|Math Coffee: "The Easiest Lights Out Games" Dr. Bruce Torrence, Randolph-Macon College
When: March 11,
Speaker: Dr. Bruce Torrence, Randolph-Macon CollegeTicket Required: No
The game Lights Out, by Tiger Electronics, is a five-by-five array of lighted buttons, each of which can be either on or off. The game starts with a random collection of buttons that are lit. Your task is to push buttons until you turn off all the lights. It sounds easy, but here's the rub: each time a button is pushed, its state changes, and so do the states of its vertically and horizontally aligned neighbors.
Lights Out has inspired an impressive body of mathematical literature. In this presentation, we'll begin with an overview of the mathematics behind the game. In particular, we'll learn how to use linear algebra to solve Lights Out games, not just on a five-by-five board, but on any square board. We'll also see how to solve games played on a board "without boundary" (essentially on a torus, where the top and bottom rows are considered adjacent, and the left and right columns are considered adjacent), again of any size. Finally, we'll consider some new research about so-called "easy" games. A Lights Out game is easy if it can be solved by pushing precisely the buttons that are initially lit. We'll find that these games can be completely classified for all board sizes, with or without boundary. Moreover, we'll discover that the notion of easy games leads to some novel strategies for attacking any Lights Out puzzle, provided that the board is of the right size.
We'll gather at 6:15 in Math Hall for our traditional light snacks.
Contact: Prof. Donna Molinek