Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free for 30 days — and the first 200 people get 20% off an annual premium subscription! Magic Square puzzles are some of my favourite recreational math puzzles. Fill up a 3x3 square with the numbers 1 through 9 each used once so every row, column, and main diagonals add up to the same number. More generally, it can be a nxn square with numbers 1 through n^2, and there are actually tonnes of variants of these. In this video we will prove that there is precisely 1 possible 3x3 magic square (up to reflections and rotations). We'll do this by computing the Magic Number, aka the fixed sum each row must add up to, then figuring out the center must always sum to 5, and finally show how we get a single possible square. What's a bit crazy is that 4x4 has 880 possibilities, 5x5 has over 275 million possibilities, and for 6x6 it is so large we've never computed the exact number! 0:00 What is a Magic Puzzle? 0:45 Try these Magic Puzzles! 1:29 Ad hoc solving 2:27 Our 3x3 theorem 3:04 Gauss' counting trick 4:14 Sum formula 5:55 Central Square 7:09 Proving the theorem 9:25 Bigger magic squares 10:19 Brilliant.org/TreforBazett Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://beautifulequations.net/pages/trefor COURSE PLAYLISTS: ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Log...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...   ► CALCULUS II:    • Calculus II (Integration Methods, Ser...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus ...   ►VECTOR CALCULUS (Calc IV)    • Calculus IV: Vector Calculus (Line In...   ►DIFFERENTIAL EQUATIONS:    • Ordinary Differential Equations (ODEs)   ►LAPLACE TRANSFORM:    • Laplace Transforms and Solving ODEs   ►GAME THEORY:    • Game Theory   OTHER PLAYLISTS: ► Learning Math Series https://www.youtube.com/watch?v=LPH2lqis3D0 ►Cool Math Series:    • Cool Math Series   BECOME A MEMBER: ►Join: null MATH BOOKS I LOVE (affilliate link): ► https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based): http://twitter.com/treforbazett ►Instagram (photography based): http://instagram.com/treforphotography