Math Problem Statement

4x4 magic square Top-left square (Magic Sum = 34):

Solution

In a 4x4 magic square, every row, column, and diagonal must sum to a given number, which is called the magic sum. For a 4x4 magic square, this magic sum is 34.

You asked for the value of the top-left square of this magic square, but the value can vary depending on the construction method or specific configuration of the magic square. However, one common example is the normal magic square using the numbers from 1 to 16, arranged so that the sum of the rows, columns, and diagonals is 34.

A commonly known 4x4 magic square looks like this:

\hline 16 & 2 & 3 & 13 \\ \hline 5 & 11 & 10 & 8 \\ \hline 9 & 7 & 6 & 12 \\ \hline 4 & 14 & 15 & 1 \\ \hline \end{array}$$ In this example, the value in the top-left corner is **16**. Would you like more details on how this magic square is constructed or have any questions? ### Related Questions: 1. What are the rules for constructing a magic square? 2. How can the magic sum be calculated for different sizes of magic squares? 3. What are other types of magic squares apart from the normal one? 4. How do the diagonals contribute to the magic sum in a magic square? 5. Can magic squares be created with sums other than 34 for a 4x4 grid? **Tip:** The magic sum of an $$n \times n$$ magic square can be calculated using the formula: $$S = \frac{n(n^2 + 1)}{2}$$

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Math Problem Analysis

Mathematical Concepts

Magic Square
Arithmetic
Number Patterns

Formulas

Magic Sum Formula: S = n(n^2 + 1) / 2

Theorems

Magic Square Theorem

Suitable Grade Level

Grades 6-8