What makes a nonogram easy or hard

A bigger grid does mean more lines to track and more cross-checking, so large puzzles take longer. But length alone doesn't make a line hard — a 20-wide row with a single big run is trivial, while a short row packed with small runs and tight gaps can need real thought. Size affects how long a puzzle takes far more than how hard each step is.

The truest measure of difficulty is what kind of reasoning the puzzle demands. The easiest puzzles are "line-solvable": you can finish them by looking at one row or column at a time, filling whatever that single line forces, and never needing to hold two lines in your head at once. Most gentle puzzles are exactly this.

Harder puzzles need you to combine information — to notice that a square's state only becomes forced once you consider a row and a column together, or a small cluster of lines at once. The deeper that combination has to go before the next square is forced, the harder the puzzle feels, regardless of its size.

Here's the reassuring part. Academic work on nonogram solving (Batenburg and Kosters, 2012) measured how much reasoning uniquely-solvable puzzles actually require. Beyond simple line-by-line solving, the next step up is a well-defined, still-deterministic technique — combining pairs of lines — and their exhaustive enumeration found that 93.8–95.5% of the non-simple puzzles are solvable by exactly that, with no guessing at all.

Even more striking: only about 0.06–0.14% of all uniquely-solvable puzzles need anything beyond that pair-of-lines reasoning. In other words, the overwhelming majority of well-formed nonograms — including every hard one you'll meet in normal play — can be solved by pure, bounded logic. Genuine trial-and-error is vanishingly rare in a fair puzzle, which is why "never guess" is such reliable advice.

There is a theoretical result sitting underneath all of this. Deciding whether an arbitrary set of row and column clues has any solution at all was proven NP-complete (Ueda and Nagao, 1996) — the same complexity class as notoriously stubborn problems like the travelling salesman. In plain terms: nobody knows a method that solves every conceivable nonogram quickly, and in the worst cases the work needed explodes as the grid grows.

That sounds alarming until you notice the gap between "every conceivable nonogram" and "the nonograms people actually publish." The NP-completeness result is about arbitrary, adversarial clue sets — many of which have no solution, or several. A real puzzle is built the other way round: it starts from a picture, and it only gets published if it has exactly one solution that logic can actually reach. That's why the numbers in the previous section hold in practice, and why the puzzle in front of you is almost certainly fair, even when it feels brutal.

Beyond deduction depth, a couple of surface features nudge the difficulty. Very sparse pictures (mostly empty) and very dense ones (mostly filled) tend to be easier, because the extremes give lots of forced squares early. The trickiest puzzles usually sit in the middle, with a balanced mix of filled and empty and plenty of short, broken-up runs that resist the quick opening moves. A clean, recognizable subject also helps a solver stay oriented, even if it doesn't change the underlying logic.

On this site, a puzzle's rating comes from how deep its solving reasoning goes, combined with shape statistics like how filled the grid is. Line-solvable puzzles land in easy; ones that need real cross-line combination move toward hard; anything that would require guessing is rejected outright rather than published. The full pipeline is described on the "how we make our nonograms" page — but the short version is that difficulty here is measured, not guessed.