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. http://en.wikipedia.org/wiki/Magic_square

learn more… | top users | synonyms

3
votes
0answers
17 views

Building a 3D matrix of positive integers

I'm trying to build a 3D matrix made up of positive integers that has very specific properties. The matrix dimensions are $N \times N \times (N+1)$ where $N$ is a positive integer. The matrix has two ...
0
votes
1answer
22 views

Magic squares using matrices

Let $M(d)_{d\in \mathbb{R}}\subset M_3(\mathbb{R})$, consisting of all the matrices such that the sum of the elements in each row, column and on the two diagonals is $d$. Such an element $M(d)$ is ...
0
votes
1answer
34 views

Conditions for magic square.

So I've messing around with magic squares and something occured to me: Assume we have a nxn grid of numbers which respects the sum conditions of a magic square as in it has the appropriate column, ...
0
votes
0answers
30 views

magic squares algorithm

as it is known in magic squares it is the matrix the the sum of any three numbers vertically, horizontally, or diagonally equals to this formula where M is the magic number n is the dimension ...
0
votes
1answer
29 views

Magic square solving

I'm trying to solve a 3x3 magic square for 99 which starts at 29. I got the rows, columns and one diagonal but the other diagonal is (way) off. Is there even a magic square which satisfies both ...
3
votes
1answer
30 views

Standard Deviation of a Magic Square

I'm not sure if this is the right stackexchange to post this question to, but I was just wondering if someone had the answer to an interesting observation I've made. I've written a program that ...
1
vote
2answers
21 views

For magic squares prove $id_v+r^2=2c $

I've been presented with the following problem: Let $V$ be the vector space of all $3\times3$ magic squares. Let $r:V\rightarrow V$ be the linear image which rotates a magic square $90^\circ$. Let ...
0
votes
0answers
22 views

How to find Magic Squares given that the magic number is 24

I just want to ask how to find a magic square already given a magic number
1
vote
0answers
24 views

Sampling from Cartesian product without replacement, but with balanced totals

I am struggling with a combinatorial task that I cannot reduce to any procedure I know: Given two sets $F, G$, I want to sample from $F \times G$ without replacement, but subject to the condition that ...
0
votes
0answers
29 views

Decision problem concerning magic squares

What is the computational complexity of the following decision problem ? Given : A list of $n^2$ natural numbers (not necessarily distinct) Question : Is there a magic square containing the given ...
3
votes
0answers
27 views

Are there associative magic squares of any size except $4k+2$?

An associative magic square is a magic square with the additional property that numbers symmetric to the center sum up to $n^2+1$. For example, the square ...
0
votes
1answer
55 views

Are there semimagic knight tours from any starting square?

There are $140$ distinct semimagic knight tours on a normal chessboard ($8\ \times\ 8$). A semimagic knight tour is a knight tour (not necessarily closed) such that a semimagic square appears if the ...
0
votes
1answer
81 views

Are there magic knight tours on a $6\times6$ or $10\times10$ board?

In mathworld, magic tour, it is mentioned that for odd $n$, only semimagic knight tours are possible on a $n\times\ n$ - board. For $n = 8$, it has been verified that there are no magic knight ...
1
vote
3answers
64 views

Relaxed magic squares

I found the definition that a relaxed magic square of type $n\times n$ has row and column sums constant, and all numbers from $1$ to $n^2$ appears exactly once. How can one enumerate those, like how ...
12
votes
0answers
167 views

determinant of a standard magic square

What is the lowest positive, what the highest possible value for the determinant of a standard-magic-square-matrix of order n ? Are there singular standard-magic-square-matrices of any order ...
1
vote
2answers
64 views

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 ...
1
vote
1answer
58 views

Why does the filling up of odd order magic square with numbers follow the knight movement?

Why does the filling up of odd order magic square with numbers follow the knight movement? I was reading about magic square, where I came up with the knight movement filling up of the magic square ...
0
votes
1answer
36 views

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.
0
votes
1answer
59 views

How many nonnegative integer matrices of size $N$ have all row and column sums equal to $D$?

Given the positive integer $N$ and $D$, generate all the non-negative integer matrices which satisfy matrix dimension is $N\times N$; sum of each row elements equals to $D$ sum of each column ...
1
vote
0answers
61 views

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 ...
1
vote
2answers
87 views

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 ...
1
vote
0answers
113 views

Proof that 12 in a row tic-tac-toe is a tie game?

How can be it proved that tic-tac-toe on an infinite grid (winning with 12 in a row, a column or a diagonal) can always end in a tie (with optimal strategies of both players)? There is a hint: to use ...
13
votes
2answers
149 views

Identity of a Mathematician Mentioned in Euler

I and several others are in the process of translating one of Euler's papers from Latin to English, in particular the one that the Euler Archive lists as E36. In it Euler proves the Chinese Remainder ...
0
votes
1answer
95 views

do you know another Magic Square with this property?

with the repeating digits of $\frac{1}{19} = 0.052631578947368421$ we can construct an exceptional magic square : The number 19 is a cyclic number with a period of 18 before the digits start to ...
15
votes
2answers
2k views

How to prove that a $3\times 3$ Magic Square must have $5$ in its middle cell?

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. ...
1
vote
1answer
144 views

“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 ...
0
votes
1answer
98 views

Mathematical model for magic square

As I spent some time on magic squares, it seems like the magic squares can be formed only with a odd number of rows/columns? Is it that.? If so why? is there a mathematical model that explains magic ...
3
votes
1answer
333 views

how to make a matrix a magic square?

Suppose I have a matrix $$\begin{pmatrix} & 3 & 6\\ 5 & & 5\\ 4 & 7 & \end{pmatrix}$$ How can I find the three numbers on the main diagonal such that the sum of the ...
2
votes
2answers
411 views

How does the Siamese method to construct any size of n-odd magic squares work?

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. To ...
5
votes
1answer
140 views

Given a number $11 \leqslant n\leqslant 99$, how to write a couple of numbers which total to $n$

Yesterday, a friend of mine asked me for a number between 11 and 99 (not 100% sure about the boundaries). I had no idea what he was up to and called 38, about half a minute later he had written down ...
0
votes
0answers
138 views

$4\times4$ magic square magic number possibilities?

How can I find all the different possibilities for the sum of rows/columns/diagonals for a $4\times4$ magic square? I am not sure how to proceed, except by brute force, which is entirely inelegant. I ...
0
votes
2answers
217 views

Anti Magic Square

Are the two examples of $4\times 4$ anti-magic squares currently on Wikipedia actually anti-magic squares under the definition given there? The examples are: $$\left[ \begin {array}{cccc} ...
3
votes
2answers
546 views

$3 \times 3 $ Magic Square of Squares

On picture below is three-by-three magic square in which seven of the entries are squared integers, found by Andrew Bremner of Arizona State University (and independently by Lee Sallows of the ...
9
votes
2answers
633 views

Eigenvector of magic square

I'm trying to show: A "magic square" $A$ is a matrix $n\times n$ with slots $1,2,\cdots, n^2$ such that the sum of the elements of each row (and column) is the same . Prove that $\frac{n(n^2+1)}{2}$ ...
6
votes
1answer
294 views

Fewest required values in magic square?

A magic square of order $n$ is an $n \times n$ grid containing each of the numbers $1,2,\dots,n^2$, so that the numbers in each row, column, and diagonal sum to the same number $n(n^2+1)/2$. This ...