In recreational mathematics and the theory of magic squares, a broken diagonal is a set of n cells forming two parallel diagonal lines in the square. Alternatively, these two lines can be thought of as wrapping around the boundaries of the square to form a single sequence. A magic square in which the broken diagonals have the same sum as the rows, columns, and diagonals is called a panmagic square. Examples of broken diagonals from the below square are as follows: 3,12,14,5; 10,1,7,16; 10,13,7,4; 15,8,2,9; 15,12,2,5; and 6,13,11,4. 111x ; ; 111x111x