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- Magic_square abstract "In recreational mathematics, a magic square is an arrangement of distinct numbers (i.e. each number is used once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the forward and backward main diagonals, all add up to the same number. A magic square has the same number of rows as it has columns, and in conventional math notation, "n" stands for the number of rows (and columns) it has. Thus, a magic square always contains n2 numbers, and its size (the number of rows [and columns] it has) is described as being "of order n". A magic square that contains the integers from 1 to n2 is called a normal magic square. (The term "magic square" is also sometimes used to refer to any of various types of word squares.)It is possible to construct a normal magic square of any size except 2 × 2 (that is, where n = 2), although the solution to a magic square where n = 1 is trivial, since it consists simply of a single cell containing the number 1. The smallest nontrivial case, shown below, is a 3 × 3 grid (that is, a magic square of order 3).The constant that is the sum of every row, column and diagonal is called the magic constant or magic sum, M. Every normal magic square has a unique constant determined solely by the value of n, which can be calculated using this formula:For example, if n = 3, the formula says M = [3 (32 + 1)]/2, which simplifies to 15. For normal magic squares of order n = 3, 4, 5, 6, 7, and 8, the magic constants are, respectively: 15, 34, 65, 111, 175, and 260. (See sequence A006003 in the OEIS)".
- Magic_square thumbnail Magicsquareexample.svg?width=300.
- Magic_square wikiPageExternalLink 0408230.
- Magic_square wikiPageExternalLink BensonDickinson.htm.
- Magic_square wikiPageExternalLink 1.
- Magic_square wikiPageExternalLink ?pa=content&sa=viewDocument&nodeId=528&bodyId=784.
- Magic_square wikiPageExternalLink home-page.
- Magic_square wikiPageExternalLink www.MagicSquaresBook.com.
- Magic_square wikiPageExternalLink magic_problem2.html.
- Magic_square wikiPageExternalLink index.html.
- Magic_square wikiPageExternalLink mag4en.htm.
- Magic_square wikiPageExternalLink article.aspx?id=19305.
- Magic_square wikiPageExternalLink abiyeving.htm.
- Magic_square wikiPageID "52202".
- Magic_square wikiPageRevisionID "606648935".
- Magic_square hasPhotoCollection Magic_square.
- Magic_square title "Magic Square".
- Magic_square urlname "MagicSquare".
- Magic_square subject Category:Magic_squares.
- Magic_square subject Category:Magic_symbols.
- Magic_square subject Category:Matrices.
- Magic_square subject Category:Unsolved_problems_in_mathematics.
- Magic_square comment "In recreational mathematics, a magic square is an arrangement of distinct numbers (i.e. each number is used once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the forward and backward main diagonals, all add up to the same number. A magic square has the same number of rows as it has columns, and in conventional math notation, "n" stands for the number of rows (and columns) it has.".
- Magic_square label "Carré magique (mathématiques)".
- Magic_square label "Cuadrado mágico".
- Magic_square label "Kwadrat magiczny (matematyka)".
- Magic_square label "Magic square".
- Magic_square label "Magisch vierkant".
- Magic_square label "Magisches Quadrat".
- Magic_square label "Quadrado mágico".
- Magic_square label "Quadrato magico".
- Magic_square label "Магический квадрат".
- Magic_square label "مربع سحري".
- Magic_square label "幻方".
- Magic_square label "魔方陣".
- Magic_square sameAs Magický_čtverec.
- Magic_square sameAs Magisches_Quadrat.
- Magic_square sameAs Cuadrado_mágico.
- Magic_square sameAs Carré_magique_(mathématiques).
- Magic_square sameAs Quadrato_magico.
- Magic_square sameAs 魔方陣.
- Magic_square sameAs 마방진.
- Magic_square sameAs Magisch_vierkant.
- Magic_square sameAs Kwadrat_magiczny_(matematyka).
- Magic_square sameAs Quadrado_mágico.
- Magic_square sameAs m.0dqt5.
- Magic_square sameAs Q192089.
- Magic_square sameAs Q192089.
- Magic_square wasDerivedFrom Magic_square?oldid=606648935.
- Magic_square depiction Magicsquareexample.svg.
- Magic_square isPrimaryTopicOf Magic_square.