15×15 Nonogram Solver — Step-by-Step Solutions for Every Configuration
The 15×15 Nonogram Solver processes any valid 15×15 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 15x15 configurations.
How to Use the Solver
Step 1 — Enter your clues: Input the clue sequences for all 30 lines of your 15×15 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 225-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 15x15 solver, not to replace the solving experience.
How the 15×15 Solver Algorithm Works
Initialisation phase: For a 15×15 grid, the solver initialises 30 line constraint sets across 225 cells. At this scale, arrangement enumeration alone can produce sets of 50 or more valid configurations per line for moderate-slack clues. The solver applies progressive initialisation: lines are initialised in ascending clue-density order, and each initialised line's confirmed cells are immediately applied to all intersecting lines before those lines are initialised — reducing the arrangement sets of later-initialised lines using information from earlier ones.
Constraint propagation phase: The 30-line propagation network uses a band-structured queue: the 30 lines are organised into six bands of five lines each, and propagation processes bands in density order — highest-arrangement-count-reduction bands first. This band structure prevents information isolation between distant grid regions and ensures that cascade chains propagate efficiently across the full 225-cell grid.
Hypothesis resolution phase: For 15×15 hypothesis configurations, the solver implements a cascade-prediction scoring system: each candidate hypothesis cell receives a score based on the estimated cascade yield across the 30-line network under both assumption states. The highest-scoring cell is selected as the hypothesis target. This scoring system, calibrated against the specific arrangement distributions of the current constraint state, selects the optimal hypothesis target with high accuracy at 15×15 scale.
Accuracy and Reliability
The 15×15 solver is guaranteed to find the unique solution to any well-formed 15×15 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 15x15 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 15×15 Nonograms
Ready to put the solver's insights into practice? The 15×15 puzzles are available across all six difficulty levels:
→ 15×15 Easy → 15×15 Medium → 15×15 Hard