Animated Magic Square Magic Totals

As described on another page, the "Magic Total" is the common sum of all numbers in each row, each column and each corner diagonal.

There is, perhaps surprisingly, a reasonably simple formula for determining what the "Magic Total" for any given "basic" Magic Square will be.

However, before giving this formula, there is another term to explain, and that is the word "basic". In this context, it means that the Magic Square is constructed using consecutive numbers, starting with one.

Well, having got that out of the way, here is the formula:

((N * N * N) + N) / 2

where "N" is the number of cells on each side of the Magic Square.

To show a few examples, here are the "Magic Totals" for the Magic Squares of "orders" three up to seven:

OrderMagic Total

If you want to calculate the "Magic Total" for a larger Magic Square, enter a number from 3 - 100 and press the Calculate button:

The "Magic Total" for a Magic Square of order will be:

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This page is Copyright © 1997, Mark S. Farrar.
Created: Sunday 4th January, 1998

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