Category Archives: recreational math

How to construct an odd order magic square?

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

[table id=3×3-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
  3. AND WHEN IT GOES:
    • 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”

These steps are useful ONLY FOR ODD NUMBER MAGIC SQUARE AND WILL NOT BE USEFUL FOR EVEN NUMBER MAGIC SQUARES.

Magic Squares – What are they?

Magic squares are a set of numbers filled in a 3×3, 4×4,… squares and after filling it, all the vertical, Horizontal and both diagonal totals are equal.

Properties of the Magic Square:

  1. Magic squares are made in 3×3, 4×4, 5×5….etc.
  2. Generally a 3×3 magic square is filled with numbers 1 to 9 and 4×4 magic square is filled with 1 to 16,…… In general a “nxn” magic square will be filled with 1 to n2 numbers.
  3. In general in a “nxn” magic square will have “n” rows and “n” columns and n2 Small squares.
  4. After filling all columns, ALL VERTICAL, ALL HORIZONTAL AND BOTH DIAGONAL THE TOTALS ARE EQUAL.
  5. A magic square done from 1 to 9, 1 to 16,… are called as Base Magic square.
  6. The total of a row/column of a Base Magic Square will be “First number plus the Last number added together, divided by two, and then multiplied by the Number of rows”. i.e. {( 1+n2 ) / 2} ……. {( 1+n2 ) divided 2}
  7. Generally natural numbers 1,2,3,… are used for forming the magic squares and we can use fractions, zero, negative numbers and squares, cubes etc etc…
  8. We can make 3×3, 4×4, 5×5… magic squares for a particular number, and for a given space interval at our choice.
  9. Also we can make magic squares for a given number, given year or given date of birth etc.

Srinivasa Ramanujan – 16×16 Biography Magic Square

This Biography Magic Square summarizes the important events that in the life of Sri Srinivasa Ramanujan.

How it was constructed:

Important dates in the life of Ramanujan were taken, two digits at a time, representing either the date or the month or the first or second part of the four-digit year. As an example, Ramanujan’s birth-day 22-12-1887 is taken in four separate entries as 22 12 18 87. These were then laid out in the top of the Magic Square, in the first column. Then, a complete Magic Square was built on top of these numbers, with the following additional feature : each  square indicated by a separate color (in this case, there are 4 such 4×4 sub-sqaures), which are magic squares themselves!

Srinivasa Ramanujan 16x16 biography Magic Square
Srinivasa Ramanujan 16×16 biography Magic Square

(Download Ramanujan_16x16_biography_Magic_Square in excel format).

This is a smaller version of the 100-by-100 and 125-by-125 biography magic squares that we have constructed.

This was earlier published in an article “A Unique Novel Homage to the Great Indian Mathematician” in the March 2013 (Volume 23, Pg 146-147) Mathematics Newsletter published by the Ramanujan Mathematics Society. (download free).

If you find this interesting, you could construct your own! If you want some help, drop a mail to me at contact[at]jollymaths[dot]com.