Verify if the provided 3×3 magic square is correct, given that the magic sum is 15.

Question

ScanSolve AI Tutor · Accepted Answer

This image shows a completed magic square. A magic square is a square grid where the sum of the numbers in each row, each column, and both main diagonals is the same. The problem states that "The total is 15."

Let's verify if the given square is correct.

The square is:

\begin{bmatrix} 2 & 9 & 4 \\ 7 & 5 & 3 \\ 6 & 1 & 8 \end{bmatrix}

Check the sum of each row.
- Row 1: $2 + 9 + 4 = 15$
- Row 2: $7 + 5 + 3 = 15$
- Row 3: $6 + 1 + 8 = 15$
Check the sum of each column.
- Column 1: $2 + 7 + 6 = 15$
- Column 2: $9 + 5 + 1 = 15$
- Column 3: $4 + 3 + 8 = 15$
Check the sum of the main diagonals.
- Main diagonal (top-left to bottom-right): $2 + 5 + 8 = 15$
- Anti-diagonal (top-right to bottom-left): $4 + 5 + 6 = 15$
All rows, columns, and diagonals sum to 15. Therefore, the given magic square is correct.

The completed magic square is:
$\boxed{ \begin{bmatrix} 2 & 9 & 4 \\ 7 & 5 & 3 \\ 6 & 1 & 8 \end{bmatrix} }$

Verify if the provided 3x3 magic square is correct, given that the magic sum is 15.

Step-by-step solution

Check the sum of each row.

Check the sum of each column.

Check the sum of the main diagonals.

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