Torrence and his father came up with what they call the “in-out” strategy. “A really good way of going about things sometimes in research is to discover an intuition for something, believe it’s true, and then once you think something’s true, developing a proof is a lot easier,” said Torrence. The next challenge was to prove that their solution could work for more complicated set-ups. After studying the algorithm for the 5x5 game, Torrence and his father found a strategy that seemed to work for any initial set up of the game and more complicated versions as the number of switches increased. Players win the game by selecting the pattern of switches that will turn all the lights out in the smallest number of moves.Ī quick search online offers strategies for a smaller 5x5 version, but Torrence realized no one had proved solutions to more complicated versions of the game. The game consists of an inner and outer layer of switches. Torrence explained that his puzzle was based on the generalized Petersen graph. Lights Out is a game consisting of a network of switches that when turned on or off affect neighboring switches. At the end of the week, the paper published Torrence’s solution and explanation. The Times included an online version of Lights Out for readers to try for themselves and see if they could come up with Torrence’s solution. Wordplay features a math-related puzzle every week in an ongoing section called Numberplay. The New York Times recently published Torrence’s version to the game in Wordplay, the paper’s crossword blog section. Torrence ’15, along with his father Bruce Torrence, Garnett Professor of Mathematics at Randolph-Macon College, created an algorithm to solve larger and more challenging digital versions of the electronic game Lights Out, created in 1995 by Tiger Toys. William & Mary math student Robert Torrence is shedding some light on a decades-old game that continues to puzzle thousands each year.

Lights out puzzle