Uploads from Physics for the Birds

Currently Playing: Solving the "Lights Out" Problem

Ever run into this funny little puzzle? It appears in Legend of Zelda: Link's Awakening, LEGO Star Wars: The Skywalker Saga, and in a 1995 electronic toy called Lights Out. It turns out that this game has some pretty rich math. In this video, we'll learn about modular arithmetic and the matrix inverse. We'll also learn about substitution ciphers in cryptography, including the Hill Cipher. Become a Patreon member: https://www.patreon.com/PhysicsfortheBirds 0:00 Intro 1:58 The Problem 6:10 Some Cryptography 8:52 Solving Each Puzzle 11:07 Your Linear Algebra Professor Was Wrong 14:38 Conclusion Jaap's Puzzles Lights Out: https://www.jaapsch.net/puzzles/lomath.htm#refs Turning Lights Out With Linear Algebra: https://people.sc.fsu.edu/~jburkardt/classes/imps_2017/11_28/2690705.pdf Lights Out Online: https://www.chiark.greenend.org.uk/~sgtatham/puzzles/js/flip.html Modular Matrices: "Cryptography: A Primer", Alan G. Konheim Chapter 3.14-3.17 Hill Cipher Summary: https://www.math.utah.edu/~gustafso/s2018/2270/labs/lab5-hillcipher.pdf