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Lizely

Lights Out

Solve a deterministic Lights Out board with exact cross toggles, complete keyboard control, independently proven solvability, and a unique shortest path.

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How to use

  1. 1.Select any tile and press it by clicking, tapping, choosing Press selected, or pressing Space; the tile and only its orthogonal neighbors toggle.
  2. 2.Plan with press parity and turn every one of the 16 lights off; the independent oracle proves that this fixed board needs at least five moves.
  3. 3.Choose Check board or press Enter after five or more moves; all off scores exactly 1,000, the first wrong complete path can be repaired, and the second locks until Restart.

About Lights Out

Lights Out is a binary toggle puzzle. Every tile is either on or off, and pressing a tile reverses its own state together with the states of its immediate up, down, left, and right neighbors. Diagonal tiles do not change. A corner press therefore affects three tiles, a non-corner edge press affects four, and an interior press affects five. The goal in this edition follows the standard all-off objective: finish with every light on the board switched off.

This Lizely edition presents one fixed 4 by 4 board created specifically for the site. The initial on cells are 1, 2, 3, 5, 9, and 10 when the board is indexed from zero across each row. The starting pattern, size, check policy, score, and two-error state machine are original product fixtures. They are not copied from GNOME, UC Berkeley, the historic handheld game, a puzzle book, or a daily challenge. GNOME's maintained Lights Off help is cited for the selected-plus-non-diagonal-neighbor behavior, and UC Berkeley GamesCrafters independently confirms both the orthogonal toggle rule and all-off goal.

Click or tap any tile to press it. The tile and its legal cross neighbors change immediately, with on becoming off and off becoming on. The currently selected tile carries a visible outline, while the other cells in its affected cross receive a lighter border preview. That preview is explanatory only and never changes state by hovering. Press selected offers the same operation as clicking the board, which helps touch, switch-control, and keyboard users keep a stable cursor. Each cell exposes its row, column, on-or-off state, and selection state in an accessible label.

Keyboard play covers the full interaction. Arrow keys move the selected cell through the rectangular grid without wrapping. Space presses the selected tile. Enter or C checks the board. The global repeat flag is ignored, so holding Space cannot produce an uncontrolled burst of parity-changing moves and holding an Arrow key cannot skip through the puzzle. The shared double-Escape gesture activates the spreadsheet-style boss screen, and a second double Escape returns to the board. Restart restores the exact six-light initial pattern, cell-zero cursor, zero moves, zero mistakes, and zero score.

Checking uses a mathematically justified completion boundary. Independent exhaustive analysis proves that this fixture cannot be solved in fewer than five presses. A check during moves zero through four is therefore objectively incomplete and records no mistake. At five or more moves, an all-off board succeeds, while a board with any remaining light represents a complete but incorrect submitted path. The first such wrong check records one mistake and remains editable. The player can continue pressing tiles, reach all off, and check successfully. A second wrong complete check deadlocks the run until Restart.

A successful check awards exactly 1,000 points. The score does not vary with speed, extra moves, device, or input method; correctness is the only scoring predicate. Completion and deadlock are terminal states. After either state, clicks, Space presses, cursor movement, selection changes, and further checks cannot modify the board. These guarantees live in the pure state-transition functions and are covered by tests, rather than depending only on disabled visual controls. The first-error repair path is tested by submitting a deliberate five-move failure, canceling its residual parity, applying a valid solution, and checking again.

The runtime game does not compare a move list with a hidden five-button answer. It stores the 16 current light booleans. A press computes the selected cell's in-bounds orthogonal cross and flips those booleans. A check accepts any 16-cell all-off state after the proven minimum boundary. This means longer valid solutions remain valid, as standard toggle algebra requires. Pressing the same cell twice restores the prior light pattern, and press order does not affect the final parity state even though the displayed move count records every physical press.

Release evidence comes from a separate GF(2) oracle that does not call the production neighbor or press functions. The test independently constructs one 16-bit effect column for each board cell. It performs binary Gaussian elimination and finds matrix rank 12, hence nullity 4. It also enumerates all 65,536 binary press masks. Those masks produce 4,096 distinct effect states, and the authored initial board has 16 all-off solution masks. This agrees with the rank-nullity result and proves the fixture is reachable rather than merely assumed solvable.

The same exhaustive oracle measures solution quality. The 16 solutions have Hamming weights 5, 7, 9, or 11. Exactly one has weight 5, so the shortest solution is unique. That solution presses zero-based cells 0, 1, 3, 5, and 6 once each. The answer is disclosed here for auditability but is not exposed inside the game widget. The test confirms that applying those five independent effect columns to the disclosed initial mask produces zero, and it confirms that no mask of weight zero through four does so.

Golden cases cover all three boundary geometries. Cell 0 affects exactly cells 0, 1, and 4. Cell 1 affects exactly cells 0, 1, 2, and 5. Interior cell 5 affects exactly cells 1, 4, 5, 6, and 9. Their total matrix contains 64 one-bits across the 16 effect columns. Other checks prove double-press cancellation, initial-state fidelity, full mask-space size, rank, reachable-state count, total solution count, minimum weight, unique optimum, incomplete checking, repair after the first wrong complete path, exact scoring, second-error deadlock, terminal freezing, cursor boundaries, and deterministic Restart.

Everything runs locally in the browser. No board state is uploaded, no account is required, no random level is requested, no timer affects the result, and no new package dependency is introduced. The square four-column grid, concise status row, large native buttons, and wrapping controls are designed to fit a 390-pixel viewport without horizontal scrolling. State is communicated with the words On and Off as well as surface contrast, so play does not rely on color alone.

This is a recreational fixed puzzle, not an intelligence test, cognitive or medical assessment, educational placement tool, or employment screen. Repeated play naturally becomes easier through memory, which is why time is not scored. To reason without seeing the disclosed answer, consider press parity: pressing one cell twice cancels, so only odd or even press counts matter for the final board. Work row by row, watch the affected-cross preview, and use the first repairable check only after at least five deliberate moves.

Methodology & sources

Represent the 4 by 4 board as 16 booleans. Pressing a valid cell flips that cell and its in-bounds orthogonal neighbors; diagonals are excluded. Check is incomplete without penalty before the independently proven five-move lower bound, awards exactly 1,000 for any all-off state at or beyond that bound, permits repair after the first complete wrong path, deadlocks after the second, and freezes both terminal states. Independently build the 16 binary effect columns, compute GF(2) rank by Gaussian elimination, enumerate all 2^16 parity masks, and verify rank 12, 4,096 reachable effects, 16 all-off solution masks, minimum weight five, and one minimum mask.

Frequently asked questions

Which tiles change when I press a light?
The pressed tile changes together with its immediate up, down, left, and right neighbors that are inside the board. Diagonal tiles never change.
Is this Lights Out starting board solvable?
Yes. An independent GF(2) oracle enumerates all 65,536 press masks and finds 16 all-off solutions for this starting state.
What is the shortest solution length?
Five presses. Exactly one of the 16 parity solutions has weight five; all other solutions use seven, nine, or eleven distinct odd-parity presses.
Is this an official level or an intelligence test?
No. The board is an original Lizely recreational fixture. GNOME and UC Berkeley are cited for rules only, and the fixed score is not a measure of intelligence, health, education, or work ability.

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