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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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Possible solution for the magic square of squares problem

I was fiddling around with this problem for 3x3 magic squares after seeing another Numberphile video and I got to a point where I'm not sure where the error in proving no such magic squares exists is, so I would appreciate someone pointing it…
milin
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Magic square variation

I have a rather difficult variation of magic squares: In the below image, all numbers from 1 to 24 must be placed in the 24 closed areas, in such a way that all numbers in areas of each circle must sum to 80. Each number must be placed only once.…
Pradeep Suny
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3 x 3 Grid Square

For a question that I need to answer, we have to show that there is only one arrangement for which, in a $3\times 3$ grid in which the numbers from $1$ to $9$ are placed and $5$ is the centre number, the sum of the $4$ numbers in every $2\times 2$…
Maths
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What are the possible sums of an $n \times n$ magic square?

An $n\times n$ magic square summing to $S$ is an assignment of distinct integers to the $n^2$ entries of an $n \times n$ grid such that each row, column, and main diagonal sums to $S$. It is well known that for $n>2$, an $n\times n$ magic square…
dshin
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Is it possible to generalize Magic Squares to infinite dimensional matrices?

I know that magic squares exist: Summing over every row or column and diagonal one gets the same sum. My question is whether it is possible to generalize magic squares in such a way that the numbers are real and instead of summing over rows and…
eeqesri
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5x5 Magic Square + Even Odd restriction

The Problem Take a $5\times 5$ grid and populate it with the numbers $1$ to $25$ such that the sum of all rows, columns, and both main diagonals are equal. Additionally, only even numbers are allowed on the corners I found the "go up one and…
Aloha
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The sum of integers in each row / column / major diagonal of a Magic Square of order $N$ is $\dfrac{N(N^2+1)}{2}$

Prove that the sum of integers in each row / column / major diagonal of a Magic Square of order $N$ is equal to $$\dfrac{N(N^2+1)}{2}$$ I have tested the formula on Durer's "1514" magic square and it holds (where N=4).
Naz
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Magic square of a given date

How to create a magic square if we know a date. Eg-22-04-2014 The first column should have 22 2nd-04 3rd-20 and 4th -14. I believe ramanujan created the same thing for his birthday but I don't know the method he used. Please help. Is there any…
geek101
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Proof of magic square algorithm?

Proof of magic square algorithm? Why does it work? Where the algorithm to create one is to add the next number above diagonally to the right. If you go off the grid, you wrap, as if he grid repeats. If the spot is taken, you write the next…
JackOfAll
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"Magic matrix" formula inaccuracy

I was reading Martin Gardner's "hexaflexagons and other mathematical diversions" in which he describes a magic matrix - a different type of magic square in which all numbers of different rows and columns add up to the "magic number" he explains the…
Math chiller
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Understanding specific explanation of centre value of 3x3 magic square

EDIT. Put another way, we know from the summation that each line must equal 15. 4 lines should equal 60, but there is some over-counting. How can we know that this over-counting is by 15, without knowing in advance that the middle square is worth…
Robin Andrews
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Why does the below process for a 4x4 grid with consecutive numbers 1-16 yield the magic constant 34?

I have encountered a procedure that produces the magic constant 34 for a 4x4 grid with the numbers 1-16 arranged in consecutive order, and I can't figure out why it works. It is as follows: Arrange the numbers 1 to 16 into a 4 by 4 grid. Choose a…
Wallfacer
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Solving magic square results in incorrect answer

I'm trying to help my daughter with her homework. I'm not looking for an answer, but the process. She has been asked to solve this: [ [ ?, 36, ? ] [ 9, 6, 4 ] [ -12, ?, ? ] ] My approach was to substitute letters for the missing…
Chris Snow
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$3\times3$ Magic Square and hidden formula [Solved]

I was doing the $3 \times3$ Magic Square of Squares problem -- found here: http://www.multimagie.com/English/SquaresOfSquaresSearch.htm -- and I figured out that if such Magic square exists with $9$ distinct numbers, then it must satisfy the…
user356448
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I did a proof for magic square of squares and perfect cuboid.

I did the proof for non-existence of magic square of squares. I am looking great guidelines on preparation and submission for publication. the main areas what I want assistance is 1. the format of proof (content) 2. the best organization for…
geinamo
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