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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);
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:
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 ...
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} .
In 2006 Google launched a beta release spreadsheet web application, this is currently known as Google Sheets and one of the applications provided in Google Drive. [16] A spreadsheet consists of a table of cells arranged into rows and columns and referred to by the X and Y locations. X locations, the columns, are normally represented by letters ...
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]
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 ...
For example, A104157 enumerates the "smallest prime of n 2 consecutive primes to form an n × n magic square of least magic constant, or 0 if no such magic square exists." The value of a(1) (a 1 × 1 magic square) is 2; a(3) is 1480028129. But there is no such 2 × 2 magic square, so a(2) is 0.