Success Institute

Tnpsc group 1
முதல் நிலைத் தேர்வை எதிர்கொள்வதற்கு குறிப்புகள் -
எனது கட்டுரை 30-08-2022
இந்து தமிழ் நாளிதழ் திசைகாட்டி பகுதியில் பிரசுரமாகியுள்ளது.

4 × 4 MAGIC SQUARES

To form a 4 × 4 Magic Square, let us take 16 positions horizontally. For instance, take first 16 natural numbers.

We can create 4 × 4 Magic Squares with any 16 numbers (positive or negative ) which form an Airthmetic progression.

Interchange the 2nd position from the left and 2nd position from the right (or 15th position from the left),
the 3rd position from the left and 3rd position from the right (or 14th position from the left).
And similarly the 5th position from the left and 5th position from the right (or 12th position from the left), the 9th position from the left and 9th position from the right (or 8th position from the left). All other positions must be as it is.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

15 14 12 9 8 5 3 2

After interchanging the positions, the new arrangement is

1 15 14 4 12 6 7 9 8 10 11 5 13 3 2 16

Original position

1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

1. - - 4. Fix all the four corner positions

- 6 7 - and central four positions as it is

- 10 11 - which is shown on the left.

13. - - 16

1 15 14 4 After the interchanged positions

12 6 7 9 is shown on the left.

8 10 11 5 Now the Magic Square formed.

13 3 2 16

Horizontally, vertically and diagonally, the total is 34.

This total is nothing but sum of Middle four numbers.

Here 6 + 7 + 10 + 11 = 34.

Moreover 1 + 15 + 12 + 6 = 34

14 + 4 + 7 + 9 = 34

8 + 10 + 13 + 3 = 34

11 + 5 + 2 + 16 = 34