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Lights Out Game – Linear Algebra and Logic Puzzle in GeoGebra

Lights Out Game – Linear Algebra and Logic Puzzle in GeoGebra
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2017-06-03 05:37
PolygonFunctionSequenceMatrix
① This interactive example demonstrates the classic 'Lights Out' puzzle: a 3×3 grid where clicking a cell toggles its own state and those of its orthogonal neighbors, with the goal of turning off all lights. ② The core mathematical concept is linear algebra over the finite field GF(2): the game state is a binary vector, each click corresponds to a toggle matrix, and solving the puzzle reduces to solving a system of linear equations modulo 2. It also involves logical reasoning, pattern recognition, and piecewise functions for state transitions. ③ Construction highlights: using GeoGebra commands Polygon, Random, Sequence, and Circle to build the grid and light nodes; objects such as S11–S33 and V11–V33 store states; Mode, SetUpMode, and GameMode control the game flow; StateVec, SolVec, MInv, and ShowSol enable solving and displaying the solution. ④ Suitable for high school and above, this example serves as an engaging tool for teaching linear algebra, matrix operations, discrete mathematics, and algorithmic thinking.

GeoGebra Commands & Parameters

  1. Polygon((0, 3), (0, 2), 4) → S11
  2. Polygon((1, 3), (1, 2), 4) → S12
  3. Polygon((2, 2), (2, 1), 4) → S23
  4. Polygon((2, 3), (2, 2), 4) → S13
  5. Polygon((0, 2), (0, 1), 4) → S21
  6. Polygon((0, 1), (0, 0), 4) → S31
  7. Polygon((1, 2), (1, 1), 4) → S22
  8. Polygon((1, 1), (1, 0), 4) → S32
  9. Polygon((2, 1), (2, 0), 4) → S33
  10. Random(0, 1) → V11
  11. Random(0, 1) → V12
  12. Random(0, 1) → V13
  13. Random(0, 1) → V21
  14. Random(0, 1) → V22
  15. Random(0, 1) → V23
  16. Random(0, 1) → V31
  17. Random(0, 1) → V32
  18. Random(0, 1) → V33
  19. Sequence(Segment[(0, i), (3, i)], i, 0, 3, 1) → FrameH
  20. Sequence(Segment[(i, 0), (i, 3)], i, 0, 3, 1) → FrameV
  21. Sequence(Mod[SolVec(i, 1), 2], i, 1, 9) → SolF
  22. Circle((0.5, 2.5), 0.2) → C11
  23. Circle((1.5, 2.5), 0.2) → C12
  24. Circle((2.5, 2.5), 0.2) → C13
  25. Circle((0.5, 1.5), 0.2) → C21
  26. Circle((1.5, 1.5), 0.2) → C22
  27. Circle((2.5, 1.5), 0.2) → C23
  28. Circle((0.5, 0.5), 0.2) → C31
  29. Circle((1.5, 0.5), 0.2) → C32
  30. Circle((2.5, 0.5), 0.2) → C33
  31. Sequence(Random[0, 1], i, 1, 9) → StateVecRandom
  32. Polygon((-1.4868418817692932, -0.8357894021661738), (-1.4868418817692932, 5.164210597833826), (7.513158118230713, 5.164210597833826), (7.513158118230713, -0.8357894021661738)) → BG, f, g, h, i

AI Drawing Prompt Reference

Draw a 3x3 grid board with square cells, each containing a circular light dot at its center. The board is framed by horizontal and vertical line segments. Each cell is a square, and the light dots are randomly lit or unlit. A large background rectangle surrounds the board. The overall look is a logic puzzle game interface with random light states and a clear grid structure.
The prompt above was compiled from the original drawing commands and is for reference only.