Tag Archives: magic square

30×30 Magic Square inside a Magic Square

30x30 Magic Squares inside a Magic Square

30×30 Magic Squares inside a Magic Square

This is a special construction of a Magic Square wherein we start with a small Magic Square (centermost one in the figure) and add rows and columns around it, ensuring that we have a Magic Square at each stage. This Magic Square has been color-coded to make the Magic Squares clearer.

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.