How to solve a magic square STD IV

HOW TO SOLVE PROBLEMS ON MAGIC SQUARE

What is a magic square?

Please see the square below:

8	15	7
9	10	11
13	5	12

 

In this square the sum of all the rows, columns and diagonals add up to 30. In a magic square the sum of the rows columns and diagonals always add up to give the same value.

What is the magic?

Rule 1:  the central number (i.e. 10 in the magic square above) multiplied by 3 is the sum of the rows or columns or diagonals.

Rule 2: The central number is always half of the adjacent two numbers, for example (8 + 12)/ 2 = 10,

(15 + 5)/2 = 10, (9 + 11)/2 = 10 or (7 + 13)/ 2 = 10

So, how do we proceed?

Let us take the above example;

9		11
13

      Can you solve this? It is so easy,

      the central number is (9 + 11)/2 = 10

      So, the sum of rows or columns or diagonals = 10 x 3 = 30

Now I am sure you can complete the table.

Let us look at other combinations possible:

		7
	10
		12

In this case since the central number is given, we immediately have the

Sum of row or column or diagonal = 10 x 3 = 30

Once you know this, rest is easy to fill up.

9
13	5

How about this combination?

Finding the central number is difficult!!

You may choose to use this formula to find the central number:

[(9 + 5) + 2 x 13]/4 = 40/4 = 10

Sum of row or column or diagonal = 10 x 3 = 30

Once you know this, rest is easy to fill up.

Now do you feel any better with magic squares?