Lights Out Linear Algebra

1112 WordsMay 30, 20115 Pages
The purpose of this project is to solve the game of Light’s Out! by using basic knowledge of Linear algebra including matrix addition, vector spaces, linear combinations, and row reducing to reduced echelon form. | Lights Out! is an electronic game that was released by Tiger Toys in 1995. It is also now a flash game online. The game consists of a 5x5 grid of lights. When the game stats a set of lights are switched to on randomly or in a pattern. Pressing one light will toggle it and the lights adjacent to it on and off. The goal of the game is to switch all the lights off in as few button presses as possible. In the folling examples, 1 will represent a “on” light and 0 will represent an “off” light. Yellow represents a button pressed…show more content…
To solve for the scalars matrix A is augmented with the original vector. This augmented matrix is then row reduced to reduced echelon form. This will result in the number of times each vector should be pressed, either zero or once. Matrix after augmenting and row reducing to reduced echelon form. 100000000000000000000000010100000000000000000000000000100000 000000000000000001000100000000000000000000000000100000000000 000000000000000100000000000000000000000000100000000000000000 01000000010000000000000000000000000010000000000000000000 00000001000000000000000 1&&&000000000010000000000000010000000000010000000000000000000000 000010000000000000000000000000010000000000010000000000000010 000000000100000000000000010000000001000000000000000010000000 00000000000000000001000000010000000000000000001000000100 000000000000000001000000000000000000000000001000000000000000 000000000001000100000000000000000000001001000000000000000000 0000010000000000000000000000000010&&& This tells us that buttons 1, 3, 7, 10, 11, 14, 15, 16, 18, 19, 22, and 23 should be pressed. Remember these buttons can be pressed in any order. This shows us that even the most elementary linear algebra skills can be useful for real world problems. Resources Lights Out! - Jaap’s Puzzle Page - Lights’s Out puzzle Wolfram Mathworld -
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