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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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Euler's 1779 Conjecture magic squares with 6x6 grid

I must be missing something, because it seems this question about Euler's 1779 Conjecture from Quanta Magazine is trivial: "Six army regiments each have six officers of six different ranks. Can the 36 officers be arranged in a 6-by-6 square so that…
Jim
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Find $y+z$ in the magic square, understanding the solution

I am having trouble understanding the alternate solution in my algebra book on system of equations for the problem below. In the magic square shown, the sums of the numbers in each row, column, and diagonal are the same. Five of these numbers are…
Bing Chilling
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I don’t get how this card trick works

So my friend made a square like this with this amount of cards in each pile 4 3 2 1 3 2 2 3 1 2 3 4 He then said that each line, horizontal and vertical, adds up to 10 cards. Then he asked me to pick a card from the cards left over after…
Boo
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Least starting fields to full resolve a $5 \times 5$ normal magic sqaure?

The image contains $16$ starting values. The remaining cells can be calculated by arithmetic operations, keeping in mind that the line sum is $65$. Now is there an arrangement where I need less starting values to full resolve the grid.
MANuNITED
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Magic Square given my condition

I am currently studying magic squares and ran into a bit of trouble. The concept I am learning about is a regular square. Below are the conditions of a regular square. We can say that an $n$-by-$n$ square is regular provided that: Each of the…
Sophia
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Strategies for solving Magic Squares

E11/38. By an exhaustive process of elimination I can work this out as 39, but there must be a quicker strategy for solving these kind of questions. Advice please.
user1495024
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Solving a 5x5 Magic Square

Is there any strategy involved in solving a 5x5 magic square like this? The array above the square are all the missing values.
Kenny Cheng
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Given a 4*4 square where all rows columns and diagonals must sum to a given value, what's the min number of squares needed to make the solution unique

If I have a $4\times 4$ square where all the rows columns and $2$ main diagonals must sum to a specific given value (same in each case), what's the minimum number of squares that are required to be filled in before there's only one possible way to…
blademan9999
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Proof of Magic Constant Formula

A magic square is a NxN square grid filled with distinct positive integers in the range 1,2...$N^2$. Each cell contains a different integer. The sum of the integers in each row, column and diagonal is equal and called magic constant. The Formula for…
atin
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Proof for Ramanujan's Oblong magic square

In his first notebook, Ramanujan discusses a $3 X 4$ magic square which he calls oblongs. In this he suggests that following would be the elements of a magic square: $$ \begin{array} {|r|r|r|} \hline A& C+D&A+2D&C+3D \\ \hline B+6D& B+4D& B+2D& B…
Deepa Kapoor
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Generate 3x3 magic square without diagonals

The question I recently bought a board game called Novem in which the set up rules indicates that 9 numbered tiles have to be organized in a square with this indication: The sum of the values of the tiles in a row or column must always equal 15 at…
SteeveDroz
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Magic square from $2010$

A multiplicative magic square (MMS) is a square array of positive integers in which the product of each row, column, and long diagonal is the same. The $16$ positive factors of $2010$ can be formed into a $4\times 4$ MMS. What is the common product…
Randin
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Magic Square question

Not sure whether this question is correct or not! Please help. Thanks.
Dinesh Potluru
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Why is $nM$ equal to $\sum_{i=1}^{n^2}i$?

In this video it is said that $nM$ for a given magic square is equal to $\sum_{i=1}^{n^2}i$, and then the result is also used for magic hexagons. Why does this have to be the case, both for squares and hexagons? I haven't found any answers or clues…
user522604
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Magic square but with multiplication

A 3x3 square is filled out with 9 positive integers such that the product of each row, column, and diagonals are equal. The sum of all 4 corners is less that 10. Find all possible configurations In this case, a square cannot be rotated to make…
Gerard L.
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