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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

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