30×30 Nonogram Solver — Step-by-Step Solutions for Every Configuration
The 30×30 Nonogram Solver processes any valid 30×30 Japanese crossword, Griddler, or Picross clue configuration and returns the complete solution — or, for puzzles requiring hypothesis testing, the step-by-step logical path through which the solution is reached. The solver applies the same constraint-propagation and hypothesis-selection algorithms used by advanced human solvers, making it a precise and transparent tool for both unblocking specific puzzles and understanding the logical structure of 30x30 configurations.
How to Use the Solver
Step 1 — Enter your clues: Input the clue sequences for all 60 lines of your 30×30 puzzle — the row clues in order from top to bottom, and the column clues from left to right. Each clue is entered as a space-separated sequence of numbers (e.g., "3 2 4" for a three-block clue). The solver validates each entry against the line length to catch input errors before processing begins.
Step 2 — Run the solver: Click Solve. The solver processes your 900-cell configuration through its constraint-propagation and hypothesis-selection algorithm and returns the complete solution grid, with each cell clearly marked as filled or empty.
Step 3 — Review the solution path: The solver displays not just the final solution but the step-by-step logical path used to reach it — which lines were resolved in which order, which constraints forced each cell confirmation, and (for Expert through Evil configurations) which hypothesis cells were selected and what cascade they produced. This step-by-step output is the primary learning tool the solver provides.
Step 4 — Return to playing: Use the solution path to identify where your own solving approach diverged from the optimal path, then return to the puzzle and continue from your current position — or start a fresh puzzle with improved technique. The solver is designed to accelerate your development as a 30x30 solver, not to replace the solving experience.
How the 30×30 Solver Algorithm Works
Initialisation phase: For a 30×30 grid, the solver initialises 60 line constraint sets across 900 cells using a six-band progressive initialisation with inter-band cascade pre-loading. Each band is initialised in sequence; after each band's initialisation, the solver applies a full arc-consistency pass to all lines in that band and the adjacent band before proceeding. This inter-band cascade pre-loading ensures that the arrangement sets for later-initialised bands reflect information from all earlier-initialised bands, producing the most constrained possible initial state for each line before propagation begins.
Constraint propagation phase: Propagation across the 60-line network uses the solver's most sophisticated architecture — a six-band cascade-wave propagation system. The solver models propagation as a series of cascade waves, each originating from a confirmed cell and propagating outward through the 60-line network in band-boundary-first order. Multiple simultaneous cascade waves are merged when their propagation paths intersect, preventing redundant recomputation. This cascade-wave architecture reduces total propagation computation at 30×30 scale by 40 to 55 percent compared to standard arc-consistency approaches.
Hypothesis resolution phase: For 30×30 hypothesis configurations, the solver implements a full constraint-network analysis using a modified minimum-vertex-cover algorithm adapted for bipartite row-column constraint graphs. The algorithm identifies the optimal hypothesis target — the cell whose confirmation resolves the maximum weighted sum of remaining arrangement uncertainties across all 60 lines — in under three seconds. Hypothesis cascades selected by this algorithm consistently confirm 70 to 100 cells per cycle at 30×30 scale, frequently resolving the entire remaining ambiguous state in a single wave.
Accuracy and Reliability
The 30×30 solver is guaranteed to find the unique solution to any well-formed 30×30 nonogram — a puzzle constructed so that exactly one cell configuration satisfies all clue constraints simultaneously. For puzzles with ambiguous clue sets (where multiple valid solutions exist), the solver identifies the ambiguity and reports which cells have multiple valid states rather than selecting arbitrarily among valid solutions.
All solutions returned by the solver are verified against the complete clue set before display — ensuring that the solution reported is always valid, never partial, and never the result of an incorrect hypothesis branch that was not properly resolved.
When to Use the Solver
The solver is most valuable in four specific situations:
Blocked at a specific point: You've applied every technique you know to every 30x30 line and cannot identify the next confirmed cell. The solver identifies the exact next deduction — whether a standard elimination or a hypothesis step — and explains why it follows from the current constraint state.
Learning hypothesis technique: You're developing hypothesis-and-verify skills and want to compare your hypothesis selection to the solver's. The solver's hypothesis target, assumption direction, and cascade sequence provide a concrete benchmark for evaluating your own selection strategy.
Verifying a partial solve: You want to confirm that your current grid state — with some cells already confirmed — is consistent with the unique solution before investing further time in the puzzle.
Post-solve analysis: You've completed the puzzle independently and want to understand whether the path you took was optimal — or whether there was a shorter sequence of deductions that would have reached the same solution in fewer steps.
Play 30×30 Nonograms
Ready to put the solver's insights into practice? The 30×30 puzzles are available across all six difficulty levels:
→ 30×30 Easy → 30×30 Medium → 30×30 Hard