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Magic Square

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Magic Square


1. The user mentions a "manic square," which seems to be a typo or misunderstanding. It is likely they meant "magic square," a grid where the sums of numbers in each row, column, and diagonal are equal. 2. A magic square is not an equation but a special arrangement of numbers. 3. To clarify, a magic square of order $n$ is an $n \times n$ grid filled with distinct positive integers such that the sum of the numbers in each row, column, and diagonal is the same. 4. The magic constant (sum) for a magic square of order $n$ with numbers from 1 to $n^2$ is given by the formula: $$ M = \frac{n(n^2 + 1)}{2} $$ 5. For example, a 3x3 magic square uses numbers 1 to 9, and the magic constant is: $$ M = \frac{3(9 + 1)}{2} = \frac{3 \times 10}{2} = 15 $$ 6. This means each row, column, and diagonal sums to 15. 7. Since the user did not provide a specific magic square or problem, this explanation clarifies what a magic square is and how to calculate its magic constant.