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.
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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
