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: 4x4

The magic square below is the sum
of the patterns that these numbers
make. Use them or enter new ones
and then click
ArrowDown ArrowDown ArrowDown ArrowDown 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.

Change the order of the
numbers "8 ,4, 2, 1" or try a
different number sequence
such as: "27, 9, 3, 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?:

By moving your Mouse over a Blue Arrow and waiting, you can observe the numbers in the Magic Square. This reveals the underlying structure of a 4x4 Pan-Magic Square - one in which all of the diagonals are magic. This method only produces pan-magic squares. You can change the sequence of the numbers you insert to get different squares. Although they may look very different there are actually only three fundamentally different designs. Rotation, reflection, and translocation provides 128 variations for each of these fundamenstal squares for a grand total of 384.

If you try putting in your own numbers you may succeed in making a magic square which is magic but where only main diagonals are magic.

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


Copyright © Mar 2010 Magic Squares
Mar 6, 2010