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

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.

Explanation:

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:
   • Numbers 20, 15, 10, 5, and 0 in one row - in any order.
   • Numbers 4, 3, 2, 1, 0, and 1 in the other row.

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".