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For example, a normal 8 × 8 square will always equate to 260 for each row, column, or diagonal. The normal magic constant of order n is n 3 + n / 2 . The largest magic constant of normal magic square which is also a: triangular number is 15 (solve the Diophantine equation x 2 = y 3 + 16y + 16, where y is divisible by 4);
The constant that is the sum of any row, or column, or diagonal is called the magic constant or magic sum, M. Every normal magic square has a constant dependent on the order n , calculated by the formula M = n ( n 2 + 1 ) / 2 {\displaystyle M=n(n^{2}+1)/2} .
A graph is vertex-magic if its vertices can be labelled so that the sum on any edge is the same. It is total magic if its edges and vertices can be labelled so that the vertex label plus the sum of labels on edges incident with that vertex is a constant. There are a great many variations on the concept of magic labelling of a graph.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
A magic hexagon of order n is an arrangement of numbers in a centered hexagonal pattern with n cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant M. A normal magic hexagon contains the consecutive integers from 1 to 3n 2 − 3n + 1. Normal magic hexagons exist only for n = 1 ...
Magic squares In 1992, Demirörs, Rafraf, and Tanik published a method for converting some magic squares into n-queens solutions, and vice versa. [18] Latin squares In an n×n matrix, place each digit 1 through n in n locations in the matrix so that no two instances of the same digit are in the same row or column. Exact cover
In contrast with its rows and columns, the diagonals of this square do not sum to 27; however, their mean is 27, as one diagonal adds to 23 while the other adds to 31.. All prime reciprocals in any base with a period will generate magic squares where all rows and columns produce a magic constant, and only a select few will be full, such that their diagonals, rows and columns collectively yield ...
In a magic square, the magic constant is the sum of numbers in each row, column, and diagonal, which is the same. For magic squares of order n, the magic constant is given by the formula (+). [4] The magic constant 9855 [5] for the magic square of order 27 can be calculated [2] as follows: