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1 Magic Squares - UC Santa Barbara

Latin SquaresInstructor: Padraic BartlettLecture 5: Latin Squares and MagicWeek 3 Mathcamp 2012 Today s application is to Magic ! Not the friendship kind, though1; instead, we re goingto talk aboutmagic Squares , an incredibly old piece of mathematics that we can studyusing Latin Magic squareis an ngrid filled with the integers{0,1, .. n2 1}, suchthat each number is used exactly once in our entire grid, and the sum of all of the entries along any row, column, the main diagonal2or the mainantidiagonal all come out to the same constant s an example for order 3:165840327 Magic Squares have been studied for a fairly ridiculously long time.

1 Magic Squares De nition. A magic square is a n n grid lled with the integers f0;1;:::n2 1g, such that each number is used exactly once in our entire grid, and the sum of all of the entries along any row, column, the main diagonal2 or the main antidiagonal all come out to the same constant value. Here’s an example for order 3:

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