How to Play:

The goal is to turn off all the lights on the board.

When you click on a light, it toggles (changes from on to off or off to on) that light and its adjacent lights (top, bottom, left, right).

Try to solve the puzzle in as few moves as possible!

Educational Objectives:

• Develop logical thinking and pattern recognition
• Understand binary state systems (on/off)
• Learn about local actions having global consequences
• Practice systematic problem-solving approaches

Tips:

• Start by focusing on one corner or edge of the board.
• Look for patterns - sometimes the solution is symmetric.
• Use the "Get Hint" button if you're stuck.
• Remember: Clicking a tile twice cancels the move!

Linear Algebra Behind Lights Out

The Lights Out puzzle can be modeled using linear algebra over the field GF(2) (where 1+1=0).

Each light configuration can be represented as a vector, and each possible move as a basis vector.

The puzzle then becomes solving a system of linear equations to find the combination of moves that will turn all lights off.

Key Mathematical Concepts:

• Binary Field GF(2): Arithmetic where 1+1=0, matching the toggle behavior
• Linear Independence: Some move combinations are redundant
• Matrix Representation: The puzzle can be represented as an n×n matrix
• Gaussian Elimination: Method to systematically find solutions

Interesting Facts:

• For a 5×5 grid, every initial configuration is solvable.
• The order in which you press the buttons doesn't matter - only which buttons are pressed an odd number of times.
• The solution can be found using Gaussian elimination on the corresponding matrix.
• On an n×n grid, there are 2^(n²) possible configurations, but only some are solvable.

You solved the puzzle in moves!

Time taken:

Minimum possible moves: