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Questions tagged [magic-square]

A puzzle related to magic squares: grids of integers where all rows, columns, and diagonals have the same sum.

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1answer
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Create a 4-by-4 regular square

We can say that an $n$-by-$n$ square is regular provided that: Each of the integers from $0$ to $n^2 − 1$ appears in exactly one cell, and each cell contains only one integer (so that the square is ...
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1answer
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9-by-9 filled, magic square

Construct a 9-by-9 filled, magic square using the integers from 0 to 80. The magic square should additionally have the property that when it is divided into ninths according to the picture below, each ...
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2answers
282 views

Warped magic squares

A $3\times3$ grid contains altogether six squares that are formed by its nine entries: there are five squares whose sides are parallel to the sides of the grid (four small ones and a big one), and ...
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2answers
285 views

Magic Matrices?

Can you determine any number of magic squares, that when treated as matrices, can be applied mathematical operations to return a new magic-matrix? You cannot use the same matrix twice! The answer ...
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5answers
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The Quite Unusual Square

Imagine an $n \times n$ grid filled with the numbers 1, ..., $n$ where $n$ > 3 each number appearing n times, where each row, column, and diagonal all equal the same number. Can you fill grid like ...
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1answer
297 views

Magic Square with more Magic Squares inside it?

Is it possible to have an $n \times n$ magic square with a another magic square of $\frac n 4 \times \frac n 4$ magic square inside it? If so provide an example, if not prove if impossible. Rules: $...
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2answers
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Magic Squares in Sudoku Grids

A 3x3 magic square is a 3x3 grid containing the numbers 1-9 once each, and in which every row, column, and diagonal sums to 15: 294 753 618 And I presume we all ...
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2answers
343 views

Magic Penteract!

(Don't worry, this is the last magic square themes question I'll be posting (as far as I know), so I picked a challenging one!) First off, let's define what a magic square is; A magic square is an ...
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1answer
627 views

How Many Undefined Magic Constants are there?

Magic Square: An nxn square where every horizontal,vertical, and diagonal line all add up to the same number. Magic Constant: The number which every line with a magic square adds up to So most magic ...
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2answers
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Does a magic rectangle exist?

My definition of a magic rectangle: Any $m \times n$ rectangle where $m \ne n$ and all the numbers $1, 2, 3,\dots, mn$ fit into the rectangle. All horizontal lines, vertical lines, and diagonal ...
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2answers
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How to Determine a Magic Constant in a Magic Square?

A magic square consists of the numbers $1,2,\ldots,m^2$ placed into $m\times m$ square grid, so that every row, column, and both diagonals have the same sum. The magic constant of the square is this ...
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1answer
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Can you fill a 3x3 grid with these numbers so the products of the rows and columns are the same?

Is it possible to form a $3\mbox{x}3$ grid containing the set of numbers: $${1,2,4,8,16,32,64,128,256}$$ in such a way that the product of the numbers in every row, column and diagonal are the same? ...
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3answers
506 views

Magic back yards

My back yard forms a rectangular grid of squares except some of the squares are missing as they are covered by pipes or a small tree. The layout is as follows. A 'x' indicates a square that is free ...
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4answers
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Puzzle of putting numbers 1-9 in 3x3 Grid to add up to 15

In a 3x3 grid, I'd have to put numbers from 1 to 9 in a manner so that respective row, column and diagonal add up to 15. I have only been able to come up with one solution: $$\begin{array}{ccc} 6 &...
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1answer
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Elegant solution to the Magic Hexagon problem

The Magic Hexagon Problem A magic hexagon of order $n$ is an arrangement of close-packed hexagons containing the numbers $1, 2, ..., H_{n-1}$, where $H_n$ is the $n^{th}$ hex number such that the ...
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2answers
986 views

What is the fewest number of filled-in squares required to uniquely define a magic square?

The magic square is a well-known grid of the numbers from 1 to 9 in which every row, column, and diagonal adds up to 15: 4 9 2 3 5 7 8 1 6 But it is also ...
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4answers
1k views

Magic square with the position of 8 fixed

A magic square (of order 3) is a 3x3 matrix consisting of distinct numbers from 1 to 9, where the numbers in each row, column and diagonal add up to 15. For example, the following would be a magic ...