Is the provided 3×3 square a magic square with a total of 45? Verify the sums of rows, columns, and…

Question

Is the provided 3×3 square a magic square with a total of 45? Verify the sums of rows, columns, and diagonals.

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 45."

Let's verify if the given square is correct.

The square is:

\begin{bmatrix} 24 & 9 & 12 \\ 3 & 15 & 27 \\ 18 & 21 & 3 \end{bmatrix}

Check the sum of each row.
- Row 1: $24 + 9 + 12 = 45$
- Row 2: $3 + 15 + 27 = 45$
- Row 3: $18 + 21 + 3 = 45$
Check the sum of each column.
- Column 1: $24 + 3 + 18 = 45$
- Column 2: $9 + 15 + 21 = 45$
- Column 3: $12 + 27 + 3 = 45$
Check the sum of the main diagonals.
- Main diagonal (top-left to bottom-right): $24 + 15 + 3 = 42$
- Anti-diagonal (top-right to bottom-left): $12 + 15 + 18 = 45$
The main diagonal ( $24 + 15 + 3$ ) sums to 42, which is not 45. Therefore, the given square is not a magic square with a total of 45.

The given square is:
$\boxed{ \begin{bmatrix} 24 & 9 & 12 \\ 3 & 15 & 27 \\ 18 & 21 & 3 \end{bmatrix} }$
❌ Incorrect. The sum of the main diagonal ( $24 + 15 + 3$ ) is 42, not 45.

Is the provided 3x3 square a magic square with a total of 45? Verify the sums of rows, columns, and diagonals.

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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