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Questions tagged [magic-square]

A Magic Square of order $n$ is an arrangement of $n^2$ numbers, usually distinct integers, in a square, such that the $n$ numbers in all rows, all columns, and both diagonals sum to the same constant.

A Magic Square of order n is an arrangement of $n^2$ numbers, usually distinct integers, in a square, such that the $n$ numbers in all rows, all columns, and both diagonals sum to the same constant.

For example, using $1\dots9$, this magic square sums to $15$: $$ \begin{matrix}2&7&6\\9&5&1\\4&3&8\end{matrix} $$

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Fill out a 3x3 square with 9 different positive integers such that the product of each row, column, and diagonal is equal to each other

I have an idea, which is to put 2 in the middle and have the rest multiply up to an even number, but I can't seem to find an even number with that many factors.
Gerard L.
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How is this a magic square?

I have the following magic square but cannot determine how the square is actually "magic". It's a 3x3 as seen below in red with the green showing a few examples of row sums. Each vertical and horizontal multiplication, for example AxBxC = 120,…
DT.DTDG
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Magic Square Diagonals Theorems/Proof

We want to describe via a picture a set of subsets of a square which are something like diagonals, but are not quite the same. We’ll call them steep diagonals. One of them, labelled e, is illustrated in the square below; the other 6 are parallel to…
Sophia
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Prove Is a Filled Magic Square

Can someone prove that if $S$ is a filled magic square, and $T$ is obtained from $S$ by switching two rows or two columns, then $T$ is also a filled magic square. So an example that I came up with was: and are magic squares related by the…
Daniella
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Constructing a magic square

I am currently learning about magic squares and I want to construct a magic square. How do I construct a 6-by-6 or a 7-by-7 filled magic square, using the integers 0 to 35 or 0 to 48.
Daniella
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Prove Magic Square

Suppose that $S$ is a square such that the sum of the entries in each row is some number $R$, and the sum of the entries in each column is some number $C$. Prove that $S$ is in fact a magic square, i.e., $R = C$. What I thought? The sum of a row is…
Daniella
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Is this magic square solvable with no more information?

This magic square question was given to my brothers sixth grader: ------------------- | 122 | | 126 | ------------------- | 129 | | | ------------------- | | | | ------------------- This is literally all the information that…
Davor
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Magic square with not consecutive numbers

A magic square should be filled with the following numbers: 7,8,9,11,12,13,15,16,17. The numbers: 15, 16 and 17 are already placed as the following: $$\begin{array}{|c|c|c|} \hline &17\\ \hline 15&&\\ \hline &&16\\ …
Husam
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Proof that magic square cannot be transformed

How do I prove that the first magic square below cannot be transformed into the second by a sequence of row and column…
Sophia
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