Question

Fill this square using all numbers from 21 to 29.

Answer 1

Let us fix $26$ on the topmost left-hand side box.

Taking the diagonal of the square, we have

$26+25=51$ and $75-51=24$

$\therefore$ put $24$ at the end of this diagonal.

Fix $22$ on the top most-right side box.

Taking the diagonal in which $22$ lies, we have

$22+25=47$ and $75-47=28$

$\therefore$ put $28$ at the end of this diagonal.

Clearly,

In $1^{st}$ row: The required number $=75-(26+22)=75-48=27$

In $1^{st}$ column: The required number $=75-(26+28)=75-54=21$

In $2^{nd}$ row: The required number $=75-(21+25)=75-46=29$

In $2^{nd}$ column: The required number $=75-(28+24)=75-52=27$

$\therefore$ the complete magic square is as shown below:

$26$	$27$	$22$
$21$	$25$	$29$
$28$	$23$	$24$