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All of the squares given by Nagarjuna are 4×4 magic squares, and one of them is called Nagarjuniya after him. Nagarjuna gave a method of constructing 4×4 magic square using a primary skeleton square, given an odd or even magic sum. [18] The Nagarjuniya square is given below, and has the sum total of 100.
The number zero for n = 6 is an example of a more general phenomenon: associative magic squares do not exist for values of n that are singly even (equal to 2 modulo 4). [3] Every associative magic square of even order forms a singular matrix, but associative magic squares of odd order can be singular or nonsingular. [4]
All 4 × 4 pandiagonal magic squares using numbers 1-16 without duplicates are obtained by letting a equal 1; letting b, c, d, and e equal 1, 2, 4, and 8 in some order; and applying some translation. For example, with b = 1 , c = 2 , d = 4 , and e = 8 , we have the magic square
The inscription containing the 4×4 most-perfect magic square. The temple has an inscription with a magic square, called the "Jaina square". This is one of the oldest known 4×4 magic squares, [8] as well as one of the oldest known most-perfect magic squares. [9] This magic square contains all the numbers from 1 to 16.
A most-perfect magic square of order n is a magic square containing the numbers 1 to n 2 with two additional properties: Each 2 × 2 subsquare sums to 2 s , where s = n 2 + 1. All pairs of integers distant n /2 along a (major) diagonal sum to s .
The first 4-magic square was constructed by Charles Devimeux in 1983 and was a 256-order square. A 4-magic square of order 512 was constructed in May 2001 by André Viricel and Christian Boyer. [1] The first 5-magic square, of order 1024 arrived about one month later, in June 2001 again by Viricel and Boyer. They also presented a smaller 4 ...
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Conway's LUX method for magic squares is an algorithm by John Horton Conway for creating magic squares of order 4n+2, ... 4 in the centre square of the top row, ...