Category Archives: Tutorial

How to construct a 3×3 Magic Square for a Given Total

Let the given Number be 63. We will get to the following 3 X 3 Magic-Total 63.

[table id=construct-magic-square-for-given-total-63__3x3 /]

  1. Let us do 3 x 3 magic square with Magic Sum of 63.
  2. From 63, minus 15 ( the row total of 3×3 base magic square. (63-15=48)
  3. Divide 48 by 3(since we have decided to do 3×3 magic square (48/3=16).
  4. Add one to this (16+1=17)
  5. Now start constructing a 3 x 3 magic square with 17 as the beginning number and (Top row middle – Just in the place of 1).


  • For constructing 3×3 magic square -15, then divide by 3, then add 1.
  • For constructing 4×4 magic square -34, then divide by 4, then add 1. and
  • For constructing 5×5 magic square -65, then divide by 5, then add 1.

While dividing by 3 or 4 or 5, if any fraction comes, put that fraction in all the squares. You should not delete or make it decimal.

How to construct 6 x 6 Magic square

Here is a 6 x 6 Magic Square with Magic-Total 111

[table id=6x6-magic-square--total-111 /]

  1. Draw a 6 x 6 empty square.
  2. Draw a bold line after the third square, Horizontally and vertically.
  3. Now the 6×6 magic square will be divided into four 3 x 3 Magic squares.
  4. Start filling the 3 x 3 magic square on the top left with numbers 1 to 9. and top right from 19 to 27, bottom left with 28 to 36 and bottom right with 10 to 18.
  5. Now exchange the numbers 8,5,4 from the top left 3×3 square to the bottommost left 3×3 squares with the numbers 35, 32, 31 and vice versa.
  6. Your 6×6 magic square is ready. All vertical, Horizontal and both diagonal totals are equal ( 111) .

How to construct a 4 x 4 magic square

This is a 4 x 4 Magic Square with Magic-Total 34

[table id=4x4-magic-square /]

  1. Draw a 4×4 empty square.
  2. Draw two diagonals.
  3. Start counting all the squares from the top left towards right.
  4. Now start writing numbers 1 to 16, count all squares and write numbers ONLY IN THE BLANK SQUARES (2,3,5,8,9,12,14,15 are to be written)
  5. Now start writing number from the bottom most right square towards left, count all squares, BUT WRITE NUMBERS ONLY IN THE SQUARES HAVING DIAGONAL LINES ONLY (1,4,6,7,10,11,13 AND 16) ARE TO BE WRITTEN.
  6. Magic square 4×4 is ready.

Note:  This method is applicable only for 4×4 magic square.  For 6×6, 8×8 there are separate methods available.


How to construct an odd order magic square?

This is a 3 X 3 Magic square with Magic-Total 15

[table id=3x3-magic-square__total-15 /]

We will discuss the construction of this, step-by-step.

  1.  Put number one in the upper middle square.
  2. Always write the next number ONE SQUARE RIGHT AND ONE SQUARE ABOVE
    • Beyond boundary in the upper side, write it vertically down most square.
    • Beyond the boundary in the right side, write it in the horizontally leftmost Square.
    • When the square is already filled with a number, just step-down one square vertically below.
  4. And after the Top right square always write the next number one square vertically below.

With these simple steps you can make any biggest “ODD NUMBER MAGIC SQUARE IN THE WORLD”