# Magic Squares – What are they?

Magic squares are a set of numbers filled in a 3 x 3, 4 x 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 x 3, 4 x 4, 5 x 5….etc.
2. Generally a 3 x 3 magic square is filled with numbers 1 to 9 and 4 x 4 magic square is filled with 1 to 16,…… In general a “n x n” magic square will be filled with 1 to n square numbers.
3. In general in a “n x n” magic square will have “n” rows and “n” columns and n square Small squares.
4. After filling all squares  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 + n square ) / 2} ……. {( 1 + n square ) 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 x 3, 4 x 4, 5 x 5… upto infinite.  Magic squares for a particular number, particular size and for a given space interval is at our choice.
9. Also we can make magic squares for a given number, given year or given date of birth etc.