How is it possible to roll dice to randomly choose 12 squares out of a grid of 144 and reveal a hidden message in the correct order? It’s not only possible, it’s actually guaranteed.
But why stop at 12 x 12? Why can’t you hide an entire book in an array of colored squares, and have a friend randomly select them until he’s re-written the entire book perfectly, start to finish? If you had enough time and space, that’s guaranteed to work, too.
First we have to have that grid of colored squares and write down all 144 (x, y) coordinates. Then roll our dice -- or you can have a friend just choose a square -- and mark that with an X. Remove all the squares above, below, and to the left and right of the choice. Then keep choosing and removing until there’s only one square left, which is your final selection.
Flip them over and you’ve got whatever message you secretly hid within the grid, and it’ll work every single time. They call it magic, but it’s really not.
Magic squares started as simple quirks of addition, and over the last 2,500 years they’ve evolved to create complex patterns of numbers, operations, and even letters. China and India were fascinated by mathematical magic squares, and the famous SATOR square of letters has been found all over Europe. But the most fascinating basic magic square might be tucked away in the corner of a 16th century German engraving.
Over centuries we’ve learned the patterns and properties of magic squares, ranging from brain teasers and riddles to… well, the presence of Birkhoff–von Neumann decomposition within the magic.
Demonstrate a magic trick? Ask someone to marry you? Re-write the entire Harry Potter series? It’s all possible with the manipulation of recreational mathematics.
Thanks to Dungeons & Dragons YouTuber Charles Khan for help finding large d12 dice! https://www.youtube.com/charleskhan
Select music from Tom Fox: https://www.youtube.com/channel/UCUIM14Vyndaq8MuDeW7BsIg
Order 4 Magic Squares: http://www.magic-squares.net/order4list.htm
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Hosted and Produced by Kevin Lieber
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Research and Writing by Matthew Tabor
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