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The first dateable instance of the fourth-order magic square occurred in 587 CE in India. Specimens of magic squares of order 3 to 9 appear in an encyclopedia from Baghdad c. 983, the Encyclopedia of the Brethren of Purity (Rasa'il Ikhwan al-Safa). By the end of the 12th century, the general methods for constructing magic squares were well ...
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.
In their book, Kathleen Ollerenshaw and David S. Brée give a method of construction and enumeration of all most-perfect magic squares. They also show that there is a one-to-one correspondence between reversible squares and most-perfect magic squares. For n = 36, there are about 2.7 × 10 44 essentially different most-perfect magic squares.
A kuberakolam, rendered kubera kolam, is a magic square of order three constructed using rice flour and drawn on the floors of several houses in South India. In Hindu mythology, Kubera is a god of riches and wealth. It is believed that if one worships the Kuberakolam as ordained in the scriptures, one would be rewarded with wealth and ...
The numbers in each row, and in each column, and the numbers that run diagonally in both directions, all add up to the number 34. M is called a strongly magic square if the following condition is satisfied: [5] For all m, n such that 1 ≤ m ≤ 4, 1 ≤ n ≤ 4, we have
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For example the following sequence can be used to form an order 3 magic square according to the Siamese method (9 boxes): 5, 10, 15, 20, 25, 30, 35, 40, 45 (the magic sum gives 75, for all rows, columns and diagonals). The magic sum in these cases will be the sum of the arithmetic progression used divided by the order of the magic square.
Consequently, all 4 × 4 pandiagonal magic squares that are associative must have duplicate cells. 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.