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Bordered magic square when it is a magic square and it remains magic when the rows and columns on the outer edge are removed. They are also called concentric bordered magic squares if removing a border of a square successively gives another smaller bordered magic square. Bordered magic square do not exist for order 4.
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order n – that is, a magic square which contains the numbers 1, 2, ..., n 2 – the magic constant is = +.
The Siamese method, or De la Loubère method, is a simple method to construct any size of n-odd magic squares (i.e. number squares in which the sums of all rows, columns and diagonals are identical). The method was brought to France in 1688 by the French mathematician and diplomat Simon de la Loubère , [ 1 ] as he was returning from his 1687 ...
He later was the first to publish diagrams of all 58 magic tesseracts of order 3. [2] Hendricks was also an authority on the design of inlaid magic squares and cubes (and in 1999, a magic tesseract). Following his retirement, he gave many public lectures on magic squares and cubes in schools and in-service teacher's conventions in Canada and ...
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.
As a running example, we consider a 10×10 magic square, where we have divided the square into four quarters. The quarter A contains a magic square of numbers from 1 to 25, B a magic square of numbers from 26 to 50, C a magic square of numbers from 51 to 75, and D a magic square of numbers from 76 to 100.
The numbers are based on a $50 a square game, with a $625 payout for the 1st and 3rd quarters, a $1,250 payout for halftime, and a $2,500 payout for the end of the game. (The cells are colored ...
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 ...