Never seen before.

By boarded magic squares we understand that if we remove the external border still we are left with magic squares of lower orders with sequential entries. Single digits bordered magic squares are well-known. This work is for double digits not non in the literature. We are bringing this concept for the first time in the literature. During these days some studies in this directions are made. These are given below in seperate parts. One for even number orders and another for odd number orders. Most of the work is done manually. A special trick is applied to bring all these magic squares.

Lower order double digits magic squares can also be calculated using software by Harry While: Downloads (

Double Digits Bordered Magic Squares:
Even Number Orders

Double Digits Bordered Magic Squares:
Odd Number Orders

The above work is done as extended study for each order. This work of double digits magic squares just given one example in each case for orders 7 to 108. See below few examples.

In the end excel files of completed work are also attached for download.

Double Digits Bordered Magic Squares: Orders 7 to 30

For more examples see the excel files below:

Excel files for Download

File 1: Odd Number Orders

File 2: Even Number Orders

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