accidentally filling that cell later and lets you focus on the remaining unknowns. Players who don't use Mark mode lose track of which cells they've ruled out and double-back on already-determined logic.
Why am I making mistakes on the Nonogram?
Most mistakes come from skipping the overlap rule and guessing. If you find yourself unsure, stop and apply the rule to every row and column. Determined cells reveal themselves systematically without needing intuition.