Puzzle result
Create or load a board to begin.
The solver will report status, moves, method, and timing.
Puzzle setup
Interactive board
Click a light to apply the selected toggle rule.
Display and accessibility
Statistics
Formula used
Each light uses binary values. Pressing a cell adds a toggle vector. Addition is performed modulo two.
The solver builds the equation A × x = b. Gaussian elimination finds valid press vectors. Nullspace search checks shorter equivalent solutions.
A × x = b (mod 2)
final board = initial board + A × x = 0
number of solutions = 2^(nullity of A)How to use this calculator
Select rows, columns, rules, and a source. Build the puzzle and click lights. Use Solve whenever guidance becomes necessary.
Hints highlight the next recommended press. Auto-solve plays every calculated move. Export buttons save the displayed results.
- Choose a board size and puzzle source.
- Select a toggle rule and edge behavior.
- Build the board, then play or edit it.
- Press Solve to calculate a valid solution.
- Use hints, steps, exports, or auto-solve.
Example data
| Grid size | Initial pattern | Rule | Expected status |
|---|---|---|---|
| 3 × 3 | Cross | Standard cross | Solvable |
| 4 × 4 | Checkerboard | Standard cross | Solver determines status |
| 5 × 5 | Random solvable | Standard cross | Solvable |
| 6 × 6 | Border | Wrap-around cross | Solver determines status |
Understanding Lights Out
What the puzzle does
Lights Out uses a grid of binary lights. A press changes nearby cells. The goal turns every light off.
Why binary arithmetic works
Every cell has only two possible states. Two toggles cancel each other. This matches arithmetic performed modulo two.
Solvable and unsolvable boards
Some rules cannot reach every possible board. The solver checks equation consistency. Inconsistent equations identify an unsolvable state.
Manual solving tips
Try chasing lights from top downward. Avoid changing completed rows unnecessarily. Compare your moves with calculated guidance.
Worked example
A single center light creates the target vector. The solver finds presses reproducing that vector. Applying them clears the complete board.
Frequently asked questions
What is the standard Lights Out rule?
A press toggles itself and four orthogonal neighbors. Edge cells affect fewer positions. Wrap-around can change that behavior.
Can every puzzle be solved?
No, solvability depends on dimensions and rules. The calculator tests equation consistency. Unsolvable boards receive a clear warning.
How is a minimum solution found?
The solver finds one valid vector first. It then explores nullspace combinations. Large searches use a practical safety limit.
What does wrap-around mean?
Edges connect to the opposite grid side. Corner presses may affect distant corners. This creates a toroidal puzzle board.
Can I create custom rules?
Yes, select the custom rule option. Choose affected offsets in the pattern editor. The solver uses your selected pattern.
How does the daily challenge work?
The current date creates a stable seed. Everyone receives the same dated pattern locally. Tomorrow generates a different challenge.
Are my statistics stored online?
No account is required for statistics. Values remain in local browser storage. Clearing storage removes saved performance data.
Why can minimum search be limited?
Some boards have many nullspace combinations. Exhaustive checking may become extremely large. The calculator then returns a valid solution.
Can I import a board?
Yes, use binary matrix input. Enter equal-length zero and one rows. Spaces and commas are also accepted.