Subjects algebra

Magic Square Center

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1. **Problem statement:** Alexa created a 3x3 magic square where the sum of numbers in each row, column, and diagonal equals $K$. Some numbers are given, and we need to find the number in the central square. 2. **Properties of a 3x3 magic square:** The magic sum $K$ is the same for all rows, columns, and diagonals. 3. **Let the central number be $x$.** 4. **Using the magic square properties:** - The sum of the middle row is $K$. - The sum of the middle column is $K$. - The sum of the two diagonals is $K$. 5. **Since the problem states numbers need not be distinct, we focus on the sums only.** 6. **In a 3x3 magic square, the center number is always $\frac{K}{3}$.** This is because the center number appears in one row, one column, and both diagonals, contributing to the total sums equally. 7. **Therefore, the number in the central square is $\frac{K}{3}$.**