direktori wisata tirta 2012 (8)

8/12/2019 Direktori Wisata Tirta 2012 (8)

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What is a magic-square ?

A magic square is a box filled with digits in such a manner that the total of allrows, columns and diagonals is the same..

Let us have a look at such a magic square…. Below is a magic square formedwith the numbers from 1 to 9

As we can see, the total of each row, column and diagonal is the same..i.e. 15

672

159

834



4 + 3+ 8 = 15

9 + 5 + 1 = 15

2 + 7+ 6 = 15

672159

834

5

Let us check the totals of each rows, columns and diagonals

ROWS COLUMNS

4 + 9 + 2 = 15

3 + 5 + 7 = 15

8 + 1+ 6 = 15

DIAGONALS

4 + 5 + 6 = 15

2 + 5 + 8 = 15



Such a square where each row, column and diagonal givesthe same total is called a Magic Square

What we saw just now was a (3 x 3) magic square…becausethere are 3 rows and 3 columns on each side

Since there were 9 squares in the grid, we used numbers from1 to 9

Next, we will see a (5 x 5) magic square



11 10 4 23 17

18 12 6 5 2425 19 13 7 1

2 21 20 14 8

9 3 22 16 15

This is a 5 by 5 magic square……

It has numbers from 1 to 25

The total of each column, row and diagonal is 65



We will now study how to form these magic squares…

Often questions on Magic Squares are asked in

competitive exams.Those who do not know the art of forming these squaresuse ‘trial and error method.’ However, it is virtuallyimpossible for most people to form these squares using‘trial and error’ method

In this presentation, I will teach you the correct method.

I will teach you which number to put where so that you

can get the correct answer instantly..Its actually very simple



There are 4 rules that we will follow :

A) Put 1 in the centre-square of last column

B) Go to South-East and put the next number thereC) If south east is full; go to west and put the next number

D) After filling the last square of the grid, GO TO WEST

NORTH

WEST EAST

SOUTH

SOUTH-EAST

DIRECTIONS



A) Put 1 in the centre-square of last columnB) Go to South-East and put the next number thereC) If south east is full; go to west and put the next number

D) After filling the last square of the grid, GO TO WEST

Let us Begin !



1

Rule 1 says put 1 in centre square of last column

So we put 1 there



2

1

Rule 2 says go to south-east

However, there is no square in south-east. So we assumean imaginary square.

But you cannot put a number in an imaginary square.Hence 2 will be written in a square farthest from it. Look

at the figure.



3

2

1

From 2 we go to south-east and put 3



3

2

1

4

From 3 we go to south-east.

But there is no square, so again we form animaginary square and put the next number in thesquare farthest from it.

This is how it will be done



3

2

15

4

From 4 we go to south-east and put 5



3

2

156

4

From 5 we go to south-east to put 6. But, south eastis full. In this case, we refer the third rule which says‘if south - east is full go to west’

So we go to the west of 5 and put 6



3

82

1756

4

From 6 we go to south-east to put 7. From 7 we go tosouth-east and put 8



39

82

1756

410

From 8 we go to south-east, use imaginary square and put 9From 9 we go to south-east use imaginary square put 10



1539

8142

17135612

41011

Next, south-east of 10 is full, so we go to west and write 11

From 11 south-east we write 12, from 12 south-east wewrite 13 and similarly write down 14 and 15



151639

8142

17135612

41011

15 is the last square of the grid. We come to the fourth andlast rule which says :‘ After filling the last square of the grid, GO TO WEST’

So, from 15 we go to west and write down 16



151639

814202

171319561218

1741011

From 16 we go to 17 From 17 we go to 18From 18 we go to 19 From 19 we go to 20



15162239

81420212

1713192524561218

172341011

From 20 we go to 21 From 21 we go to 22From 22 we go to 23 From 23 we go to 24

From 24 we go to 25



15162239

81420212

1713192524561218

172341011

And Lo !

Our Magic Square is Formed !!



Using this technique, you can form Magic Squares of (3x3),(5x5) (7x7) and so on. You cannot use this technique toform magic squares of even numbers like (2x2), (4x4) etc.

Here’s a magic square of (7 x 7). Observe carefully, how thenumbers are placed.



22 21 13 5 46 38 3031 23 15 14 6 47 3940 32 24 16 8 7 48

49 41 33 25 17 9 12 43 42 34 26 18 1011 3 44 36 35 27 19

20 12 4 45 37 29 28

direktori wisata tirta 2012 (8)

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