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A random assortment of puzzles, together with reader responses to earlier problems 1976 Jan: A breakthrough in magic squares, and the first perfect magic cube: 1976 Feb: Some elegant brick-packing problems, and a new order-7 perfect magic cube 1976 Mar: On the fabric of inductive logic, and some probability paradoxes 1976 Apr
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.
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Print/export Download as PDF; Printable version; In other projects ... Pages in category "Magic squares" The following 47 pages are in this category, out of 47 total.
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.
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]