Question

Using the numbers from 5 to 13, construct a $$3\times 3$$ magic square. What is the magic sum here? What relation is there between the magic sum and the number in the central cell?

Answer 1

Hint: We have to construct a magic square of three rows and three columns. Magic square means a square which contains sub-squares, where each sub-square contains a number such that the sum of numbers in rows, columns and diagonals are the same.

Complete step-by-step answer:
We will construct a magic square using the numbers from 5 to 13 such that we will get the same value of sum of numbers along the rows, columns and diagonals.
Let’s draw the magic box of size $$3\times 3$$.

We can easily see that the sum of numbers in rows, columns and diagonals are the same. Sum is 27.
Hence, the magic sum is 27.
Now, we will find the relation between the number in the central cell and the magic sum.
The number in the central cell is 9 and the value of sum is 27.
We can write magic sum as;
Magic sum$$=3\times 9$$
We know the number in the central cell is 9.
Therefore,
Magic sum $$=3\times$$ number of central cell
Hence, this is the required relation between the magic sum and the number in the central cell.

Note: We have constructed a magic square in this question of 3 rows and 3 columns i.e. $$3\times 3$$. We need to keep in mind that the numbers can’t be repeated in the magic square i.e. the one number can appear only once in the magic square. The magic sum is equal to the product of the number of rows or columns and the number in the central cell.