Question
What is a magic square? Complete entries in the following and make it a magic square.
| 8 | 21 | 1 | |
| 11 | 7 | 2 | |
| 10 | 5 | 3 | |
| 4 | 6 | 9 |
Illustrate the methods used for filling the entries. Also explain why the method work?
Answer :
Word Count : 520
A magic square is a square grid of numbers where the sum of the numbers in each row, each column, and both diagonals is the same. This sum is called the "magic constant" or "magic sum." Let's solve the incomplete magic square step-by-step. ### Given Grid: \[ \begin{array}{|c|c|c|c|} \hline & 8 & 21 & 1 \\ \hline 11 & 7 & & 2 \\ \hline 10 & 5 & 3 & \\ \hline 4 & & 6 & 9 \\ \hline \end{array} \] ### Step 1: Find the magic constant (sum) The magic constant for a 4x4 magic square can be calculated using the formula: \[ \text{Magic Constant} = \frac{n(n^2 + 1)}{2} \] Where \( n \) is the size of the square (4 in this case). \[ \text{Magic Constant} ______ ________ ___ _________ ___ _____.
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A magic square is a square grid of numbers where the sum of the numbers in each row, each column, and both diagonals is the same. This sum is called the "magic constant" or "magic sum." Let's solve the incomplete magic square step-by-step. ### Given Grid: \[ \begin{array}{|c|c|c|c|} \hline & 8 & 21 & 1 \\ \hline 11 & 7 & & 2 \\ \hline 10 & 5 & 3 & \\ \hline 4 & & 6 & 9 \\ \hline \end{array} \] ### Step 1: Find the magic constant (sum) The magic constant for a 4x4 magic square can be calculated using the formula: \[ \text{Magic Constant} = \frac{n(n^2 + 1)}{2} \] Where \( n \) is the size of the square (4 in this case). \[ \text{Magic Constant} ______ ________ ___ _________ ___ _____.
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