Magic Squares Explained

Magic Squares Explained Magic Squares are simple to explain yet they can easily lead to hours of fun mathematical explorations For those of you who are new to the Magic Squares problem the idea is this Given n greater than or equal to 3 can you find an n by n grid of n 2 consecutive numbers where all the columns rows and diagonals add up to the same magic number

A magic square is an arrangement of numbers in a square in which the sum of each row column and main diagonal is the same The name for this shared total is the magic number Traditionally magic squares contain the integers from 1 to n2 where n is the order of the magic square A magic square is a square array of numbers consisting of the distinct positive integers 1 2 n 2 arranged such that the sum of the n numbers in any horizontal vertical or main diagonal line is always the same number Kraitchik 1942 p 142 Andrews 1960 p 1 Gardner 1961 p 130 Madachy 1979 p 84 Benson and Jacoby 1981 p 3

Magic Squares Explained

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Magic Squares Explained
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Magic Squares Spheres And Tori Area Magic Squares Of Order 4
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What is Magic Square Magic squares are square grids with a special arrangement of numbers in those grids The numbers are special because every row column and the diagonal sum is the same number No number is Semi magic square when its rows and columns sum to give the magic constant Simple magic square when its rows columns and two diagonals sum to give magic constant and no more They are also known as ordinary magic squares or normal magic squares

Magic Squares are square grids with a special arrangement of numbers in them These numbers are special because every row column and diagonal adds up to the same number So for the example below 15 is the magic number Magic squares have intrigued people for thousands of years and in ancient times they were thought to be connected with the supernatural and hence magical Today we might still think of them as being magical for the sum of each row column and diagonal is a constant the magic constant

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A magic square is a n n grid of numbers such that the sum of each row is equal and equal to the sum of each column Some de nitions also require the sum along the main diagonals to add to the same total Leonhard Euler Magic SquaresPoyraz Ali G ner The Basics of Magic Squares Imagine waking up in a room finding a plane with a 3x3 grid painted on it balanced on a little marble with 45 cubes next to it

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Magic Squares are simple to explain yet they can easily lead to hours of fun mathematical explorations For those of you who are new to the Magic Squares problem the idea is this Given n greater than or equal to 3 can you find an n by n grid of n 2 consecutive numbers where all the columns rows and diagonals add up to the same magic number

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The Maths Of Magic Squares

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A magic square is an arrangement of numbers in a square in which the sum of each row column and main diagonal is the same The name for this shared total is the magic number Traditionally magic squares contain the integers from 1 to n2 where n is the order of the magic square


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Magic Squares Explained - Semi magic square when its rows and columns sum to give the magic constant Simple magic square when its rows columns and two diagonals sum to give magic constant and no more They are also known as ordinary magic squares or normal magic squares