Question

Complete the magic square whose magic number is $39.0$

	$1.2$	$15.0$	$10.8$	$6.6$
$1.8$		$11.4$	$7.2$	$6.0$
			$3.6$
$9.6$		$4.2$
$9.0$		$0.6$	$14.4$

Accepted Answer

Given,

There is a magic square whose magic number is $39.0$ , we need to complete the given magic square.

$1.2$ $15.0$ $10.8$ $6.6$

$1.8$ $11.4$ $7.2$ $6.0$

$3.6$

$9.6$ $4.2$

$9.0$ $0.6$ $14.4$

The centre of the magic square = $39.0 \div 5 = 7.8$ (As, the square is a $5 \times 5$ square, so, the given magic number will be divide by $5$ )

Therefore, Cell $(3, 3) = 7.8$ (As, cell (i, j) means the number of rows are i and the number of columns are j)

As per rules of magic square, we fill Cell $(2, 4)$ after filling Cell $(3, 3)$ . And we observe that as we move upwards along the right diagonal, the numbers in the magic square decreases by $0.6 .$

Example: Cell $(3, 3)$ $-$ Cell $(2, 4) = 0.6$

Cell $(2, 4)$ $-$ Cell $(1, 5) = 0.6$

While trying to move upwards along the right diagonal, if we are unable to do so due to a number that already exists, then we move one cell vertically downwards.

Following all the rules of filling a Magic square, we get the final result as follows:

$5.4$ $1.2$ $15.0$ $10.8$ $6.6$

$1.8$ $12.6$ $11.4$ $7.2$ $6.0$

$13.2$ $12.0$ $7.8$ $3.6$ $2.4$

$9.6$ $8.4$ $4.2$ $3.0$ $13.8$

$9.0$ $4.8$ $0.6$ $14.4$ $10.2$

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