# Questions tagged [magic-square]

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

62 questions
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### Unsolved Mysteries: Magic Square of Squares

This is the first in what will hopefully be a series of Unsolved Mysteries posts. Note that this puzzle has no known solution, nor any proof that a solution is impossible. We will see how ...
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### The 5040 Square

Fill a $4\times4$ grid with positive integers so that: Every cell has a different integer The product of the numbers in each row is $5040$, and similarly for the columns Source: This was an NPR ...
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### 3x3 “Magic Square” of Prime Numbers

During the thinking and analysis of some mathematical problems, I came up with this puzzle: Just like any magic square, one has to fill in $9$ different numbers $P_1, P_2, \dots P_9$ to a $3 \times 3$...
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### A riddle that has been killing me the whole day

So I'm walking around in London and found the following number riddle. The rules say, that what ever pattern you find, must be true for the rows as well as the columns. The answer in level 1 is for ...
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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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### 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 ...
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### 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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### Magic square using numbers 0,2,3,4,5,6,7,8,10

I have to make a 3x3 magic square using the numbers 0-10 without 1 and 9. I have tried various things but am not good at this. The sums of each row, column, and diagonal have to be equal; I added all ...
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### Put numbers to a star-shaped puzzle

For users who can not see picture, see description below ...
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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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### 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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This was given as an assignment to a group of sixth graders, who were told they could use calculators. Beyond that, no real assistance was provided. They were not working on it as a group, so ...
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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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### Modify a magic square

This is a 3x3 magic square of summation, in which sums of each row, column, and diagonal are equal. $$\begin{array}{c|c|c} 4&9&2\\\hline 3&5&7\\\hline 8&1&6 \end{array}$$ Now ...
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### Complete the magic square!

So, my math teacher gave us a magic math square with the 9 in the bottom right corner, the 7 in the left column middle row, and the 1 in the middle column top row. She said she would give whoever ...
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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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### 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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### The magic of the primes

A mathematician, a physicist, and an engineer found themselves caught in an ancient anecdote. Lacking a chemist to brew them an anecdote antidote, they fell to arguing over which of them was to be the ...
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### How big can a witchcraft square be?

A witchcraft square is defined to be an $n\times n$ square of distinct natural numbers such that the row sums and column sums form a set of $2n$ consecutive natural numbers. For example, 5 11 14 ...
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