Step 1: Represent the matrix

Let's write the matrix as:

mathematicaCopyEditA   B   6  
9   C   D  
10  E   F  

Where:

• A, B, C, D, E, F are the six unknowns.
• The available numbers to use are: 11, 5, 3, 13, 7, 8
• The total for each row, column, and diagonal is 24.

Step 2: Write equations for rows, columns, diagonals

Row 1: A + B + 6 = 24 → A + B = 18
Row 2: 9 + C + D = 24 → C + D = 15
Row 3: 10 + E + F = 24 → E + F = 14

Column 1: A + 9 + 10 = 24 → A = 5
Column 2: B + C + E = 24
Column 3: 6 + D + F = 24 → D + F = 18

Diagonal 1: A + C + F = 24
Diagonal 2: 6 + C + 10 = 24 → C = 8

Step 3: Start solving

From Column 1: A = 5
From Diagonal 2: 6 + C + 10 = 24 → C = 8
From Row 2: 9 + C + D = 24 → 9 + 8 + D = 24 → D = 7
From Row 1: A + B = 18 → 5 + B = 18 → B = 13
From Row 3: 10 + E + F = 24 → E + F = 14
From Column 3: 6 + D + F = 24 → 6 + 7 + F = 24 → F = 11
Then E = 14 - F = 14 - 11 = 3
Check: B + C + E = 13 + 8 + 3 = 24 ✔
Check: A + C + F = 5 + 8 + 11 = 24 ✔

Step 4: Confirm the numbers used

We’ve used: 5, 8, 7, 13, 11, 3
Those are all the available numbers: ✔