The sum of each row, column, and diagonal in the magic square below is 60. Fill in the missing numbers.

Question

ScanSolve AI Tutor · Accepted Answer

To fill in the missing numbers in the magic square, we use the rule that every row, column, and diagonal must add up to the given total, which is 60 for square 4.

Let the magic square be represented as:

\begin{bmatrix} A & B & C \\ D & E & F \\ G & H & I \end{bmatrix}

From the image, we have the following known values:
$A = 21$
$C = 23$
$G = 17$
$I = 19$

Find the center number $E$ using the main diagonal.
The sum of the main diagonal ( $A+E+I$ ) must be 60.
$21 + E + 19 = 60$ $40 + E = 60$ $E = 60 - 40$ $E = 20$
Find $B$ using the first row.
The sum of the first row ( $A+B+C$ ) must be 60.
$21 + B + 23 = 60$ $44 + B = 60$ $B = 60 - 44$ $B = 16$
Find $H$ using the third row.
The sum of the third row ( $G+H+I$ ) must be 60.
$17 + H + 19 = 60$ $36 + H = 60$ $H = 60 - 36$ $H = 24$
Find $D$ using the first column.
The sum of the first column ( $A+D+G$ ) must be 60.
$21 + D + 17 = 60$ $38 + D = 60$ $D = 60 - 38$ $D = 22$
Find $F$ using the third column.
The sum of the third column ( $C+F+I$ ) must be 60.
$23 + F + 19 = 60$ $42 + F = 60$ $F = 60 - 42$ $F = 18$
The completed magic square is:
$\boxed{ \begin{bmatrix} 21 & 16 & 23 \\ 22 & 20 & 18 \\ 17 & 24 & 19 \end{bmatrix} }$

The sum of each row, column, and diagonal in the magic square below is 60. Fill in the missing numbers.

Step-by-step solution

Find the center number $E$ using the main diagonal.

Find $B$ using the first row.

Find $H$ using the third row.

Find $D$ using the first column.

Find $F$ using the third column.

Still stuck on this one?

More Mathematics Questions

The sum of each row, column, and diagonal in the magic square below is 60. Fill in the missing numbers.

Step-by-step solution

Find the center number EEE using the main diagonal.

Find BBB using the first row.

Find HHH using the third row.

Find DDD using the first column.

Find FFF using the third column.

Still stuck on this one?

More Mathematics Questions

Find the center number $E$ using the main diagonal.

Find $B$ using the first row.

Find $H$ using the third row.

Find $D$ using the first column.

Find $F$ using the third column.