Grogono Photo Pages
Size:  Index   3x3   4x4   5x5   6x6   7x7   8x8   9x9   10x10   11x11   12x12   13x13 

Make Your Own: Any Prime   3x3   4x4   5x5 

 Make Your Own Magic Square: 5x5

The magic square below is the sum
of the patterns that these numbers
make. Use them or enter new ones
and then click
ArrowRight ArrowDown
To understand the structure, move the
mouse over the blue arrows and wait.
Look at the pattern of your numbers
in the square below
The Bottom Right number
(under the blue down arrow)
above is the first number in
the sequence for the square.
By convention it is "1", but
any number can be used.

Try changing the bottom row
above: use "5,4,3,2,1,0"
instead, do you get the same
result as "4,3,2,1,0,1"?

You can also try experimenting
by writing in your own numbers
in the red squares. To see the
totals, press
The numbers at the top and
the left are the sums for the
diagonal rows - including the
broken diagonals.


The numbers in the Red Squares form the 3x3 magic Square. The numbers beside the Red Squares show the totals for each row. The horizontal and vertical totals are to the right and below in green squares. The other, blue, squares show the diagonal totals - including all of the "broken diagonals". You can make your own Magic Square in two ways. Try both methods:

  1. Enter your own numbers into the Red Squares and then click on "Add Rows". You can experiment with any numbers using any strategy.
  2. Put numbers in the top set of squares and click on "Make Square". If you try this method try any numbers you like. But, to get a conventional square use:

How does this Work?:

Move your Mouse over a Blue Arrow and WAIT. Observe the numbers in the Magic Square. This reveals the underlying structure of a 5x5 Magic Square. One pattern represents the large numbers and the other the small ones. All 5x5 Pan-Magic Squares have a similar underlying structure. By changing the order of the numbers in these two sets of numbers, 144 distinct squares are possible. Reflecting, rotating, and translocating, each square multiplies this by 200 to give a grand total of 28,800 different 5x5 pan-magic squares. This method always produces "Pan-magic" squares, i.e., all the Diagonals are always "Magic".

Make Your Own: Any Prime   3x3   4x4   5x5 


Copyright © Mar 2010 Magic Squares
Mar 6, 2010