Definition:Pandiagonal Magic Square

Definition

A pandiagonal magic square is an arrangement of $n^2$ numbers into an $n \times n$ square array such that:

the sum of the elements of each row

the sum of the elements in each column

the sum of the elements along each diagonal

the sum of the elements along each broken diagonal

are the same.

Hence a pandiagonal magic square is a magic square, with the added property of the broken diagonals.

Also known as

A pandiagonal magic square is also known as:

a diabolic square, a diabolical square or a diabolical magic square

a panmagic square.

Examples

Order $4$

$\begin {array} {|c|c|c|c|} \hline 1 & 8 & 11 & 14 \\ \hline 12 & 13 & 2 & 7 \\ \hline 6 & 3 & 16 & 9 \\ \hline 15 & 10 & 5 & 4 \\ \hline \end {array}$

Also see

• Definition:Magic Square

• Results about pandiagonal magic squares can be found here.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): magic square

• Weisstein, Eric W. "Panmagic Square." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PanmagicSquare.html
• Weisstein, Eric W. "Magic Square." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MagicSquare.html