# Kakuro / Fillomino / Masyu / Yajilin / Hashiwokakero / Nurikabe / Slitherlink / Star Battle Puzzle Generator with Uniqueness Prover Deterministically seeded generator for eight Nikoli logic-puzzle families — each board is grown solution-first, rendered as puzzle + solution SVGs, and verified by an exhaustive backtracking solver that counts solutions to two, so “unique” is a proof (and an exhausted budget is reported as unproven, never guessed). > Canonical page: https://elysiatools.com/en/tools/kakuro-fillomino-masyu-yajilin-hashiwokakero-nurikabe-slitherlink-and-star-battle-puzzle-generator-with-uniqueness-prover - **Category:** Games - **Keywords:** kakuro, fillomino, masyu, yajilin, hashiwokakero, nurikabe, slitherlink, star battle, puzzle generator, uniqueness prover, nikoli, logic puzzle ## Overview Solvers (all exhaustive, never heuristic): Kakuro cell-by-cell with row/column sum bounds; Fillomino region placement over fixed polyominoes anchored in scan order (each tiling counted once; the checkerboard reveal guarantees completeness — every region of ≥2 cells contains a revealed clue); Masyu/Yajilin cycle enumeration (anchor edge-order dedupe, pearl/loop rules validated on exit); Hashiwokakero per-line 0/1/2 bridge backtracking with degree caps, precomputed crossings and final connectivity; Nurikabe region placement (each island holds exactly one matching clue, sea connected, no 2×2 pool); Slitherlink vertex-grouped edge backtracking with union-find cycle closure; Star Battle row-by-row star pairs. Difficulty = solver nodes (<2k easy, <30k medium, else hard). Uniqueness: counting stops at two solutions — count=1 without exhausting the budget is a proof of uniqueness; exhaustion is reported honestly as “unproven”. The same family + seed always regenerates the identical board. ## Inputs - **Puzzle family** (select) - **Seed (deterministic)** (number): 12345 - **Show solution SVG** (checkbox) ## When to use - When you need verified, unique Nikoli logic puzzles for print publications, web games, or competition sheets. - When you require deterministic puzzle reproduction using identical seed values across different sessions. - When you want objective difficulty ratings calculated from exact solver search node counts rather than heuristics. ## How it works - Select your target Nikoli puzzle family (such as Slitherlink, Star Battle, or Nurikabe) and input an integer seed. - The generator builds a valid solution-first board layout and minimises clues while preserving solvability. - An exhaustive backtracking solver searches for up to two valid solutions, proving uniqueness if exactly one solution exists before the search budget completes. - The tool outputs the difficulty rating, solver node count, proof status, and clean SVG visualisations for both the unsolved grid and the complete solution. ## Use cases - Publishing logic puzzle books and newspapers requiring high-resolution vector SVGs and verified single-solution grids. - Creating algorithmic benchmark boards and test suites for discrete constraint solvers and SAT engines. - Generating fair, seeded puzzle rounds with answer keys for competitive logic puzzle tournaments. ## Frequently asked questions ### Which puzzle families can be generated? The tool supports eight Nikoli families: Kakuro, Fillomino, Masyu, Yajilin, Hashiwokakero (Bridges), Nurikabe, Slitherlink, and Star Battle. ### How is puzzle uniqueness proven? An exhaustive backtracking solver counts solutions up to two. If exactly one solution is found without exceeding the node search budget, uniqueness is mathematically proven. ### What does an 'unproven' status mean? It means the solver reached its search node budget limit before confirming that no second solution exists, so uniqueness cannot be guaranteed. ### How is the puzzle difficulty determined? Difficulty is classified directly by search node count: under 2,000 nodes is Easy, under 30,000 nodes is Medium, and higher node counts are Hard. ### Can I reproduce the exact same puzzle later? Yes. 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