Skip to content
Lizely

Nurikabe

Solve a compact, uniquely determined Nurikabe board with explicit wall, island, and unknown marks, complete keyboard support, and mechanically verified rules.

Privacy: your files never leave your device. All processing happens locally in your browser.

How to use

  1. 1.Tap a non-clue cell to cycle unknown, wall, and island, or use the dedicated mark buttons; numbered cells remain fixed islands.
  2. 2.Make each orthogonal white island contain exactly one clue with matching area, connect every black wall cell, and avoid every solid 2 by 2 black block.
  3. 3.Mark all 16 cells before checking; an incomplete check costs nothing, the first wrong full board can be repaired, and the unique solution earns exactly 1,000 points.

About Nurikabe

Nurikabe is a grid-partition logic puzzle built from numbered white islands and a surrounding black wall. Each white island must contain exactly one number, and the island must contain exactly as many orthogonally connected cells as that number. All black cells must belong to one orthogonally connected wall, while no two-by-two square may be completely black. Islands that touch only at a corner remain separate because diagonal contact does not create a connection. Together, these compact rules turn every mark into a question about local area and global connectivity.

This version presents one fixed 4 by 4 board authored specifically for Lizely. Its clues are 2 in the upper-left corner, 1 in the second row and third column, and 5 in the third row and fourth column. Those clue values total eight, so the finished board has eight white island cells and eight black wall cells. The fixture is not presented as an official Nikoli board, a Conceptis board, a historical puzzle, or a copied newspaper challenge. Nikoli and Conceptis are cited only for the standard rule definitions. The clue placement, completed grid, interaction model, score, and mistake policy are original product fixtures.

To play with a mouse or touchscreen, tap an open cell to cycle it from unknown to wall, from wall to island, and from island back to unknown. Numbered cells are fixed white island cells and cannot be changed. Dedicated Wall, Island, and Clear controls make correction easier when cycling would be inconvenient. The board always shows each state explicitly: black fill means wall, a light cell with a centered dot means island, and a blank light cell remains unknown. This avoids relying on color alone in accessible names and in automated browser checks.

Keyboard play covers the complete interaction. Use the Arrow keys to move the visible cursor through the four-by-four grid. Press W or Space to mark the current non-clue cell as wall, I to mark it as island, and Delete or Backspace to return it to unknown. Press Enter to check the board. The shared double-Escape gesture opens the spreadsheet-style boss screen and the same gesture returns to the puzzle. Restart clears every non-clue mark, restores the three fixed clues, returns the cursor to the first editable cell, and resets score and mistakes.

Check board deliberately distinguishes incomplete work from a finished attempt. If any editable cell is still unknown, the game asks you to continue and records no mistake. Once all cells are explicitly wall or island, the validator applies every published Nurikabe rule. A wrong full board records one mistake but remains editable, so the first complete error can be diagnosed and repaired. A second wrong full check deadlocks the run until Restart. A correct full check awards exactly 1,000 points. Completion and deadlock are terminal states: board taps, mark buttons, keyboard marks, cursor moves, and later checks cannot alter the frozen result.

Runtime validation does not compare the board with a hidden bitmap. It builds orthogonal components from the cells marked island and confirms that each component contains exactly one clue whose value equals the component's size. Because components are defined through shared edges, different valid islands cannot be orthogonally joined; diagonal contact remains legal. The validator separately builds wall components and requires exactly one. It then scans every possible two-by-two window and rejects any window containing four walls. Fixed clue cells are also required to remain islands, and every board cell must have an explicit final state.

The release test proves uniqueness independently from that runtime validator. The three clues are fixed as island cells, leaving 13 cells that can each be either wall or island. A separate exhaustive oracle evaluates all 8,192 assignments. Its own neighbor routine, breadth-first component construction, clue lookup, area comparison, wall-connectivity check, and two-by-two scan do not call the production analysis function. Exactly one assignment survives. The disclosed solution marks cells 2, 3, 4, 6, 8, 9, 10, and 11 as walls when cells are numbered from 1 across each row; the other cells are islands.

Golden checks exercise the rules with direct counterexamples. They reject a white component containing two clues, a white component containing no clue, an island whose size differs from its number, disconnected wall fragments, and a solid two-by-two wall block. They confirm that corner-only contact stays disconnected, that the authored wall is one component, that the three authored islands have areas 2, 1, and 5, and that every cell belongs to exactly one final state. Product-state checks also cover incomplete checking, a repair after the first wrong board, exact scoring, the second-error deadlock, terminal freezing, cursor boundaries, fixed clue protection, and Restart.

Everything runs locally in the browser as a small React client game. It sends no board state to a server, requests no account, downloads no daily puzzle, uses no random generator, and introduces no package dependency. The compact four-column layout, square native buttons, minimum-height controls, wrapping status row, and constrained content width are designed to fit a 390-pixel phone without horizontal scrolling. Every cell exposes its row, column, clue or state, selection position, and stable test identifier for assistive technology and production browser verification.

This is a short recreational puzzle, not an intelligence test, medical or psychological assessment, educational placement tool, or employment screen. Replaying a fixed board naturally becomes easier through memory, so completion time is intentionally absent from scoring. For a fresh solve, begin with the clue 1 because every adjacent non-clue cell must be wall. Then consider how the clue 2 can acquire exactly one partner without touching another island, and preserve a route that keeps all wall cells connected. Use unknown marks while reasoning, explicit island marks when an area is established, and the repairable first check only after every cell has a deliberate state.

Methodology & sources

Fix the three clue cells as islands and represent every other cell explicitly as unknown, wall, or island. On a complete check, form orthogonal island components; require exactly one clue in each component and component size equal to its clue. Form orthogonal wall components and require exactly one, then scan all nine 2 by 2 windows for an all-wall block. Award 1,000 only if every predicate passes, record no error for unknown cells, permit repair after the first wrong complete check, deadlock after the second, and freeze both terminal states. Independently enumerate all 2^13 assignments with separate neighbor, component, clue, connectivity, and block code to prove one fixture solution.

Frequently asked questions

What are the standard Nurikabe rules?
Each orthogonally connected white island contains exactly one number and has that many cells. All black cells form one orthogonally connected wall, and no 2 by 2 square can be entirely black.
Does this fixed puzzle have only one solution?
Yes. An independent test exhausts all 8,192 assignments of the 13 non-clue cells with separate component and rule logic, finding exactly one valid board.
Can I play Nurikabe on a phone or without a mouse?
Yes. The four-column board has touch controls, and keyboard players can use Arrow keys, W or Space for wall, I for island, Delete to clear, and Enter to check.
Is this an official puzzle or an intelligence assessment?
No. The board is an original Lizely recreational fixture. Nikoli and Conceptis are cited for rules only, and the score is not a cognitive, health, education, or employment measure.

Related tools

Mini Games guides

View all