No other language version is available for this page.
No — and the failure rate is measurable. Solving arbitrary nonograms is NP-complete (Ueda & Nagao, 1996), so no rule can crack every board without search. In our own measurement (400 random boards per size at typical 48–62% fill density, August 2026), the share solvable by pure row-and-column reasoning falls steadily with size: 81% at 5×5, 70% at 10×10, 49% at 15×15 and 43% at 20×20. On large grids, the majority of random boards force a guess — which is why unverified puzzle sites keep serving boards that feel "broken." Guess-free nonograms exist, but they must be constructed and verified, board by board.
| Grid size | Random boards tested | Solvable by line logic alone |
|---|---|---|
| 5×5 | 400 | 81.0% |
| 10×10 | 400 | 70.5% |
| 15×15 | 400 | 49.0% |
| 20×20 | 150 | 43.3% |
Method: uniformly random fills at 48–62% density; a board counts as line-solvable when iterating row/column constraint intersection to a fixpoint completes the grid with no search. Deterministic seeds; reproducible with the open generator.
Many sites advertise "unique solution" — a weaker guarantee than most players realize. A board can have exactly one solution that still requires bifurcation (try a cell, follow consequences, backtrack) to find. Line-solvability implies uniqueness; the reverse does not hold. If the property you care about is never having to guess, uniqueness is the wrong thing to verify.
Generate candidate boards, run the line-logic fixpoint, and discard every board it cannot finish — at 15×15 that means throwing away roughly half of all candidates. Every daily nonogram on this site passes that filter before publication, and the same standard applies to the 100 nonograms in Gridlings-Bench, our open LLM reasoning benchmark. The check is machine-run and reproducible, which makes "no guessing" a verifiable property of each board rather than a marketing line.
No. Solving arbitrary nonograms is NP-complete (Ueda & Nagao, 1996), and in our measurement most large random boards cannot be completed by line logic alone — only 43% of random 20×20 boards pass. Guess-free nonograms exist, but they must be constructed and verified, not assumed.
Because the puzzle was published without checking line-solvability. At typical fill densities our solver found 19% of random 5×5 boards, 30% of 10×10, 51% of 15×15 and 57% of 20×20 boards stall under pure row/column reasoning — the larger the grid, the more likely a random board forces a guess.
Generate with a solver in the loop: propagate row and column constraints to a fixpoint, and publish the board only if that process alone completes the grid. Every daily nonogram on this site passes that check before publication, which is a verifiable property, not a promise.
No — uniqueness is weaker than guess-freedom. A board can have exactly one solution that still requires trial-and-error search to find. Line-solvability implies uniqueness, but not the reverse; that is why we verify line-solvability directly.